Fast and Accurate Pseudoinverse with Sparse Matrix Reordering and Incremental Approach

• URL: http://arxiv.org/abs/2011.04235v1
• Date: Mon, 9 Nov 2020 07:47:10 GMT
• Title: Fast and Accurate Pseudoinverse with Sparse Matrix Reordering and Incremental Approach
• Authors: Jinhong Jung and Lee Sael
• Abstract summary: A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized in machine learning. FastPI is a novel incremental singular value decomposition (SVD) based pseudoinverse method for sparse matrices. We show that FastPI computes the pseudoinverse faster than other approximate methods without loss of accuracy.
• Score: 4.710916891482697
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental building block for solving linear systems in machine learning. However, an approximate computation, let alone an exact computation, of pseudoinverse is very time-consuming due to its demanding time complexity, which limits it from being applied to large data. In this paper, we propose FastPI (Fast PseudoInverse), a novel incremental singular value decomposition (SVD) based pseudoinverse method for sparse matrices. Based on the observation that many real-world feature matrices are sparse and highly skewed, FastPI reorders and divides the feature matrix and incrementally computes low-rank SVD from the divided components. To show the efficacy of proposed FastPI, we apply them in real-world multi-label linear regression problems. Through extensive experiments, we demonstrate that FastPI computes the pseudoinverse faster than other approximate methods without loss of accuracy. %and uses much less memory compared to full-rank SVD based approach. Results imply that our method efficiently computes the low-rank pseudoinverse of a large and sparse matrix that other existing methods cannot handle with limited time and space.

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