@article{Cutler1994,
  title = {Archetypal Analysis},
  author = {Cutler, Adele and Breiman, Leo},
  date = {1994},
  year = {1994},
  journaltitle = {Technometrics : a journal of statistics for the physical, chemical, and engineering sciences},
  journal = {Technometrics},
  volume = {36},
  number = {4},
  pages = {338--347},
  issn = {0040-1706},
  doi = {10.1080/00401706.1994.10485840},
  abstract = {Archetypal analysis represents each individual in a data set as a mixture of individuals of pure type or archetypes. The archetypes themselves are restricted to being mixtures of the individuals in the data set. Archetypes are selected by minimizing the squared error in representing each individual as a mixture of archetypes. The usefulness of archetypal analysis is illustrated on several data sets. Computing the archetypes is a nonlinear least squares problem, which is solved using an alternating minimizing algorithm.}
}

@article{Shoval2012,
  title = {Evolutionary Trade-Offs, Pareto Optimality, and the Geometry of Phenotype Space},
  author = {Shoval, O. and Sheftel, H. and Shinar, G. and Hart, Y. and Ramote, O. and Mayo, A. and Dekel, E. and Kavanagh, K. and Alon, U.},
  date = {2012-06},
  journaltitle = {Science},
  journal = {Science},
  volume = {336},
  number = {6085},
  eprint = {22539553},
  eprinttype = {pubmed},
  pages = {1157--1160},
  issn = {0036-8075, 1095-9203},
  doi = {10.1126/science.1217405},
  url = {https://www.science.org/doi/10.1126/science.1217405},
  urldate = {2024-12-07},
  abstract = {Managing Trade-Offs                            Most organisms experience selection on a host of traits to determine their likelihood to succeed evolutionarily. However, specific traits may experience trade-offs in determining an organism's optimal phenotype.                                Shoval                 et al.                              (p.               1157               ; see the Perspective by                                Noor and Milo                              ) relate physical traits to the task that they are optimizing using a Pareto curve, a power law probability distribution, to show that a single set of trait values optimizes performance at a given task and that performance decreases as an organism's phenotype moves away from this set of trait values. The results suggest how selection makes the best trade-offs for an arbitrary number of tasks and traits and may explain examples of evolutionary variation.                        ,              The fitness of an organism can be modeled graphically to determine how phenotypic trade-offs are maximized.           ,              Biological systems that perform multiple tasks face a fundamental trade-off: A given phenotype cannot be optimal at all tasks. Here we ask how trade-offs affect the range of phenotypes found in nature. Using the Pareto front concept from economics and engineering, we find that best–trade-off phenotypes are weighted averages of archetypes—phenotypes specialized for single tasks. For two tasks, phenotypes fall on the line connecting the two archetypes, which could explain linear trait correlations, allometric relationships, as well as bacterial gene-expression patterns. For three tasks, phenotypes fall within a triangle in phenotype space, whose vertices are the archetypes, as evident in morphological studies, including on Darwin’s finches. Tasks can be inferred from measured phenotypes based on the behavior of organisms nearest the archetypes.},
  langid = {english},
  local-url = {file://localhost/Users/pschafer/Documents/Papers\_PDFs/2012\_Shoval\_Alon\_Evolutionary}
}

@article{Hart2015,
  title = {Inferring Biological Tasks Using Pareto Analysis of High-Dimensional Data},
  author = {Hart, Yuval and Sheftel, Hila and Hausser, Jean and Szekely, Pablo and Ben-Moshe, Noa Bossel and Korem, Yael and Tendler, Avichai and Mayo, Avraham E and Alon, Uri},
  date = {2015-03},
  journaltitle = {Nature Methods},
  journal = {Nat Methods},
  volume = {12},
  number = {3},
  eprint = {25622107},
  eprinttype = {pubmed},
  pages = {233--235},
  issn = {1548-7091, 1548-7105},
  doi = {10.1038/nmeth.3254},
  url = {https://www.nature.com/articles/nmeth.3254},
  urldate = {2024-12-07},
  abstract = {Pareto task inference (ParTI) computes a polytype that encloses a data set and determines the enrichment of features around the vertices (archetypes) of the polytype, which allows the identification of the task the archetype represents. We present the Pareto task inference method (ParTI; http://www.weizmann.ac.il/mcb/UriAlon/download/ParTI) for inferring biological tasks from high-dimensional biological data. Data are described as a polytope, and features maximally enriched closest to the vertices (or archetypes) allow identification of the tasks the vertices represent. We demonstrate that human breast tumors and mouse tissues are well described by tetrahedrons in gene expression space, with specific tumor types and biological functions enriched at each of the vertices, suggesting four key tasks.},
  langid = {english}
}

@article{Korem2015,
  title = {Geometry of the Gene Expression Space of Individual Cells},
  author = {Korem, Yael and Szekely, Pablo and Hart, Yuval and Sheftel, Hila and Hausser, Jean and Mayo, Avi and Rothenberg, Michael E. and Kalisky, Tomer and Alon, Uri},
  editor = {Iakoucheva, Lilia M.},
  year = {2015},
  month = jul,
  journal = {PLOS Computational Biology},
  volume = {11},
  number = {7},
  pages = {e1004224},
  issn = {1553-7358},
  doi = {10.1371/journal.pcbi.1004224},
  urldate = {2024-12-07},
  abstract = {There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.},
  langid = {english},
  pmcid = {PMC4498931},
  pmid = {26161936},
}

@article{Adler2019,
  title = {Continuum of Gene-Expression Profiles Provides Spatial Division of Labor within a Differentiated Cell Type},
  author = {Adler, Miri and Korem Kohanim, Yael and Tendler, Avichai and Mayo, Avi and Alon, Uri},
  date = {2019-01},
  year = {2019},
  journaltitle = {Cell Systems},
  journal = {Cell Systems},
  volume = {8},
  number = {1},
  eprint = {30638811},
  eprinttype = {pubmed},
  pages = {43-52.e5},
  issn = {24054712},
  doi = {10.1016/j.cels.2018.12.008},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S2405471218304824},
  urldate = {2024-12-07},
  abstract = {Single-cell gene expression reveals the diversity within a differentiated cell type. Often, cells of the same type show a continuum of gene-expression patterns. The origin of such continuum gene-expression patterns is unclear. To address this, we develop a theory to understand how a continuum provides division of labor in a tissue in which cells collectively contribute to several tasks. We find that a continuum is optimal when there are spatial gradients in the tissue that affect the performance in each task. The continuum is bounded inside a polyhedron whose vertices are expression profiles optimal at each task. We test this using single-cell gene expression for intestinal villi and liver hepatocytes, which form a curved 1D trajectory and a full 3D tetrahedron in gene-expression space, respectively. We infer the tasks for both cell types and characterize the spatial zonation of the task-specialist cells. This approach can be generally applied to other tissues.},
  langid = {english}
}

@article{Adler2023,
  title = {Emergence of Division of Labor in Tissues through Cell Interactions and Spatial Cues},
  author = {Adler, Miri and Moriel, Noa and Goeva, Aleksandrina and Avraham-Davidi, Inbal and Mages, Simon and Adams, Taylor S. and Kaminski, Naftali and Macosko, Evan Z. and Regev, Aviv and Medzhitov, Ruslan and Nitzan, Mor},
  date = {2023-05},
  year = {2023},
  journaltitle = {Cell Reports},
  journal = {Cell Reports},
  volume = {42},
  number = {5},
  eprint = {37086403},
  eprinttype = {pubmed},
  pages = {112412},
  issn = {22111247},
  doi = {10.1016/j.celrep.2023.112412},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S2211124723004230},
  urldate = {2024-12-07},
  abstract = {Most cell types in multicellular organisms can perform multiple functions. However, not all functions can be optimally performed simultaneously by the same cells. Functions incompatible at the level of individual cells can be performed at the cell population level, where cells divide labor and specialize in different functions. Division of labor can arise due to instruction by tissue environment or through self-organization. Here, we develop a computational framework to investigate the contribution of these mechanisms to division of labor within a cell-type population. By optimizing collective cellular task performance under trade-offs, we find that distinguishable expression patterns can emerge from cell-cell interactions versus instructive signals. We propose a method to construct ligand-receptor networks between specialist cells and use it to infer division-oflabor mechanisms from single-cell RNA sequencing (RNA-seq) and spatial transcriptomics data of stromal, epithelial, and immune cells. Our framework can be used to characterize the complexity of cell interactions within tissues.},
  langid = {english},
  pmcid = {PMC10242439},
}

@article{morupArchetypalAnalysisMachine2012,
  title = {Archetypal Analysis for Machine Learning and Data Mining},
  author = {Mørup, Morten and Hansen, Lars Kai},
  date = {2012-03},
  year = {2012},
  journaltitle = {Neurocomputing},
  journal = {Neurocomputing},
  volume = {80},
  pages = {54--63},
  issn = {09252312},
  doi = {10.1016/j.neucom.2011.06.033},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0925231211006060},
  urldate = {2024-12-07},
  abstract = {Archetypal analysis (AA) proposed by Cutler and Breiman (1994) [7] estimates the principal convex hull (PCH) of a data set. As such AA favors features that constitute representative ‘corners’ of the data, i.e., distinct aspects or archetypes. We currently show that AA enjoys the interpretability of clustering –without being limited to hard assignment and the uniqueness of SVD – without being limited to orthogonal representations. In order to do large scale AA, we derive an efficient algorithm based on projected gradient as well as an initialization procedure we denote FURTHESTSUM that is inspired by the FURTHESTFIRST approach widely used for K-means (Hochbaum and Shmoys, 1985 [14]). We generalize the AA procedure to KERNEL-AA in order to extract the principal convex hull in potential infinite Hilbert spaces and derive a relaxation of AA when the archetypes cannot be represented as convex combinations of the observed data. We further demonstrate that the AA model is relevant for feature extraction and dimensionality reduction for a large variety of machine learning problems taken from computer vision, neuroimaging, chemistry, text mining and collaborative filtering leading to highly interpretable representations of the dynamics in the data. Matlab code for the derived algorithms is available for download from www.mortenmorup.dk.},
  langid = {english}
}

@online{Bauckhage2014,
  title = {A Note on Archetypal Analysis and the Approximation of Convex Hulls},
  author = {Bauckhage, Christian},
  date = {2014-09-27},
  year = {2014},
  eprint = {1410.0642},
  eprinttype = {arXiv},
  eprintclass = {cs},
  doi = {10.48550/arXiv.1410.0642},
  url = {http://arxiv.org/abs/1410.0642},
  urldate = {2024-12-07},
  abstract = {We briefly review the basic ideas behind archetypal analysis for matrix factorization and discuss its behavior in approximating the convex hull of a data sample. We then ask how good such approximations can be and consider different cases. Understanding archetypal analysis as the problem of computing a convexity constrained low-rank approximation of the identity matrix provides estimates for archetypal analysis and the SiVM heuristic.},
  langid = {english},
}

