sinkhorn_divergence — COLORTRANSPORT `transport` op

• Data kinds: signal × signal × matrix → scalar

• Call: import colortransport; colortransport.sinkhorn_divergence(a, b, cost, cost_aa=None, cost_bb=None, reg=0.05, **kw) (or opscolortransport.get("sinkhorn_divergence"))

Usage

The debiased Sinkhorn distance (Genevay, Peyré & Cuturi, AISTATS 2018).

> The detailed description below is the original text — the summary and the headings are translated.

`S(a,b) - (S(a,a) + S(b,b)) / 2。:func:sinkhorn_distance` は正則化のぶん

系統的に上振れし、自分自身との「距離」が 0 にならない(実測 reg=0.2 で

0.05 超)。同じ偏りを自分自身との距離から引くと相殺され、**自分自身との値が

0 に戻る** ―― TRIZ でいう釣り合い(反作用で打ち消す)そのもの。

`cost_aa / cost_bb は a 同士・b` 同士の費用行列。1 点集合を

自分自身と比べる意味なので、**省略すると `cost` が正方のときだけ**

それを流用する(非正方で省略したら例外 ―― 適当な行列で埋めると、

引き算する量が別物になり、打ち消したつもりで別の偏りが載る)。

Background guides (the physics and conventions behind this op)

• colorimetry — 測色と分光の知識 — 色は「分光 × 光源 × 観測者」でしか決まらない

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)

• color_transport — py -3.11 examples/color_transport.py

Ops the type connects to (they accept `scalar` as input)

—

Same category (`transport`)

wasserstein_1d · transport_plan_1d · sinkhorn · sinkhorn_distance

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

sinkhorn_divergence — COLORTRANSPORT transport op