Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clustering
We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal. For arbitrary positive row marginals of equal total mass, the joint KL projection reduces exactly to a strictly convex gauge-fixed dual with only $r-1$ effective variables; its Hessian is a sum of categorical covariance terms and admits $O((n+m)r)$ matrix-free Hessian--vector products. The projection theorem is objective-independent. We then specialize this geometry to doubly stochastic (DS) graph learning through $W=U\operatorname{Diag}(g)^{-1}V^\top$, where row-simplex factors with a common column mass induce an e...
| Authors | Enliang Hu |
|---|---|
| Primary category | cs.LG |
| Published | 9 August 2026 |
| Last updated at source | 9 August 2026 |
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