{"title": "Fast Deterministic CUR Matrix Decomposition with Accuracy Assurance", "book": "Proceedings of the International Conference on Machine Learning", "page_first": 2495, "page_last": 2504, "abstract": "The deterministic CUR matrix decomposition is a low-rank approximation method to analyze a data matrix.\nIt has attracted considerable attention due to its high interpretability, which results from the fact that the decomposed matrices consist of subsets of the original columns and rows of the data matrix.\nThe subset is obtained by optimizing an objective function with sparsity-inducing norms via coordinate descent.\nHowever, the existing algorithms for optimization incur high computation costs.\nThis is because coordinate descent iteratively updates all the parameters in the objective until convergence.\nThis paper proposes a fast deterministic CUR matrix decomposition.\nOur algorithm safely skips unnecessary updates by efficiently evaluating the optimality conditions for the parameters to be zeros.\nIn addition, we preferentially update the parameters that must be nonzeros.\nTheoretically, our approach guarantees the same result as the original approach.\nExperiments demonstrate that our algorithm speeds up the deterministic CUR while achieving the same accuracy.", "full_text": null, "award": [], "sourceid": 1463, "authors": [{"given_name": "Yasutoshi", "family_name": "Ida", "institution": "NTT"}, {"given_name": "Sekitoshi", "family_name": "Kanai", "institution": "NTT Software Innovation Center"}, {"given_name": "Yasuhiro", "family_name": "Fujiwara", "institution": "NTT Communication Science Laboratories"}, {"given_name": "Tomoharu", "family_name": "Iwata", "institution": "NTT"}, {"given_name": "Koh", "family_name": "Takeuchi", "institution": "NTT"}, {"given_name": "Hisashi", "family_name": "Kashima", "institution": "Kyoto University/RIKEN Center for AIP"}]}