Flexible Online Representation Learning Based on Similarity Matching

2026-05-31

AI Summary

This work addresses the challenge of online learning of high-dimensional sparse representations under row-sum constraints—such as doubly stochasticity—in large-scale settings. The authors propose a similarity-matching-based online learning algorithm that circumvents computationally expensive relaxations like completely positive or doubly nonnegative matrix factorizations. By incorporating translation invariance and explicit sparsity constraints, the method flexibly accommodates diverse tasks including clustering, manifold tiling, and sparse coding. Notably, it achieves the first efficient online sparse representation learning framework that enforces row-sum constraints, thereby significantly enhancing scalability and practicality for large-scale applications while preserving biological interpretability.

Abstract

Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning. Conventional algorithms optimize in the space of computationally intractable completely positive matrices or relax the problem to the space of doubly nonnegative matrices that scale with sample size in a way rendering them impractical for large data sets. Some of these methods also impose a row sum constraint, such as double stochasticity. Row sum constraints have the added advantage of being shift-invariant, in the context of manifold tiling. Constraints on the row sum of output similarity matrices require nontrivial online learning rules. Addressing these needs, we propose a versatile online biologically plausible learning algorithm capable of learning sparse shift-invariant representations, useful for clustering, manifold tiling, or sparse coding, depending on the data structure.

Problem

• sparse representation
• online learning
• similarity matching
• shift-invariance
• manifold tiling

Innovation

• online learning
• sparse representation
• shift-invariance
• similarity matching
• manifold tiling