Learning Approach For Fast Approximate Matrix Factorizations
Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random sketching matrix...
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| Veröffentlicht in: | Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) S. 5408 - 5412 |
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23.05.2022
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| ISSN: | 2379-190X |
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| Abstract | Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random sketching matrix A of much smaller size, and then computing the orthonormal basis as well as low-rank factorizations of the tall matrix XA. While a random matrix A is the de facto choice, in this work, we improve upon its performance by utilizing a learning approach to find an adaptive sketching matrix A from a set of training data. We derive a closed-form formulation for the gradient of the training problem, enabling us to use efficient gradient-based algorithms. We also extend this approach for learning structured sketching matrix, such as the sparse sketching matrix that performs as selecting a few number of representative columns from the input data. Our experiments on both synthetical and real data show that both learned dense and sparse sketching matrices outperform the random ones in finding the approximate orthonormal basis and low-rank approximations. |
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| AbstractList | Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random sketching matrix A of much smaller size, and then computing the orthonormal basis as well as low-rank factorizations of the tall matrix XA. While a random matrix A is the de facto choice, in this work, we improve upon its performance by utilizing a learning approach to find an adaptive sketching matrix A from a set of training data. We derive a closed-form formulation for the gradient of the training problem, enabling us to use efficient gradient-based algorithms. We also extend this approach for learning structured sketching matrix, such as the sparse sketching matrix that performs as selecting a few number of representative columns from the input data. Our experiments on both synthetical and real data show that both learned dense and sparse sketching matrices outperform the random ones in finding the approximate orthonormal basis and low-rank approximations. |
| Author | Zhu, Zhihui Yu, Haiyan Qin, Zhen |
| Author_xml | – sequence: 1 givenname: Haiyan surname: Yu fullname: Yu, Haiyan email: haiyan.yu@du.edu organization: University of Denver,Electrical and Computer Engineering,Denver,CO,USA,80208 – sequence: 2 givenname: Zhen surname: Qin fullname: Qin, Zhen email: zhen.qin@du.edu organization: University of Denver,Electrical and Computer Engineering,Denver,CO,USA,80208 – sequence: 3 givenname: Zhihui surname: Zhu fullname: Zhu, Zhihui email: zhihui.zhu@du.edu organization: University of Denver,Electrical and Computer Engineering,Denver,CO,USA,80208 |
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| SubjectTerms | Acoustics Approximation algorithms Conferences learning approach Low-rank matrix approximation Signal processing Signal processing algorithms sketching algorithm Training Training data |
| Title | Learning Approach For Fast Approximate Matrix Factorizations |
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