@article{10.1146/annurev-cellbio-120420-113830,
  title = {Tissue Biology: In Search of a New Paradigm},
  shorttitle = {Tissue Biology},
  author = {Adler, Miri and Chavan, Arun R. and Medzhitov, Ruslan},
  date = {2023-10-16},
  journaltitle = {Annual Review of Cell and Developmental Biology},
  journal = {Annu. Rev. Cell Dev. Biol.},
  volume = {39},
  number = {1},
  eprint = {37607470},
  eprinttype = {pubmed},
  pages = {67--89},
  issn = {1081-0706, 1530-8995},
  doi = {10.1146/annurev-cellbio-120420-113830},
  url = {https://www.annualreviews.org/doi/10.1146/annurev-cellbio-120420-113830},
  urldate = {2024-12-07},
  abstract = {Animal tissues are made up of multiple cell types that are increasingly well-characterized, yet our understanding of the core principles that govern tissue organization is still incomplete. This is in part because many observable tissue characteristics, such as cellular composition and spatial patterns, are emergent properties, and as such, they cannot be explained through the knowledge of individual cells alone. Here we propose a complex systems theory perspective to address this fundamental gap in our understanding of tissue biology. We introduce the concept of cell categories, which is based on cell relations rather than cell identity. Based on these notions we then discuss common principles of tissue modularity, introducing compositional, structural, and functional tissue modules. Cell diversity and cell relations provide a basis for a new perspective on the underlying principles of tissue organization in health and disease.},
  langid = {english},
  local-url = {file://localhost/Users/pschafer/Documents/Papers\_PDFs/2023\_Adler\_Medzhitov\_Tissue},
}

@article{mohammadiMultiresolutionFrameworkCharacterize2020,
  title = {A Multiresolution Framework to Characterize Single-Cell State Landscapes},
  author = {Mohammadi, Shahin and Davila-Velderrain, Jose and Kellis, Manolis},
  date = {2020-10-26},
  journaltitle = {Nature Communications},
  journal = {Nat Commun},
  volume = {11},
  number = {1},
  pages = {5399},
  issn = {2041-1723},
  doi = {10.1038/s41467-020-18416-6},
  url = {https://www.nature.com/articles/s41467-020-18416-6},
  urldate = {2024-12-07},
  abstract = {Dissecting the cellular heterogeneity embedded in single-cell transcriptomic data is challenging. Although many methods and approaches exist, identifying cell states and their underlying topology is still a major challenge. Here, we introduce the concept of multiresolution cell-state decomposition as a practical approach to simultaneously capture both fine- and coarse-grain patterns of variability. We implement this concept in ACTIONet, a comprehensive framework that combines archetypal analysis and manifold learning to provide a ready-to-use analytical approach for multiresolution single-cell state characterization. ACTIONet provides a robust, reproducible, and highly interpretable single-cell analysis platform that couples dominant pattern discovery with a corresponding structural representation of the cell state landscape. Using multiple synthetic and real data sets, we demonstrate ACTIONet’s superior performance relative to existing alternatives. We use ACTIONet to integrate and annotate cells across three human cortex data sets. Through integrative comparative analysis, we define a consensus vocabulary and a consistent set of gene signatures discriminating against the transcriptomic cell types and subtypes of the human prefrontal cortex.},
  langid = {english}
}

@article{eugsterSpiderManHeroArchetypal2009,
  title = {From Spider-Man to Hero - Archetypal Analysis in {\mkbibemph{R}}},
  author = {Eugster, Manuel J. A. and Leisch, Friedrich},
  date = {2009},
  journaltitle = {Journal of Statistical Software},
  journal = {J. Stat. Soft.},
  volume = {30},
  number = {8},
  issn = {1548-7660},
  doi = {10.18637/jss.v030.i08},
  url = {http://www.jstatsoft.org/v30/i08/},
  urldate = {2024-12-07},
  abstract = {Archetypal analysis has the aim to represent observations in a multivariate data set as convex combinations of extremal points. This approach was introduced by Cutler and Breiman (1994); they defined the concrete problem, laid out the theoretical foundations and presented an algorithm written in Fortran. In this paper we present the R package archetypes which is available on the Comprehensive R Archive Network. The package provides an implementation of the archetypal analysis algorithm within R and different exploratory tools to analyze the algorithm during its execution and its final result. The application of the package is demonstrated on two examples.},
  langid = {english}
}

@article{MarrahiNipmap2023,
  title = {NIPMAP: Niche-Phenotype Mapping of Multiplex Histology Data by Community Ecology},
  shorttitle = {NIPMAP},
  author = {El Marrahi, Anissa and Lipreri, Fabio and Kang, Ziqi and Gsell, Louise and Eroglu, Alper and Alber, David and Hausser, Jean},
  date = {2023-11-07},
  year = {2023},
  journaltitle = {Nature Communications},
  journal = {Nat Commun},
  volume = {14},
  number = {1},
  eprint = {37935691},
  eprinttype = {pubmed},
  pages = {7182},
  issn = {2041-1723},
  doi = {10.1038/s41467-023-42878-z},
  url = {https://www.nature.com/articles/s41467-023-42878-z},
  urldate = {2024-12-07},
  abstract = {Advances in multiplex histology allow surveying millions of cells, dozens of cell types, and up to thousands of phenotypes within the spatial context of tissue sections. This leads to a combinatorial challenge in (a) summarizing the cellular and phenotypic architecture of tissues and (b) identifying phenotypes with interesting spatial architecture. To address this, we combine ideas from community ecology and machine learning into niche-phenotype mapping (NIPMAP). NIPMAP takes advantage of geometric constraints on local cellular composition imposed by the niche structure of tissues in order to automatically segment tissue sections into niches and their interfaces. Projecting phenotypes on niches and their interfaces identifies previously-reported and previously-unreported spatially-driven phenotypes, concisely summarizes the phenotypic architecture of tissues, and reveals fundamental properties of tissue architecture. NIPMAP is applicable to both protein and RNA multiplex histology of healthy and diseased tissue. An open-source R/Python package implements NIPMAP.},
  langid = {english},
  pmcid = {PMC10630431}
}

@article{heStarfyshIntegratesSpatial2024,
  title = {Starfysh Integrates Spatial Transcriptomic and Histologic Data to Reveal Heterogeneous Tumor-Immune Hubs},
  date = {2024-03-21},
  journaltitle = {Nature Biotechnology},
  journal = {Nat Biotechnol},
  pages = {1--13},
  issn = {1087-0156, 1546-1696},
  doi = {10.1038/s41587-024-02173-8},
  url = {https://www.nature.com/articles/s41587-024-02173-8},
  urldate = {2024-12-07},
  abstract = {Spatially resolved gene expression profiling provides insight into tissue organization and cell-cell crosstalk; however, sequencing-based spatial transcriptomics (ST) lacks single-cell resolution. Current ST analysis methods require single-cell RNA sequencing data as a reference for rigorous interpretation of cell states, mostly do not use associated histology images and are not capable of inferring shared neighborhoods across multiple tissues. Here we present Starfysh, a computational toolbox using a deep generative model that incorporates archetypal analysis and any known cell type markers to characterize known or new tissue-specific cell states without a single-cell reference. Starfysh improves the characterization of spatial dynamics in complex tissues using histology images and enables the comparison of niches as spatial hubs across tissues. Integrative analysis of primary estrogen receptor (ER)-positive breast cancer, triple-negative breast cancer (TNBC) and metaplastic breast cancer (MBC) tissues led to the identification of spatial hubs with patient- and disease-specific cell type compositions and revealed metabolic reprogramming shaping immunosuppressive hubs in aggressive MBC.},
  langid = {english},
  author = {He, Siyu and Jin, Yinuo and Nazaret, Achille and Shi, Lingting and Chen, Xueer and Rampersaud, Sham and Dhillon, Bahawar S. and Valdez, Izabella and others and Mehdi, Kaleem and Rohde, Madeline and McFaline-Figueroa, José L. and Blei, David and Leong, Kam W. and Rudensky, Alexander Y. and Plitas, George and Azizi, Elham}
}

@article{Persad2013,
  title = {SEACells Infers Transcriptional and Epigenomic Cellular States from Single-Cell Genomics Data},
  author = {Persad, Sitara and Choo, Zi-Ning and Dien, Christine and Sohail, Noor and Masilionis, Ignas and Chaligné, Ronan and Nawy, Tal and Brown, Chrysothemis C. and Sharma, Roshan and Pe’er, Itsik and Setty, Manu and Pe’er, Dana},
  date = {2023-12},
  journaltitle = {Nature Biotechnology},
  journal = {Nat Biotechnol},
  volume = {41},
  number = {12},
  eprint = {36973557},
  eprinttype = {pubmed},
  pages = {1746--1757},
  issn = {1087-0156, 1546-1696},
  doi = {10.1038/s41587-023-01716-9},
  url = {https://www.nature.com/articles/s41587-023-01716-9},
  urldate = {2024-12-07},
  abstract = {Metacells are cell groupings derived from single-cell sequencing data that represent highly granular, distinct cell states. Here we present single-cell aggregation of cell states (SEACells), an algorithm for identifying metacells that overcome the sparsity of single-cell data while retaining heterogeneity obscured by traditional cell clustering. SEACells outperforms existing algorithms in identifying comprehensive, compact and well-separated metacells in both RNA and assay for transposase-accessible chromatin (ATAC) modalities across datasets with discrete cell types and continuous trajectories. We demonstrate the use of SEACells to improve gene–peak associations, compute ATAC gene scores and infer the activities of critical regulators during differentiation. Metacell-level analysis scales to large datasets and is particularly well suited for patient cohorts, where per-patient aggregation provides more robust units for data integration. We use our metacells to reveal expression dynamics and gradual reconfiguration of the chromatin landscape during hematopoietic differentiation and to uniquely identify CD4 T cell differentiation and activation states associated with disease onset and severity in a Coronavirus Disease 2019 (COVID-19) patient cohort.},
  langid = {english},
  pmcid = {PMC10713451}
}

