Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866908321059962880 |
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| author | Cai, HanQin Huang, Longxiu Li, Pengyu Needell, Deanna |
| author_facet | Cai, HanQin Huang, Longxiu Li, Pengyu Needell, Deanna |
| contents | While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in real-world applications. In this work, we propose a novel and easy-to-implement sampling strategy, coined Cross-Concentrated Sampling (CCS). By bridging uniform sampling and CUR sampling, CCS provides extra flexibility that can potentially save sampling costs in applications. In addition, we also provide a sufficient condition for CCS-based matrix completion. Moreover, we propose a highly efficient non-convex algorithm, termed Iterative CUR Completion (ICURC), for the proposed CCS model. Numerical experiments verify the empirical advantages of CCS and ICURC against uniform sampling and its baseline algorithms, on both synthetic and real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09723 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling Cai, HanQin Huang, Longxiu Li, Pengyu Needell, Deanna Machine Learning Numerical Analysis While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in real-world applications. In this work, we propose a novel and easy-to-implement sampling strategy, coined Cross-Concentrated Sampling (CCS). By bridging uniform sampling and CUR sampling, CCS provides extra flexibility that can potentially save sampling costs in applications. In addition, we also provide a sufficient condition for CCS-based matrix completion. Moreover, we propose a highly efficient non-convex algorithm, termed Iterative CUR Completion (ICURC), for the proposed CCS model. Numerical experiments verify the empirical advantages of CCS and ICURC against uniform sampling and its baseline algorithms, on both synthetic and real-world datasets. |
| title | Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2208.09723 |