GENERALIZED MATRIX LOCAL LOW RANK REPRESENTATION BY RANDOM PROJECTION AND SUBMATRIX PROPAGATION

Pengtao Dang, Wennan Chang, Haiqi Zhu, Changlin Wan, Tong Zhao, Tingo Guo, Paul Salama, Sha Cao, Chi Zhang

Keywords: Matrix decomposition, Local Low Rank matrix detection, Representation learning, Subspace learning

TL;DR: We developed a sub-matrix propagation based approach to solve the fundamental mathematical problem of matrix local low rank representation.

Abstract: Detecting distinct submatrices of low rank property is a highly desirable matrix representation learning technique for the ease of data interpretation, called the matrix local low rank representation (MLLRR). Based on different mathematical assumptions of the local pattern, the MLLRR problem could be categorized into two sub-problems, namely local constant variation (LCV) and local linear low rank (LLR). Existing solutions on MLLRR only focused on the LCV problem, which misses a substantial amount of true and interesting patterns. In this work, we develop a novel matrix computational framework called RPSP (Random Probing based submatrix Propagation) that provides an effective solution for both of the LCV and LLR problems. RPSP detects local low rank patterns that grow from small submatrices of low rank property, which are determined by a random projection approach. RPSP is supported by theories of random projection. Experiments on synthetic data demonstrate that RPSP outperforms all state-of-the-art methods, with the capacity to robustly and correctly identify the low rank matrices under both LCV and LLR settings. On real-world datasets, RPSP also demonstrates its effectiveness in identifying interpretable local low rank matrices.

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