@article{militeInterpretableMultiOmicsData2024,
  title = {Interpretable Multi-Omics Data Integration with Deep Archetypal Analysis},
  author = {Milite, Salvatore and Caravagna, Giulio and Sottoriva, Andrea},
  date = {2024},
  journaltitle = {bioRxiv : the preprint server for biology},
  journal = {bioRxiv},
  pages = {2024.04.05.588238},
  doi = {10.1101/2024.04.05.588238},
  abstract = {High-throughput multi-omics technologies offer a lens through which the concurrent states of biological systems can be viewed. However, the integration and interpretation of high-dimensional, sparse, and noisy multi-omics datasets is challenging, often requiring leveraging algorithms for dimensionality reduction. Here we introduce Deep Archetypal Analysis for the Representation of Integrated Omics (DAARIO), a framework that combines archetypal analysis with deep learning. Using the concept of archetypes – extreme data points that define the geometry of the latent space – our model preserves the complexity of biological interactions while retaining an interpretable latent space, a crucial feature to decipher the underlying biology. We show on real and simulated multi-omics data how DAARIO outperforms other state-of-the-art methods in identifying parsimonious, interpretable, and biologically relevant patterns.},
  langid = {english},
}

@article{hanProbabilisticMethodsApproximate2023,
  title = {Probabilistic Methods for Approximate Archetypal Analysis},
  author = {Han, Ruijian and Osting, Braxton and Wang, Dong and Xu, Yiming},
  date = {2023-02-02},
  journaltitle = {Information and Inference: A Journal of the IMA},
  volume = {12},
  number = {1},
  pages = {466--493},
  issn = {2049-8772},
  doi = {10.1093/imaiai/iaac008},
  url = {https://academic.oup.com/imaiai/article/12/1/466/6576183},
  urldate = {2024-12-07},
  abstract = {Abstract             Archetypal analysis (AA) is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of AA in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided data are approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of AA. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of AA. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets.},
  langid = {english},
}

@article{aloiseNPhardnessEuclideanSumofsquares2009,
  title = {NP-Hardness of Euclidean Sum-of-Squares Clustering},
  author = {Aloise, Daniel and Deshpande, Amit and Hansen, Pierre and Popat, Preyas},
  date = {2009-05},
  journaltitle = {Machine Learning},
  journal = {Mach Learn},
  volume = {75},
  number = {2},
  pages = {245--248},
  issn = {0885-6125, 1573-0565},
  doi = {10.1007/s10994-009-5103-0},
  url = {http://link.springer.com/10.1007/s10994-009-5103-0},
  urldate = {2024-12-07},
  abstract = {A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al. (Mach. Learn. 56:9-33, 2004), is not valid. An alternate short proof is provided.},
  langid = {english},
}

@article{wangNonlinearArchetypalAnalysis2022,
  title = {Non-Linear Archetypal Analysis of Single-Cell RNA-Seq Data by Deep Autoencoders},
  author = {Wang, Yuge and Zhao, Hongyu},
  editor = {Li, Mingyao},
  date = {2022-04-01},
  journaltitle = {PLOS Computational Biology},
  journal = {PLoS Comput Biol},
  volume = {18},
  number = {4},
  pages = {e1010025},
  issn = {1553-7358},
  doi = {10.1371/journal.pcbi.1010025},
  url = {https://dx.plos.org/10.1371/journal.pcbi.1010025},
  urldate = {2024-12-07},
  abstract = {Advances in single-cell RNA sequencing (scRNA-seq) have led to successes in discovering novel cell types and understanding cellular heterogeneity among complex cell populations through cluster analysis. However, cluster analysis is not able to reveal continuous spectrum of states and underlying gene expression programs (GEPs) shared across cell types. We introduce scAAnet, an autoencoder for single-cell non-linear archetypal analysis, to identify GEPs and infer the relative activity of each GEP across cells. We use a count distribution-based loss term to account for the sparsity and overdispersion of the raw count data and add an archetypal constraint to the loss function of scAAnet. We first show that scAAnet outperforms existing methods for archetypal analysis across different metrics through simulations. We then demonstrate the ability of scAAnet to extract biologically meaningful GEPs using publicly available scRNA-seq datasets including a pancreatic islet dataset, a lung idiopathic pulmonary fibrosis dataset and a prefrontal cortex dataset.},
  langid = {english},
}

@online{kellerDeepArchetypalAnalysis2020,
  title = {Deep Archetypal Analysis},
  author = {Keller, Sebastian Mathias and Samarin, Maxim and Wieser, Mario and Roth, Volker},
  date = {2020-01-24},
  eprint = {1901.10799},
  eprinttype = {arXiv},
  eprintclass = {cs},
  doi = {10.48550/arXiv.1901.10799},
  url = {http://arxiv.org/abs/1901.10799},
  urldate = {2024-12-07},
  abstract = {Deep Archetypal Analysis (DeepAA) generates latent representations of high-dimensional datasets in terms of intuitively understandable basic entities called archetypes. The proposed method extends linear Archetypal Analysis (AA), an unsupervised method to represent multivariate data points as convex combinations of extremal data points. Unlike the original formulation, Deep AA is generative and capable of handling side information. In addition, our model provides the ability for data-driven representation learning which reduces the dependence on expert knowledge. We empirically demonstrate the applicability of our approach by exploring the chemical space of small organic molecules. In doing so, we employ the archetype constraint to learn two different latent archetype representations for the same dataset, with respect to two chemical properties. This type of supervised exploration marks a distinct starting point and let us steer de novo molecular design.},
  langid = {english},
}

@article{halloranArchetypalAnalysisInjury2022,
  title = {Archetypal Analysis of Injury in Kidney Transplant Biopsies Identifies Two Classes of Early AKI},
  author = {Halloran, Philip F. and Böhmig, Georg A. and Bromberg, Jonathan and Einecke, Gunilla and Eskandary, Farsad A. and Gupta, Gaurav and Myslak, Marek and Viklicky, Ondrej and Perkowska-Ptasinska, Agnieszka and Madill-Thomsen, Katelynn S. and {The INTERCOMEX Investigators}},
  date = {2022-04-07},
  journaltitle = {Frontiers in Medicine},
  journal = {Front. Med.},
  volume = {9},
  pages = {817324},
  issn = {2296-858X},
  doi = {10.3389/fmed.2022.817324},
  url = {https://www.frontiersin.org/articles/10.3389/fmed.2022.817324/full},
  urldate = {2024-12-07},
  abstract = {All transplanted kidneys are subjected to some degree of injury as a result of the donation-implantation process and various post-transplant stresses such as rejection. Because transplants are frequently biopsied, they present an opportunity to explore the full spectrum of kidney response-to-wounding from all causes. Defining parenchymal damage in transplanted organs is important for clinical management because it determines function and survival. In this study, we classified the scenarios associated with parenchymal injury in genome-wide microarray results from 1,526 kidney transplant indication biopsies collected during the INTERCOMEX study. We defined injury groups by using archetypal analysis (AA) of scores for gene sets and classifiers previously identified in various injury states. Six groups and their characteristics were defined in this population: No injury, minor injury, two classes of acute kidney injury (“AKI,” AKI1, and AKI2), chronic kidney disease (CKD), and CKD combined with AKI. We compared the two classes of AKI, namely, AKI1 and AKI2. AKI1 had a poor function and increased parenchymal dedifferentiation but minimal response-to-injury and inflammation, instead having increased expression of PARD3, a gene previously characterized as being related to epithelial polarity and adherens junctions. In contrast, AKI2 had a poor function and increased response-to-injury, significant inflammation, and increased macrophage activity. In random forest analysis, the most important predictors of function (estimated glomerular filtration rate) and graft loss were injury-based molecular scores, not rejection scores. AKI1 and AKI2 differed in 3-year graft survival, with better survival in the AKI2 group. Thus, injury archetype analysis of injury-induced gene expression shows new heterogeneity in kidney response-to-wounding, revealing AKI1, a class of early transplants with a poor function but minimal inflammation or response to injury, a deviant response characterized as PC3, and an increased risk of failure. Given the relationship between parenchymal injury and kidney survival, further characterization of the injury phenotypes in kidney transplants will be important for an improved understanding that could have implications for understanding native kidney diseases (               ClinicalTrials.gov               \#NCT01299168).},
  langid = {english},
}

@article{kocillariSignatureParetoOptimization2018,
  title = {Signature of Pareto Optimization in the Escherichia Coli Proteome},
  author = {Koçillari, Loren and Fariselli, Piero and Trovato, Antonio and Seno, Flavio and Maritan, Amos},
  date = {2018-06-14},
  journaltitle = {Scientific Reports},
  journal = {Sci Rep},
  volume = {8},
  number = {1},
  pages = {9141},
  issn = {2045-2322},
  doi = {10.1038/s41598-018-27287-3},
  url = {https://www.nature.com/articles/s41598-018-27287-3},
  urldate = {2024-12-07},
  abstract = {Proteins have coevolved with cellular environments to improve or preserve their functions, maintaining at the same time the degree of hydrophobicity necessary to fold correctly and enough solubility to perform their biological roles. Here, we study the               Escherichia coli               proteome using a Pareto front analysis in the solubility-hydrophobicity space. The results indicate the existence of a Pareto optimal front, a triangle whose vertices correspond to archetypal proteins specialized in distinct tasks, such as regulatory processes, membrane transport, outer-membrane pore formation, catalysis, and binding. The vertices are further enriched with proteins that occupy different subcellular compartments, namely, cytoplasmic, inner membrane, outer membrane, and outer membrane bounded periplasmic space. The combination of various enriching features offers an interpretation of how bacteria use the physico-chemical properties of proteins, both to drive them into their final destination in the cell and to have their tasks accomplished.},
  langid = {english},
}

@article{turosChrysalisDecodingTissue2024,
  title = {Chrysalis: Decoding Tissue Compartments in Spatial Transcriptomics with Archetypal Analysis},
  shorttitle = {Chrysalis},
  author = {Túrós, Demeter and Vasiljevic, Jelica and Hahn, Kerstin and Rottenberg, Sven and Valdeolivas, Alberto},
  date = {2024-11-16},
  year = {2024},
  journal = {Communications Biology},
  volume = {7},
  number = {1},
  pages = {1520},
  issn = {2399-3642},
  doi = {10.1038/s42003-024-07165-7},
  url = {https://www.nature.com/articles/s42003-024-07165-7},
  urldate = {2024-12-07},
  langid = {english}
}

