Reviews: Deep Subspace Clustering Networks

The paper addresses the problem of subspace clustering, i.e., separating a collection of data points lying in a union of subspaces according to underlying subspaces, using deep neural networks. To do so, the paper builds on the sparse subspace clustering idea: among all possible representations of a data point as a combination of other points in the dataset, the representation that uses the minimum number of points, corresponds to points from the same subspace. In other words, SSC uses the idea that for a data matrix X, a sparse solution of X X C (subject to diag(C) 0) represents each point as a combination of a few other points from the same subspace. The paper proposes a deep neural network to transform the data into a new representation Z f_W(X) for which one searches for a sparse representation of Z Z C, with the hope to learn more effective representations of data for clustering. To achieve this, the paper uses an auto-encoder scheme, where the middle hidden layer outputs are used as Z .