A connection between sparse and low rank matrices. Let S be a sparse similarity matrix, for example the distances of the 3 nearest neighbours in a low dimensional manifold. Can you recover S if you have a low rank (dense) matrix L from in a high dimensional space? This paper provides a geometric interpretation for S = max(0,L). It proposes a decomposition algorithm, that can be modelled as a ReLU neural network layer.

#MachineLearning #SparseDecomposition #LowRank #TMLR
https://openreview.net/forum?id=p8gncJbMit