@article{nathEvolutionCoreArchetypal2021,
  title = {Evolution of Core Archetypal Phenotypes in Progressive High Grade Serous Ovarian Cancer},
  date = {2021-05-24},
  journaltitle = {Nature Communications},
  journal = {Nat Commun},
  volume = {12},
  number = {1},
  pages = {3039},
  issn = {2041-1723},
  doi = {10.1038/s41467-021-23171-3},
  url = {https://www.nature.com/articles/s41467-021-23171-3},
  urldate = {2024-12-07},
  abstract = {Abstract             The evolution of resistance in high-grade serous ovarian cancer (HGSOC) cells following chemotherapy is only partially understood. To understand the selection of factors driving heterogeneity before and through adaptation to treatment, we profile single-cell RNA-sequencing (scRNA-seq) transcriptomes of HGSOC tumors collected longitudinally during therapy. We analyze scRNA-seq data from two independent patient cohorts to reveal that HGSOC is driven by three archetypal phenotypes, defined as oncogenic states that describe the majority of the transcriptome variation. Using a multi-task learning approach to identify the biological tasks of each archetype, we identify metabolism and proliferation, cellular defense response, and DNA repair signaling as consistent cell states found across patients. Our analysis demonstrates a shift in favor of the metabolism and proliferation archetype versus cellular defense response archetype in cancer cells that received multiple lines of treatment. While archetypes are not consistently associated with specific whole-genome driver mutations, they are closely associated with subclonal populations at the single-cell level, indicating that subclones within a tumor often specialize in unique biological tasks. Our study reveals the core archetypes found in progressive HGSOC and shows consistent enrichment of subclones with the metabolism and proliferation archetype as resistance is acquired to multiple lines of therapy.},
  langid = {english},
  author = {Nath, Aritro and Cosgrove, Patrick A. and Mirsafian, Hoda and Christie, Elizabeth L. and Pflieger, Lance and Copeland, Benjamin and Majumdar, Sumana and Cristea, Mihaela C. and others and Traficante, Nadia and Salgia, Ravi and Werner, Theresa and Cohen, Adam L. and Moos, Philip and Chang, Jeffrey T. and Bowtell, David D. L. and Bild, Andrea H.}
}

@article{sethProbabilisticArchetypalAnalysis2016,
  title = {Probabilistic Archetypal Analysis},
  author = {Seth, Sohan and Eugster, Manuel J. A.},
  date = {2016-01},
  journaltitle = {Machine Learning},
  journal = {Mach Learn},
  volume = {102},
  number = {1},
  pages = {85--113},
  issn = {0885-6125, 1573-0565},
  doi = {10.1007/s10994-015-5498-8},
  url = {http://link.springer.com/10.1007/s10994-015-5498-8},
  urldate = {2024-12-07},
  abstract = {Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be real–valued. This, unfortunately, is not compatible with many practical situations. In this paper we revisit archetypal analysis from the basic principles, and propose a probabilistic framework that accommodates other observation types such as integers, binary, and probability vectors. We corroborate the proposed methodology with convincing real-world applications on finding archetypal soccer players based on performance data, archetypal winter tourists based on binary survey data, archetypal disaster-affected countries based on disaster count data, and document archetypes based on term-frequency data. We also present an appropriate visualization tool to summarize archetypal analysis solution better.},
  langid = {english},
}

@online{mairArchetypalAnalysisRethinking2024,
  title = {Archetypal Analysis++: Rethinking the Initialization Strategy},
  shorttitle = {Archetypal Analysis++},
  author = {Mair, Sebastian and Sjölund, Jens},
  date = {2024-05-13},
  year = {2024},
  eprint = {2301.13748},
  eprinttype = {arXiv},
  journal = {Transactions on Machine Learning Research},
  eprintclass = {cs},
  doi = {10.48550/arXiv.2301.13748},
  url = {http://arxiv.org/abs/2301.13748},
  urldate = {2024-12-07},
  abstract = {Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential, but frequently used initialization methods yield either sub-optimal starting points or are prone to get stuck in poor local minima. In this paper, we propose archetypal analysis++ (AA++), a probabilistic initialization strategy for archetypal analysis that sequentially samples points based on their influence on the objective function, similar to k-means++. In fact, we argue that k-means++ already approximates the proposed initialization method. Furthermore, we suggest to adapt an efficient Monte Carlo approximation of k-means++ to AA++. In an extensive empirical evaluation of 15 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost always outperforms all baselines, including the most frequently used ones.},
  langid = {english},
}

@article{gimbernat-mayolArchetypalAnalysisPopulation2022,
  title = {Archetypal Analysis for Population Genetics},
  author = {Gimbernat-Mayol, Julia and Dominguez Mantes, Albert and Bustamante, Carlos D. and Mas Montserrat, Daniel and Ioannidis, Alexander G.},
  editor = {Wheeler, Heather E.},
  date = {2022-08-25},
  journaltitle = {PLOS Computational Biology},
  journal = {PLoS Comput Biol},
  volume = {18},
  number = {8},
  pages = {e1010301},
  issn = {1553-7358},
  doi = {10.1371/journal.pcbi.1010301},
  url = {https://dx.plos.org/10.1371/journal.pcbi.1010301},
  urldate = {2024-12-07},
  abstract = {The estimation of genetic clusters using genomic data has application from genome-wide association studies (GWAS) to demographic history to polygenic risk scores (PRS) and is expected to play an important role in the analyses of increasingly diverse, large-scale cohorts. However, existing methods are computationally-intensive, prohibitively so in the case of nationwide biobanks. Here we explore Archetypal Analysis as an efficient, unsupervised approach for identifying genetic clusters and for associating individuals with them. Such unsupervised approaches help avoid conflating socially constructed ethnic labels with genetic clusters by eliminating the need for exogenous training labels. We show that Archetypal Analysis yields similar cluster structure to existing unsupervised methods such as ADMIXTURE and provides interpretative advantages. More importantly, we show that since Archetypal Analysis can be used with lower-dimensional representations of genetic data, significant reductions in computational time and memory requirements are possible. When Archetypal Analysis is run in such a fashion, it takes several orders of magnitude less compute time than the current standard, ADMIXTURE. Finally, we demonstrate uses ranging across datasets from humans to canids.},
  langid = {english},
}

@article{kellerLearningExtremalRepresentations2021,
  title = {Learning Extremal Representations with Deep Archetypal Analysis},
  author = {Keller, Sebastian Mathias and Samarin, Maxim and Arend Torres, Fabricio and Wieser, Mario and Roth, Volker},
  date = {2021-04},
  journal = {International Journal of Computer Vision},
  volume = {129},
  number = {4},
  pages = {805--820},
  issn = {0920-5691, 1573-1405},
  doi = {10.1007/s11263-020-01390-3},
  url = {http://link.springer.com/10.1007/s11263-020-01390-3},
  urldate = {2024-12-07},
  abstract = {Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided.},
  langid = {english},
}

@article{perezSinglecellRNAseqReveals2022,
  title = {Single-Cell RNA-Seq Reveals Cell Type–Specific Molecular and Genetic Associations to Lupus},
  date = {2022-04-08},
  year = {2022},
  journal = {Science},
  volume = {376},
  number = {6589},
  pages = {eabf1970},
  publisher = {American Association for the Advancement of Science},
  doi = {10.1126/science.abf1970},
  url = {https://www.science.org/doi/10.1126/science.abf1970},
  urldate = {2025-02-05},
  abstract = {Systemic lupus erythematosus (SLE) is a heterogeneous autoimmune disease. Knowledge of circulating immune cell types and states associated with SLE remains incomplete. We profiled more than 1.2 million peripheral blood mononuclear cells (162 cases, 99 controls) with multiplexed single-cell RNA sequencing (mux-seq). Cases exhibited elevated expression of type 1 interferon–stimulated genes (ISGs) in monocytes, reduction of naïve CD4+ T cells that correlated with monocyte ISG expression, and expansion of repertoire-restricted cytotoxic GZMH+ CD8+ T cells. Cell type–specific expression features predicted case-control status and stratified patients into two molecular subtypes. We integrated dense genotyping data to map cell type–specific cis–expression quantitative trait loci and to link SLE-associated variants to cell type–specific expression. These results demonstrate mux-seq as a systematic approach to characterize cellular composition, identify transcriptional signatures, and annotate genetic variants associated with SLE.},
  author = {Perez, Richard K. and Gordon, M. Grace and Subramaniam, Meena and Kim, Min Cheol and Hartoularos, George C. and Targ, Sasha and Sun, Yang and Ogorodnikov, Anton and others and Fong, Lawrence and Dall’Era, Maria and Balliu, Brunilda and Regev, Aviv and Yazdany, Jinoos and Criswell, Lindsey A. and Zaitlen, Noah and Ye, Chun Jimmie}
}

@article{eugsterWeightedRobustArchetypal2011,
  title = {Weighted and Robust Archetypal Analysis},
  author = {Eugster, Manuel J. A. and Leisch, Friedrich},
  date = {2011-03-01},
  year = {2011},
  journal = {Computational Statistics \& Data Analysis},
  volume = {55},
  number = {3},
  pages = {1215--1225},
  issn = {0167-9473},
  doi = {10.1016/j.csda.2010.10.017},
  url = {https://www.sciencedirect.com/science/article/pii/S0167947310004056},
  urldate = {2025-02-06},
  abstract = {Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. The original algorithm is adapted to be a robust M-estimator and an iteratively reweighted least squares fitting algorithm is presented. As a required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using an artificial example, a real world example and a detailed simulation study.},
  langid = {english},
}

@article{coboArchetypalAnalysisApplications2022,
  title = {Archetypal Analysis and Applications},
  author = {Cobo, Guillermo García},
  date = {2022},
  url = {https://github.com/atmguille/archetypal-analysis/blob/main/Thesis/%5BEnglish%5D%20Archetypal%20analysis%20and%20applications.pdf},
  langid = {english},
}

@article{jaggiRevisitingFrankWolfeProjectionFree2013,
  title = {Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization},
  shorttitle = {Revisiting Frank-Wolfe},
  booktitle = {Proceedings of the 30th International Conference on Machine Learning},
  author = {Jaggi, Martin},
  date = {2013-02-13},
  pages = {427--435},
  publisher = {PMLR},
  issn = {1938-7228},
  url = {https://proceedings.mlr.press/v28/jaggi13.html},
  urldate = {2025-02-08},
  abstract = {We provide stronger and more general primal-dual convergence results for Frank-Wolfe-type algorithms (a.k.a. conditional gradient) for constrained convex optimization, enabled by a simple framework of duality gap certificates. Our analysis also holds if the linear subproblems are only solved approximately (as well as if the gradients are inexact), and is proven to be worst-case optimal in the sparsity of the obtained solutions.    On the application side, this allows us to unify a large variety of existing sparse greedy methods, in particular for optimization over convex hulls of an atomic set, even if those sets can only be approximated, including sparse (or structured sparse) vectors or matrices, low-rank matrices, permutation matrices, or max-norm bounded matrices.    We present a new general framework for convex optimization over matrix factorizations, where every Frank-Wolfe iteration will consist of a low-rank update, and discuss the broad application areas of this approach.},
  eventtitle = {International Conference on Machine Learning},
  langid = {english},
}

