提出一种在线学习算法，实现稀疏高维表示的灵活建模。
Flexible Online Representation Learning Based on Similarity Matching
- 基于相似性匹配设计在线学习机制，无需复杂优化
- 支持稀疏、平移不变的表示，适用于聚类与流形铺砌
- 生物可解释性强，适合大规模数据的结构探索
稀疏高维表示有助于在无监督数据探索中揭示非平凡结构，适用于图的稠密连接问题（如社区检测），也可用于流形铺砌和特征学习。传统方法需在计算上不可行的完全正定矩阵空间中优化，或退化到随样本量增长而变得不实用的双非负矩阵空间。部分方法还施加行和约束（如双随机性），虽具平移不变性优势，但导致在线学习规则复杂。为此，我们提出一种通用的在线生物可解释学习算法，能灵活学习稀疏、平移不变的表示，根据数据结构适用于聚类、流形铺砌或稀疏编码。
原文摘要 · Abstract (English)
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.
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