On the Optimality of the Oja's Algorithm for Online PCA
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916146880446464 |
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| author | Liang, Xin |
| author_facet | Liang, Xin |
| contents | In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an efficient, gap-free, global convergence rate to approximate an principal component subspace for any sub-Gaussian distribution. Moreover, it is the first time to show that the convergence rate, namely the upper bound of the approximation, exactly matches the lower bound of an approximation obtained by the offline/classical PCA up to a constant factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2104_00512 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the Optimality of the Oja's Algorithm for Online PCA Liang, Xin Machine Learning Optimization and Control 62H25, 68W27, 65F15 In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an efficient, gap-free, global convergence rate to approximate an principal component subspace for any sub-Gaussian distribution. Moreover, it is the first time to show that the convergence rate, namely the upper bound of the approximation, exactly matches the lower bound of an approximation obtained by the offline/classical PCA up to a constant factor. |
| title | On the Optimality of the Oja's Algorithm for Online PCA |
| topic | Machine Learning Optimization and Control 62H25, 68W27, 65F15 |
| url | https://arxiv.org/abs/2104.00512 |