@article{mairCoresetsArchetypalAnalysis2019,
  title = {Coresets for Archetypal Analysis},
  booktitle = {Advances in Neural Information Processing Systems},
  journal = {Advances in Neural Information Processing Systems},
  author = {Mair, Sebastian and Brefeld, Ulf},
  year = {2019},
  date = {2019},
  volume = {32},
  publisher = {Curran Associates, Inc.},
  url = {https://papers.nips.cc/paper_files/paper/2019/hash/7f278ad602c7f47aa76d1bfc90f20263-Abstract.html},
  urldate = {2025-02-09},
  abstract = {Archetypal analysis represents instances as linear mixtures of prototypes (the archetypes) that lie on the boundary of the convex hull of the data. Archetypes are thus  often better interpretable than factors computed by other matrix factorization techniques. However, the interpretability comes with high computational cost due to additional convexity-preserving constraints. In this paper, we propose efficient coresets for archetypal analysis. Theoretical guarantees are derived by showing that quantization errors of k-means upper bound archetypal analysis; the computation of a provable absolute-coreset can be performed in only two passes over the data. Empirically, we show that the coresets lead to improved performance on several data sets.},
}

@article{chenFastRobustArchetypal2014,
  title = {Fast and Robust Archetypal Analysis for Representation Learning},
  booktitle = {2014 IEEE Conference on Computer Vision and Pattern Recognition},
  author = {Chen, Yuansi and Mairal, Julien and Harchaoui, Zaid},
  date = {2014-06},
  pages = {1478--1485},
  publisher = {IEEE},
  location = {Columbus, OH, USA},
  doi = {10.1109/CVPR.2014.192},
  url = {https://ieeexplore.ieee.org/document/6909588},
  urldate = {2025-02-10},
  abstract = {We revisit a pioneer unsupervised learning technique called archetypal analysis [5], which is related to successful data analysis methods such as sparse coding [18] and non-negative matrix factorization [19]. Since it was proposed, archetypal analysis did not gain a lot of popularity even though it produces more interpretable models than other alternatives. Because no efficient implementation has ever been made publicly available, its application to important scientific problems may have been severely limited.},
  eventtitle = {2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  isbn = {978-1-4799-5118-5},
  langid = {english},
}

@article{bauckhageArchetypalAnalysisAutoencoder2015,
  journal = {Workshop "New Challenges in Neural Computation" (NC2) 2015},
  title = {Archetypal Analysis as an Autoencoder},
  author = {Bauckhage, Christian and Kersting, Kristian and Hoppe, F. and Thurau, Christian},
  date = {2015},
  year = {2015},
  url = {https://www.ml.informatik.tu-darmstadt.de/papers/autoencode2015nc2.pdf},
  urldate = {2025-02-10},
  abstract = {We present an efficient approach to archetypal analysis where we use sub-gradient algorithms for optimization over the simplex to determine archetypes and reconstruction coefficients. Runtime evaluations reveal our approach to be notably more efficient than previous techniques. As an practical application, we consider archetypal analysis for autoencoding.},
  eventtitle = {Workshop "New Challenges in Neural Computation" (NC2) 2015},
  langid = {english},
}

@article{bauckhageMakingArchetypalAnalysis2009,
  title = {Making Archetypal Analysis Practical},
  booktitle = {Pattern Recognition},
  author = {Bauckhage, Christian and Thurau, Christian},
  editor = {Denzler, Joachim and Notni, Gunther and Süße, Herbert},
  date = {2009},
  year = {2009},
  pages = {272--281},
  publisher = {Springer},
  location = {Berlin, Heidelberg},
  doi = {10.1007/978-3-642-03798-6_28},
  abstract = {Archetypal analysis represents the members of a set of multivariate data as a convex combination of extremal points of the data. It allows for dimensionality reduction and clustering and is particularly useful whenever the data are superpositions of basic entities. However, since its computation costs grow quadratically with the number of data points, the original algorithm hardly applies to modern pattern recognition or data mining settings. In this paper, we introduce ways of notably accelerating archetypal analysis. Our experiments are the first successful application of the technique to large scale data analysis problems.},
  isbn = {978-3-642-03798-6},
  langid = {english},
}

@article{clarksonCoresetsSparseGreedy2010,
  title = {Coresets, Sparse Greedy Approximation, and the Frank-Wolfe Algorithm},
  author = {Clarkson, Kenneth L.},
  date = {2010-09-03},
  journaltitle = {ACM Trans. Algorithms},
  journal = {ACM Trans. Algorithms},
  volume = {6},
  number = {4},
  pages = {63:1--63:30},
  issn = {1549-6325},
  doi = {10.1145/1824777.1824783},
  url = {https://doi.org/10.1145/1824777.1824783},
  urldate = {2025-02-11},
  abstract = {The problem of maximizing a concave function f(x) in the unit simplex Δ can be solved approximately by a simple greedy algorithm. For given k, the algorithm can find a point x(k) on a k-dimensional face of Δ, such that f(x(k) ≥ f(x*) − O(1/k). Here f(x*) is the maximum value of f in Δ, and the constant factor depends on f. This algorithm and analysis were known before, and related to problems of statistics and machine learning, such as boosting, regression, and density mixture estimation. In other work, coming from computational geometry, the existence of ϵ-coresets was shown for the minimum enclosing ball problem by means of a simple greedy algorithm. Similar greedy algorithms, which are special cases of the Frank-Wolfe algorithm, were described for other enclosure problems. Here these results are tied together, stronger convergence results are reviewed, and several coreset bounds are generalized or strengthened.},
  langid = {english},
}

@article{linProjectedGradientMethods2007,
  title = {Projected Gradient Methods for Nonnegative Matrix Factorization},
  author = {Lin, Chih-Jen},
  date = {2007-10},
  journaltitle = {Neural Computation},
  volume = {19},
  number = {10},
  pages = {2756--2779},
  issn = {0899-7667},
  doi = {10.1162/neco.2007.19.10.2756},
  url = {https://ieeexplore.ieee.org/document/6795860},
  urldate = {2025-03-30},
  abstract = {Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.},
  eventtitle = {Neural Computation},
}

@article{eggertSparseCodingNMF2004,
  title = {Sparse Coding and NMF},
  booktitle = {2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541)},
  author = {Eggert, J. and Korner, E.},
  date = {2004-07},
  volume = {4},
  pages = {2529-2533 vol.4},
  issn = {1098-7576},
  doi = {10.1109/IJCNN.2004.1381036},
  url = {https://ieeexplore.ieee.org/document/1381036},
  urldate = {2025-03-30},
  abstract = {Non-negative matrix factorization (NMF) is a very efficient parameter-free method for decomposing multivariate data into strictly positive activations and basis vectors. However, the method is not suited for overcomplete representations, where usually sparse coding paradigms apply. We show how to merge the concepts of non-negative factorization with sparsity conditions. The result is a multiplicative algorithm that is comparable in efficiency to standard NMF, but that can be used to gain sensible solutions in the overcomplete cases. This is of interest e.g. for the case of learning and modeling of arrays of receptive fields arranged in a visual processing map, where an overcomplete representation is unavoidable.},
}

@article{militeMIDAADeepArchetypal2025,
  title = {MIDAA: Deep Archetypal Analysis for Interpretable Multi-Omic Data Integration Based on Biological Principles},
  shorttitle = {MIDAA},
  author = {Milite, Salvatore and Caravagna, Giulio and Sottoriva, Andrea},
  date = {2025-04-08},
  journaltitle = {Genome Biology},
  journal = {Genome Biology},
  volume = {26},
  number = {1},
  pages = {90},
  issn = {1474-760X},
  doi = {10.1186/s13059-025-03530-9},
  url = {https://doi.org/10.1186/s13059-025-03530-9},
  urldate = {2025-04-15},
  abstract = {High-throughput multi-omic molecular profiling allows the probing of biological systems at unprecedented resolution. However, integrating and interpreting high-dimensional, sparse, and noisy multimodal datasets remains challenging. Deriving new biological insights with current methods is difficult because they are not rooted in biological principles but prioritise tasks like dimensionality reduction. Here, we introduce a framework that combines archetypal analysis, an approach grounded in biological principles, with deep learning. Using archetypes based on evolutionary trade-offs and Pareto optimality, MIDAA finds extreme data points that define the geometry of the latent space, preserving the complexity of biological interactions while retaining an interpretable output. We demonstrate that these extreme points represent cellular programmes reflecting the underlying biology. Moreover, we show that, compared to alternative methods, MIDAA can identify parsimonious, interpretable, and biologically relevant patterns from real and simulated multi-omics.},
}

@misc{foxRobustRegrssion2013,
  title = {Robust Regrssion},
  author = {Fox, John and Weisberg},
  date = {2013-08-10},
  url = {http://users.stat.umn.edu/~sandy/courses/8053/handouts/robust.pdf},
}

@book{petersenMatrixCookbook2012,
  title = {The Matrix Cookbook},
  author = {Petersen, Kaare Brandt and Pedersen, Michael Syskind},
  date = {2012},
  publisher = {Technical University of Denmark},
  url = {https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf},
  abstract = {Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.},
  langid = {english},
}

@article{abrolGeometricApproachArchetypal2020,
  title = {A Geometric Approach to Archetypal Analysis via Sparse Projections},
  booktitle = {Proceedings of the 37th International Conference on Machine Learning},
  author = {Abrol, Vinayak and Sharma, Pulkit},
  date = {2020-11-21},
  pages = {42--51},
  publisher = {PMLR},
  issn = {2640-3498},
  url = {https://proceedings.mlr.press/v119/abrol20a.html},
  urldate = {2025-04-22},
  abstract = {Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data. This work presents a computationally efficient greedy AA (GAA) algorithm. GAA leverages the underlying geometry of AA, is scalable to larger datasets, and has significantly faster convergence rate. To achieve this, archetypes are learned via sparse projection of data. In the transformed space, GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations. The work further presents the use of GAA algorithm for extended AA models such as robust and kernel AA. Experimental results show that GAA is considerably faster while performing comparable to existing methods for tasks such as classification, data visualization/categorization.},
  eventtitle = {International Conference on Machine Learning},
  langid = {english},
}

@online{damleGeometricApproachArchetypal2015,
  title = {A Geometric Approach to Archetypal Analysis and Non-Negative Matrix Factorization},
  author = {Damle, Anil and Sun, Yuekai},
  date = {2015-11-03},
  eprint = {1405.4275},
  eprinttype = {arXiv},
  eprintclass = {stat},
  doi = {10.48550/arXiv.1405.4275},
  url = {http://arxiv.org/abs/1405.4275},
  urldate = {2025-04-22},
  abstract = {Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by interpreting both problems as finding extreme points of the data cloud. We also develop and analyze an efficient approach to finding extreme points in high dimensions. For modern massive datasets that are too large to fit on a single machine and must be stored in a distributed setting, our approach makes only a small number of passes over the data. In fact, it is possible to obtain the NMF or perform archetypal analysis with just two passes over the data.},
}

