RETHINKING LOCAL LOW RANK MATRIX DETECTION:A MULTIPLE-FILTER BASED NEURAL NETWORK FRAMEWORK
The matrix local low rank representation (MLLRR) is a critical technique used in recommender systems, text mining and computer vision. In MLLRR, how to identify the row and column indices that form a distinct low rank sub-matrix is the main challenge. Existing solutions on MLLRR all leverage problem-specific assumptions, which makes them lack generalizability and prohibits the detection of a substantial amount of true patterns. In this work, we first organize the general MLLRR problem into three subproblems based on different low rank properties ,and we argue that most of existing efforts focus on only one category, which leaves the other two unsolved. Based on our categorization, we develop a novel multiple filter based neural network framework, namely FLLRM, which is the first of its kind of method to solve all three MLLRR problems. We systematically benchmark FLLRM with stat-of-the-art methods on an extensive set of synthetic data of the three subproblems, empowered by a robustness evaluation of parameters and theoretic discussions. Experimental results show that FLLRM outperforms all existing methods and enables a general solution to the two unsolved sub problems. Experiments on two real-world datasets also validate the effectiveness of FLLRM on identifying local low rank matrices corresponding to novel context specific knowledge.
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