Flexible Online Representation Learning Based on Similarity Matching
This work provides a versatile online learning algorithm for unsupervised representation learning, which is significant for practitioners needing scalable, biologically plausible methods for high-dimensional data.
The paper proposes a biologically plausible online learning algorithm that learns sparse, shift-invariant representations for clustering, manifold tiling, and sparse coding, addressing scalability issues of existing methods. The algorithm is demonstrated to be effective on various data structures.
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.