@article{mairFramebasedDataFactorizations2017,
  title = {Frame-Based Data Factorizations},
  booktitle = {Proceedings of the 34th International Conference on Machine Learning},
  author = {Mair, Sebastian and Boubekki, Ahcène and Brefeld, Ulf},
  date = {2017-07-17},
  pages = {2305--2313},
  publisher = {PMLR},
  issn = {2640-3498},
  url = {https://proceedings.mlr.press/v70/mair17a.html},
  urldate = {2025-04-22},
  abstract = {Archetypal Analysis is the method of choice to compute interpretable matrix factorizations. Every data point is represented as a convex combination of factors, i.e., points on the boundary of the convex hull of the data. This renders computation inefficient. In this paper, we show that the set of vertices of a convex hull, the so-called frame, can be efficiently computed by a quadratic program. We provide theoretical and empirical results for our proposed approach and make use of the frame to accelerate Archetypal Analysis. The novel method yields similar reconstruction errors as baseline competitors but is much faster to compute.},
  eventtitle = {International Conference on Machine Learning},
  langid = {english},
}

@article{dimentArchetypalAnalysisAudio2015,
  title = {Archetypal Analysis for Audio Dictionary Learning},
  booktitle = {2015 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)},
  author = {Diment, Aleksandr and Virtanen, Tuomas},
  date = {2015-10},
  pages = {1--5},
  publisher = {IEEE},
  location = {New Paltz, NY, USA},
  doi = {10.1109/WASPAA.2015.7336903},
  url = {http://ieeexplore.ieee.org/document/7336903/},
  urldate = {2025-04-22},
  eventtitle = {2015 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)},
  isbn = {978-1-4799-7450-4},
}

@article{meiOnlineDictionaryLearning2018,
  title = {Online Dictionary Learning for Approximate Archetypal Analysis},
  booktitle = {Computer Vision - ECCV 2018},
  author = {Mei, Jieru and Wang, Chunyu and Zeng, Wenjun},
  editor = {Ferrari, Vittorio and Hebert, Martial and Sminchisescu, Cristian and Weiss, Yair},
  date = {2018},
  pages = {501--516},
  publisher = {Springer International Publishing},
  location = {Cham},
  doi = {10.1007/978-3-030-01219-9_30},
  abstract = {Archetypal analysis is an unsupervised learning approach which represents data by convex combinations of a set of archetypes. The archetypes generally correspond to the extremal points in the dataset and are learned by requiring them to be convex combinations of the training data. In spite of its nice property of interpretability, the method is slow. We propose a variant of archetypal analysis which scales gracefully to large datasets. The core idea is to decouple the binding between data and archetypes and require them to be unit normalized. Geometrically, the method learns a convex hull inside the unit sphere and represents the data by their projections on the closest surfaces of the convex hull. By minimizing the representation error, the method pushes the convex hull surfaces close to the regions of the sphere where the data reside. The vertices of the convex hull are the learned archetypes. We apply the method to human faces and poses to validate its effectiveness in the context of reconstructions and classifications.},
  isbn = {978-3-030-01219-9},
  langid = {english},
}

@online{alcacerSurveyArchetypalAnalysis2025,
  title = {A Survey on Archetypal Analysis},
  author = {Alcacer, Aleix and Epifanio, Irene and Mair, Sebastian and Mørup, Morten},
  date = {2025-04-16},
  eprint = {2504.12392},
  eprinttype = {arXiv},
  eprintclass = {stat},
  doi = {10.48550/arXiv.2504.12392},
  url = {http://arxiv.org/abs/2504.12392},
  urldate = {2025-04-22},
  abstract = {Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure to extract the distinct aspects called archetypes in observations with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data with wide applications throughout the sciences. However, AA also faces challenges, particularly as the associated optimization problem is non-convex. This survey provides researchers and data mining practitioners an overview of methodologies and opportunities that AA has to offer surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data using AA and limitations. The survey concludes by explaining important future research directions concerning AA.},
}

@article{sulemanValidationArchetypalAnalysis2017,
  title = {Validation of Archetypal Analysis},
  booktitle = {2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)},
  author = {Suleman, Abdul},
  date = {2017-07},
  pages = {1--6},
  issn = {1558-4739},
  doi = {10.1109/FUZZ-IEEE.2017.8015385},
  url = {https://ieeexplore.ieee.org/document/8015385},
  urldate = {2025-04-23},
  abstract = {We use an information-theoretic criterion to assess the goodness-of-fit of the output of archetypal analysis (AA), also intended as a fuzzy clustering tool. It is an adaptation of an existing AIC-like measure to the specifics of AA. We test its effectiveness using artificial data and some data sets arising from real life problems. In most cases, the results achieved are similar to those provided by an external similarity index. The average reconstruction accuracy is about 93\%.},
  eventtitle = {2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)},
}

@online{wedenborgArchetypalAnalysisBinary2025,
  title = {Archetypal Analysis for Binary Data},
  author = {Wedenborg, A. Emilie J. and Mørup, Morten},
  date = {2025-02-06},
  eprint = {2502.04172},
  eprinttype = {arXiv},
  eprintclass = {cs},
  doi = {10.48550/arXiv.2502.04172},
  url = {http://arxiv.org/abs/2502.04172},
  urldate = {2025-04-26},
  abstract = {Archetypal analysis (AA) is a matrix decomposition method that identifies distinct patterns using convex combinations of the data points denoted archetypes with each data point in turn reconstructed as convex combinations of the archetypes. AA thereby forms a polytope representing trade-offs of the distinct aspects in the data. Most existing methods for AA are designed for continuous data and do not exploit the structure of the data distribution. In this paper, we propose two new optimization frameworks for archetypal analysis for binary data. i) A second order approximation of the AA likelihood based on the Bernoulli distribution with efficient closed-form updates using an active set procedure for learning the convex combinations defining the archetypes, and a sequential minimal optimization strategy for learning the observation specific reconstructions. ii) A Bernoulli likelihood based version of the principal convex hull analysis (PCHA) algorithm originally developed for least squares optimization. We compare these approaches with the only existing binary AA procedure relying on multiplicative updates and demonstrate their superiority on both synthetic and real binary data. Notably, the proposed optimization frameworks for AA can easily be extended to other data distributions providing generic efficient optimization frameworks for AA based on tailored likelihood functions reflecting the underlying data distribution.},
}

@article{richardsonReceiverOperatingCharacteristic2024,
  title = {The Receiver Operating Characteristic Curve Accurately Assesses Imbalanced Datasets},
  author = {Richardson, Eve and Trevizani, Raphael and Greenbaum, Jason A. and Carter, Hannah and Nielsen, Morten and Peters, Bjoern},
  date = {2024-06-14},
  journaltitle = {Patterns},
  journal = {Patterns},
  volume = {5},
  number = {6},
  pages = {100994},
  issn = {2666-3899},
  doi = {10.1016/j.patter.2024.100994},
  url = {https://www.sciencedirect.com/science/article/pii/S2666389924001090},
  urldate = {2025-04-27},
  abstract = {Many problems in biology require looking for a “needle in a haystack,” corresponding to a binary classification where there are a few positives within a much larger set of negatives, which is referred to as a class imbalance. The receiver operating characteristic (ROC) curve and the associated area under the curve (AUC) have been reported as ill-suited to evaluate prediction performance on imbalanced problems where there is more interest in performance on the positive minority class, while the precision-recall (PR) curve is preferable. We show via simulation and a real case study that this is a misinterpretation of the difference between the ROC and PR spaces, showing that the ROC curve is robust to class imbalance, while the PR curve is highly sensitive to class imbalance. Furthermore, we show that class imbalance cannot be easily disentangled from classifier performance measured via PR-AUC.},
}

@online{gillisSuccessiveProjectionAlgorithm2019,
  title = {Successive Projection Algorithm Robust to Outliers},
  author = {Gillis, Nicolas},
  date = {2019-08-12},
  eprint = {1908.04109},
  eprinttype = {arXiv},
  eprintclass = {eess},
  doi = {10.48550/arXiv.1908.04109},
  url = {http://arxiv.org/abs/1908.04109},
  urldate = {2025-04-27},
  abstract = {The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix \$X\$, SPA identifies an index set \$\textbackslash mathcal\{K\}\$ such that there exists a nonnegative matrix \$H\$ with \$X \textbackslash approx X(:,\textbackslash mathcal\{K\})H\$. SPA has been successfully used as a pure-pixel search algorithm in hyperspectral unmixing and for anchor word selection in document classification. Moreover, SPA is provably robust in low-noise settings. The main drawbacks of SPA are that it is not robust to outliers and does not take the data fitting term into account when selecting the indices in \$\textbackslash mathcal\{K\}\$. In this paper, we propose a new SPA variant, dubbed Robust SPA (RSPA), that is robust to outliers while still being provably robust in low-noise settings, and that takes into account the reconstruction error for selecting the indices in \$\textbackslash mathcal\{K\}\$. We illustrate the effectiveness of RSPA on synthetic data sets and hyperspectral images.},
  langid = {english},
}

@online{mirzasoleimanCoresetsDataefficientTraining2020,
  title = {Coresets for Data-Efficient Training of Machine Learning Models},
  author = {Mirzasoleiman, Baharan and Bilmes, Jeff and Leskovec, Jure},
  date = {2020-11-16},
  eprint = {1906.01827},
  eprinttype = {arXiv},
  eprintclass = {cs},
  doi = {10.48550/arXiv.1906.01827},
  url = {http://arxiv.org/abs/1906.01827},
  urldate = {2025-04-29},
  abstract = {Incremental gradient (IG) methods, such as stochastic gradient descent and its variants are commonly used for large scale optimization in machine learning. Despite the sustained effort to make IG methods more data-efficient, it remains an open question how to select a training data subset that can theoretically and practically perform on par with the full dataset. Here we develop CRAIG, a method to select a weighted subset (or coreset) of training data that closely estimates the full gradient by maximizing a submodular function. We prove that applying IG to this subset is guaranteed to converge to the (near)optimal solution with the same convergence rate as that of IG for convex optimization. As a result, CRAIG achieves a speedup that is inversely proportional to the size of the subset. To our knowledge, this is the first rigorous method for data-efficient training of general machine learning models. Our extensive set of experiments show that CRAIG, while achieving practically the same solution, speeds up various IG methods by up to 6x for logistic regression and 3x for training deep neural networks.},
}

