Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908628589477888 |
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| author | Nkurunziza, Jean Pacifique Nahayo, Fulgence Gillis, Nicolas |
| author_facet | Nkurunziza, Jean Pacifique Nahayo, Fulgence Gillis, Nicolas |
| contents | Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence Nkurunziza, Jean Pacifique Nahayo, Fulgence Gillis, Nicolas Machine Learning Information Retrieval Signal Processing Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing. |
| title | Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence |
| topic | Machine Learning Information Retrieval Signal Processing |
| url | https://arxiv.org/abs/2410.07786 |