states_participation_ratio — CONNGRAPH dimension op

• Data kinds: matrix → measurement

• Call: import fullseye as fs; fs.ledger.states_participation_ratio(X: 'Any') -> 'float' (to call the implementation directly, import conngraph; conngraph.states_participation_ratio(X: 'Any') -> 'float'; from the registry, opsconngraph.get("states_participation_ratio"))

Usage

Effective dimension of the state sequence X (N, n) = participation ratio PR = (Σλ)² / Σλ² (λ are the eigenvalues of the covariance, Gao et al. 2017). It is n if all columns are independent with equal variance, and 1 if the states lie along 1 direction.

It depends on the sample count N (when N is small, PR levels off at PR ≤ N), so align N when comparing. 0 for a constant (variance 0).

Detailed usage guide

• conngraph family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_connectome_motor_bottleneck — py -3.11 examples/poc_connectome_motor_bottleneck.py

Ops the type connects to (they accept measurement as input)

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Same category (dimension)

graph_block_shuffle · graph_layer_propagate · states_layer_dimension

*Provenance: conngraph.py — CONNGRAPH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.