@book{mincNonnegativeMatrices1988,
  title = {Nonnegative Matrices},
  author = {Minc, Henryk},
  date = {1988},
  series = {Wiley-Interscience Series in Discrete Mathematics and Optimization},
  edition = {2. print},
  publisher = {Wiley},
  location = {New York},
  isbn = {978-0-471-83966-8},
  langid = {english},
  pagetotal = {206},
}

@article{beckArchetypalAnalysisNeuronal2022,
  title = {Archetypal Analysis for Neuronal Clique Detection in Low-Rate Calcium Fluorescence Imaging},
  booktitle = {2022 44th Annual International Conference of the IEEE Engineering in Medicine \& Biology Society (EMBC)},
  author = {Beck, Connor and Kunze, Anja and Zosso, Dominique},
  date = {2022-07},
  pages = {162--166},
  issn = {2694-0604},
  doi = {10.1109/EMBC48229.2022.9871404},
  url = {https://ieeexplore.ieee.org/document/9871404},
  urldate = {2025-04-30},
  abstract = {Archetypal analysis (AA) is a versatile data analysis method to cluster distinct features within a data set. Here, we demonstrate a framework showing the power of AA to spatio-temporally resolve events in calcium imaging, an imaging modality commonly used in neurobiology and neuroscience to capture neuronal communication patterns. After validation of our AA-based approach on synthetic data sets, we were able to characterize neuronal communication patterns in recorded calcium waves. Clinical relevance– Transient calcium events play an essential role in brain cell communication, growth, and network formation, as well as in neurodegeneration. To reliably interpret calcium events from personalized medicine data, where patterns may differ from patient to patient, appropriate image processing and signal analysis methods need to be developed for optimal network characterization.},
  eventtitle = {2022 44th Annual International Conference of the IEEE Engineering in Medicine \& Biology Society (EMBC)},
}

@article{chapmanLargescaleViewMarine2022,
  title = {A Large-Scale View of Marine Heatwaves Revealed by Archetype Analysis},
  author = {Chapman, Christopher C. and Monselesan, Didier P. and Risbey, James S. and Feng, Ming and Sloyan, Bernadette M.},
  date = {2022-12-21},
  journaltitle = {Nature Communications},
  journal = {Nat Commun},
  volume = {13},
  number = {1},
  pages = {7843},
  publisher = {Nature Publishing Group},
  issn = {2041-1723},
  doi = {10.1038/s41467-022-35493-x},
  url = {https://www.nature.com/articles/s41467-022-35493-x},
  urldate = {2025-04-30},
  abstract = {Marine heatwaves can have disastrous impacts on ecosystems and marine industries. Given their potential consequences, it is important to understand how broad-scale climate variability influences the probability of localised extreme events. Here, we employ an advanced data-mining methodology, archetype analysis, to identify large scale patterns and teleconnections that lead to marine extremes in certain regions. This methodology is applied to the Australasian region, where it identifies instances of anomalous sea-surface temperatures, frequently associated with marine heatwaves, as well as the broadscale oceanic and atmospheric conditions associated with those extreme events. Additionally, we use archetype analysis to assess the ability of a low-resolution climate model to accurately represent the teleconnection patterns associated with extreme climate variability, and discuss the implications for the predictability of these impactful events.},
  langid = {english},
}

@online{javadiNonnegativeMatrixFactorization2017,
  title = {Non-Negative Matrix Factorization via Archetypal Analysis},
  author = {Javadi, Hamid and Montanari, Andrea},
  date = {2017-05-08},
  eprint = {1705.02994},
  eprinttype = {arXiv},
  eprintclass = {stat},
  doi = {10.48550/arXiv.1705.02994},
  url = {http://arxiv.org/abs/1705.02994},
  urldate = {2025-05-01},
  abstract = {Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse), a regime that is captured by the separability condition and its generalizations. In this paper, we study an approach to NMF that can be traced back to the work of Cutler and Breiman (1994) and does not require the data to be separable, while providing a generally unique decomposition. We optimize the trade-off between two objectives: we minimize the distance of the data points from the convex envelope of the archetypes (which can be interpreted as an empirical risk), while minimizing the distance of the archetypes from the convex envelope of the data (which can be interpreted as a data-dependent regularization). The archetypal analysis method of (Cutler, Breiman, 1994) is recovered as the limiting case in which the last term is given infinite weight. We introduce a `uniqueness condition' on the data which is necessary for exactly recovering the archetypes from noiseless data. We prove that, under uniqueness (plus additional regularity conditions on the geometry of the archetypes), our estimator is robust. While our approach requires solving a non-convex optimization problem, we find that standard optimization methods succeed in finding good solutions both for real and synthetic data.},
}

@article{bachemOneshotCoresetsCase2018,
  title = {One-Shot Coresets: The Case of k-Clustering},
  shorttitle = {One-Shot Coresets},
  booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
  author = {Bachem, Olivier and Lucic, Mario and Lattanzi, Silvio},
  date = {2018-03-31},
  pages = {784--792},
  publisher = {PMLR},
  issn = {2640-3498},
  url = {https://proceedings.mlr.press/v84/bachem18a.html},
  urldate = {2025-05-04},
  abstract = {Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably good and small summaries, they are inherently problem dependent - the practitioner has to commit to a fixed clustering objective before even exploring the data. However, can one construct small data summaries for a wide range of clustering problems simultaneously? In this work, we affirmatively answer this question by proposing an efficient algorithm that constructs such one-shot summaries for k-clustering problems while retaining strong theoretical guarantees.},
  eventtitle = {International Conference on Artificial Intelligence and Statistics},
  langid = {english},
}

@article{bachemScalableMeansClustering2018,
  title = {Scalable k -Means Clustering via Lightweight Coresets},
  booktitle = {Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
  author = {Bachem, Olivier and Lucic, Mario and Krause, Andreas},
  date = {2018-07-19},
  series = {KDD '18},
  pages = {1119--1127},
  publisher = {Association for Computing Machinery},
  location = {New York, NY, USA},
  doi = {10.1145/3219819.3219973},
  url = {https://dl.acm.org/doi/10.1145/3219819.3219973},
  urldate = {2025-05-04},
  abstract = {\textbackslash emphCoresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k -means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel, and the resulting coresets are smaller. We further show that the proposed approach naturally generalizes to statistical k -means clustering and that, compared to existing results, it can be used to compute smaller summaries for empirical risk minimization. In extensive experiments, we demonstrate that the proposed algorithm outperforms existing data summarization strategies in practice.},
  isbn = {978-1-4503-5552-0},
}

@article{thogersenArchetypalAnalysisDiverse2013,
  title = {Archetypal Analysis of Diverse Pseudomonas Aeruginosatranscriptomes Reveals Adaptation in Cystic Fibrosis Airways},
  author = {Thøgersen, Juliane Charlotte and Mørup, Morten and Damkiær, Søren and Molin, Søren and Jelsbak, Lars},
  date = {2013-09-23},
  journaltitle = {BMC Bioinformatics},
  journal = {BMC Bioinformatics},
  volume = {14},
  number = {1},
  pages = {279},
  issn = {1471-2105},
  doi = {10.1186/1471-2105-14-279},
  url = {https://doi.org/10.1186/1471-2105-14-279},
  urldate = {2025-05-05},
  abstract = {Analysis of global gene expression by DNA microarrays is widely used in experimental molecular biology. However, the complexity of such high-dimensional data sets makes it difficult to fully understand the underlying biological features present in the data.},
}

@article{dijkFindingArchetypalSpaces2019,
  title = {Finding Archetypal Spaces Using Neural Networks},
  booktitle = {2019 IEEE International Conference on Big Data (Big Data)},
  author = {van Dijk, David and and Burkhardt, Daniel B. and Amodio, Matthew and Tong, Alexander and Wolf, Guy and Krishnaswamy, Smita},
  date = {2019-12},
  pages = {2634--2643},
  doi = {10.1109/BigData47090.2019.9006484},
  url = {https://ieeexplore.ieee.org/document/9006484},
  urldate = {2025-05-05},
  abstract = {Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of ”pure types” or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between features, such as in biology where different combinations of traits provide optimal fitness for different environments. Existing methods for archetypal analysis work well when a linear relationship exists between the feature space and the archetypal space. However, such methods are not applicable to systems where the feature space is generated non-linearly from the combination of archetypes, such as in biological systems or image transformations. Here, we propose a reformulation of the problem such that the goal is to learn a non-linear transformation of the data into a latent archetypal space. To solve this problem, we introduce Archetypal Analysis network (AAnet), which is a deep neural network framework for learning and generating from a latent archetypal representation of data. We demonstrate state-of-the-art recovery of ground-truth archetypes in non-linear data domains, show AAnet can generate from data geometry rather than from data density, and use AAnet to identify biologically meaningful archetypes in single-cell gene expression data.},
  eventtitle = {2019 IEEE International Conference on Big Data (Big Data)},
}

@article{behdinSparseNMFArchetypal,
  title = {Sparse NMF with Archetypal Regularization: Computational and Robustness Properties},
  author = {Behdin, Kayhan and Mazumder, Rahul},
  abstract = {We consider the problem of sparse nonnegative matrix factorization (NMF) using archetypal regularization. The goal is to represent a collection of data points as nonnegative linear combinations of a few nonnegative sparse factors with appealing geometric properties, arising from the use of archetypal regularization. We generalize the notion of robustness studied in Javadi and Montanari (2019) (without sparsity) to the notions of (a) strong robustness that implies each estimated archetype is close to the underlying archetypes and (b) weak robustness that implies there exists at least one recovered archetype that is close to the underlying archetypes. Our theoretical results on robustness guarantees hold under minimal assumptions on the underlying data, and applies to settings where the underlying archetypes need not be sparse. We present theoretical results and illustrative examples to strengthen the insights underlying the notions of robustness. We propose new algorithms for our optimization problem; and present numerical experiments on synthetic and real data sets that shed further insights into our proposed framework and theoretical developments.},
  langid = {english},
}

@book{alonIntroductionSystemsBiology2020,
  title = {An Introduction to Systems Biology: Design Principles of Biological Circuits},
  shorttitle = {An Introduction to Systems Biology},
  author = {Alon, Uri},
  date = {2020},
  edition = {Second edition},
  publisher = {CRC Press, Taylor \& Francis Group},
  location = {Boca Raton London New York},
  doi = {10.1201/9780429283321},
  isbn = {978-1-4398-3717-7 978-0-429-28332-1},
  langid = {english},
  pagetotal = {1},
}

