RETHINKING LOCAL LOW RANK MATRIX DETECTION:A MULTIPLE-FILTER BASED NEURAL NETWORK FRAMEWORK

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

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

Abstract: The matrix local low rank representation (MLLRR) is a critical dimension reduction technique widely used in recommendation systems, text mining and computer vision. In MLLRR, how to robustly identify the row and column indices that forma distinct low rank sub-matrix is a major challenge. In this work, we first organized the general MLLRR problem into three inter-connected sub-problems based on different low rank properties, namely, LLR-1C, LLR-1, and LLR-r. Existing solutions on MLLRR all leverage problem-specific assumptions and mainly focused on the LLR-1C problem, which lacks the capacity to detect a substantial amount of true and interesting patterns generalizability and prohibits. In this work, we developed a novel multiple-filter based neural network framework, namely FLLRM, which is the first of its kind to solve all three MLLRR problems.We systematically benchmarked FLLRM with state-of-the-art methods on an extensive set of synthetic data, empowered by a robustness evaluation of parameters and theoretical discussions. Experimental results showed that FLLRM outperforms all existing methods and enables a general solution to all the three sub-problems. Experiments on real-world datasets also validated the effectiveness of FLLRM on identifying local low rank matrices corresponding to novel context specific knowledge.

One-sentence Summary: We developed a multiple-filter based neural network approach to solve the fundamental mathematical problem of matrix local low rank representation.

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