@article{10.1038/nature21065,
  title = {Single-Cell Spatial Reconstruction Reveals Global Division of Labour in the Mammalian Liver},
  author = {Halpern, Keren Bahar and Shenhav, Rom and {Matcovitch-Natan}, Orit and T{\'o}th, Be{\'a}ta and Lemze, Doron and Golan, Matan and Massasa, Efi E. and Baydatch, Shaked and Landen, Shanie and Moor, Andreas E. and Brandis, Alexander and Giladi, Amir and {Stokar-Avihail}, Avigail and David, Eyal and Amit, Ido and Itzkovitz, Shalev},
  year = {2017},
  month = feb,
  journal = {Nature},
  volume = {542},
  number = {7641},
  pages = {352--356},
  issn = {0028-0836, 1476-4687},
  doi = {10.1038/nature21065},
  urldate = {2024-12-07},
  abstract = {Single-molecule fluorescence in situ hybridization is performed to identify several landmark genes in the liver and their level of expression in single-cell RNA sequencing is used to spatially reconstruct the zonation of all liver genes. A few important liver genes are differentially expressed in a radial fashion from the central vein outward, but the extent of such spatial division, or zonation, has remained unknown. Shalev Itzkovitz, Ido Amit and colleagues performed single-molecule fluorescence in situ hybridization against several landmark genes, and used their level of expression to spatially reconstruct the zonation of all liver genes. They find that around half of the genes in the liver are zonated, and surprisingly also find that several genes peak in the middle of the liver lobules. The succession of gene expression profiles matches the position of proteins in the bile-acid biosynthetic cascade. The mammalian liver consists of hexagon-shaped lobules that are radially polarized by blood flow and morphogens1,2,3,4. Key liver genes have been shown to be differentially expressed along the lobule axis, a phenomenon termed zonation5,6, but a detailed genome-wide reconstruction of this spatial division of labour has not been achieved. Here we measure the entire transcriptome of thousands of mouse liver cells and infer their lobule coordinates on the basis of a panel of zonated landmark genes, characterized with single-molecule fluorescence in situ hybridization7. Using this approach, we obtain the zonation profiles of all liver genes with high spatial resolution. We find that around 50\% of liver genes are significantly zonated and uncover abundant non-monotonic profiles that peak at the mid-lobule layers. These include a spatial order of bile acid biosynthesis enzymes that matches their position in the enzymatic cascade. Our approach can facilitate the reconstruction of similar spatial genomic blueprints for other mammalian organs.},
  langid = {english},
  pmcid = {PMC5321580},
  pmid = {28166538}
}

@article{benMoshe2022,
  title = {The Spatiotemporal Program of Zonal Liver Regeneration Following Acute Injury},
  author = {{Ben-Moshe}, Shani and Veg, Tamar and Manco, Rita and Dan, Stav and Papinutti, Delfina and Lifshitz, Aviezer and Kolodziejczyk, Aleksandra A. and Bahar Halpern, Keren and Elinav, Eran and Itzkovitz, Shalev},
  year = {2022},
  month = jun,
  journal = {Cell Stem Cell},
  volume = {29},
  number = {6},
  pages = {973-989.e10},
  issn = {19345909},
  doi = {10.1016/j.stem.2022.04.008},
  urldate = {2024-12-07},
  abstract = {The liver carries a remarkable ability to regenerate rapidly after acute zonal damage. Single-cell approaches are necessary to study this process, given the spatial heterogeneity of liver cell types. Here, we use spatially resolved single-cell RNA sequencing (scRNA-seq) to study the dynamics of mouse liver regeneration after acute acetaminophen (APAP) intoxication. We find that hepatocytes proliferate throughout the liver lobule, creating the mitotic pressure required to repopulate the necrotic pericentral zone rapidly. A subset of hepatocytes located at the regenerating front transiently upregulate fetal-specific genes, including Afp and Cdh17, as they reprogram to a pericentral state. Zonated endothelial, hepatic stellate cell (HSC), and macrophage populations are differentially involved in immune recruitment, proliferation, and matrix remodeling. We observe massive transient infiltration of myeloid cells, yet stability of lymphoid cell abundance, in accordance with a global decline in antigen presentation. Our study provides a resource for understanding the coordinated programs of zonal liver regeneration.},
  langid = {english},
  pmid = {35659879}
}

@article{Kukanja2024,
  title = {Cellular Architecture of Evolving Neuroinflammatory Lesions and Multiple Sclerosis Pathology},
  author = {Kukanja, Petra and Langseth, Christoffer M. and {Rubio Rodr{\'i}guez-Kirby}, Leslie A. and Agirre, Eneritz and Zheng, Chao and Raman, Amitha and Yokota, Chika and Avenel, Christophe and Tiklov{\'a}, Katarina and {Guerreiro-Cacais}, Andr{\'e} O. and Olsson, Tomas and Hilscher, Markus M. and Nilsson, Mats and {Castelo-Branco}, Gon{\c c}alo},
  year = {2024},
  month = apr,
  journal = {Cell},
  volume = {187},
  number = {8},
  pages = {1990-2009.e19},
  issn = {00928674},
  doi = {10.1016/j.cell.2024.02.030},
  urldate = {2024-12-08},
  abstract = {Multiple sclerosis (MS) is a neurological disease characterized by multifocal lesions and smoldering pathology. Although single-cell analyses provided insights into cytopathology, evolving cellular processes underlying MS remain poorly understood. We investigated the cellular dynamics of MS by modeling temporal and regional rates of disease progression in mouse experimental autoimmune encephalomyelitis (EAE). By performing single-cell spatial expression profiling using in situ sequencing (ISS), we annotated disease neighborhoods and found centrifugal evolution of active lesions. We demonstrated that disease-associated (DA)-glia arise independently of lesions and are dynamically induced and resolved over the disease course. Single-cell spatial mapping of human archival MS spinal cords confirmed the differential distribution of homeostatic and DA-glia, enabled deconvolution of active and inactive lesions into sub-compartments, and identified new lesion areas. By establishing a spatial resource of mouse and human MS neuropathology at a single-cell resolution, our study unveils the intricate cellular dynamics underlying MS.},
  langid = {english},
  pmid = {38513664},
}

@article{muhlSinglecellAnalysisUncovers2020,
  title = {Single-Cell Analysis Uncovers Fibroblast Heterogeneity and Criteria for Fibroblast and Mural Cell Identification and Discrimination},
  year = {2020},
  month = aug,
  journal = {Nature Communications},
  volume = {11},
  number = {1},
  pages = {3953},
  publisher = {Nature Publishing Group},
  issn = {2041-1723},
  doi = {10.1038/s41467-020-17740-1},
  urldate = {2025-03-26},
  abstract = {Many important cell types in adult vertebrates have a mesenchymal origin, including fibroblasts and vascular mural cells. Although their biological importance is undisputed, the level of mesenchymal cell heterogeneity within and between organs, while appreciated, has not been analyzed in detail. Here, we compare single-cell transcriptional profiles of fibroblasts and vascular mural cells across four murine muscular organs: heart, skeletal muscle, intestine and bladder. We reveal gene expression signatures that demarcate fibroblasts from mural cells and provide molecular signatures for cell subtype identification. We observe striking inter- and intra-organ heterogeneity amongst the fibroblasts, primarily reflecting differences in the expression of extracellular matrix components. Fibroblast subtypes localize to discrete anatomical positions offering novel predictions about physiological function(s) and regulatory signaling circuits. Our data shed new light on the diversity of poorly defined classes of cells and provide a foundation for improved understanding of their roles in physiological and pathological processes.},
  copyright = {2020 The Author(s)},
  langid = {english},
  author = {Muhl, Lars and Genov{\'e}, Guillem and Leptidis, Stefanos and Liu, Jianping and He, Liqun and Mocci, Giuseppe and Sun, Ying and Gustafsson, Sonja and others and Segerstolpe, {\AA}sa and Raschperger, Elisabeth and Hansson, Emil M. and Bj{\"o}rkegren, Johan L. M. and Peng, Xiao-Rong and Vanlandewijck, Michael and Lendahl, Urban and Betsholtz, Christer}
}

@inproceedings{lucicStrongCoresetsHard2016,
  title = {Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures},
  booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
  author = {Lucic, Mario and Bachem, Olivier and Krause, Andreas},
  year = {2016},
  month = may,
  pages = {1--9},
  publisher = {PMLR},
  journal = {PMLR},
  issn = {1938-7228},
  urldate = {2025-06-11},
  abstract = {Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now, the algorithms and the corresponding theory were usually specific to each clustering problem.  We propose a single, practical algorithm to construct strong coresets for a large class of hard and soft clustering problems based on Bregman divergences. This class includes hard clustering with popular distortion measures such as the Squared Euclidean distance, the Mahalanobis distance, KL-divergence and Itakura-Saito distance. The corresponding soft clustering problems are directly related to popular mixture models due to a dual relationship between Bregman divergences and Exponential family distributions. Our theoretical results further imply a randomized polynomial-time approximation scheme for hard clustering. We demonstrate the practicality of the proposed algorithm in an empirical evaluation.},
  langid = {english},
}

@article{cell2location,
  title = {Cell2location Maps Fine-Grained Cell Types in Spatial Transcriptomics},
  year = {2022},
  month = may,
  journal = {Nature Biotechnology},
  volume = {40},
  number = {5},
  pages = {661--671},
  issn = {1087-0156, 1546-1696},
  doi = {10.1038/s41587-021-01139-4},
  urldate = {2024-12-07},
  abstract = {Spatial transcriptomic technologies promise to resolve cellular wiring diagrams of tissues in health and disease, but comprehensive mapping of cell types in situ remains a challenge. Here we present {\cyrchar\cyrs}ell2location, a Bayesian model that can resolve fine-grained cell types in spatial transcriptomic data and create comprehensive cellular maps of diverse tissues. Cell2location accounts for technical sources of variation and borrows statistical strength across locations, thereby enabling the integration of single-cell and spatial transcriptomics with higher sensitivity and resolution than existing tools. We assessed cell2location in three different tissues and show improved mapping of fine-grained cell types. In the mouse brain, we discovered fine regional astrocyte subtypes across the thalamus and hypothalamus. In the human lymph node, we spatially mapped a rare pre-germinal center B cell population. In the human gut, we resolved fine immune cell populations in lymphoid follicles. Collectively, our results present {\cyrchar\cyrs}ell2location as a versatile analysis tool for mapping tissue architectures in a comprehensive manner. A Bayesian model maps the location of cell types in tissues with higher sensitivity.},
  langid = {english},
  pmid = {35027729},
  author = {Kleshchevnikov, Vitalii and Shmatko, Artem and Dann, Emma and Aivazidis, Alexander and King, Hamish W. and Li, Tong and Elmentaite, Rasa and Lomakin, Artem and others and Ramona, Lauma and Tuck, Elizabeth and Arutyunyan, Anna and {Vento-Tormo}, Roser and Gerstung, Moritz and James, Louisa and Stegle, Oliver and Bayraktar, Omer Ali}
}
