Simple and deterministic matrix sketching
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast approximation of matrix coherence and statistical leverage
The Journal of Machine Learning Research
A scalable approach to column-based low-rank matrix approximation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
The Journal of Machine Learning Research
A note on sparse least-squares regression
Information Processing Letters
Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
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We consider low-rank reconstruction of a matrix using a subset of its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our results are: (i) the use of fast approximate SVD-like decompositions for column-based matrix reconstruction, and (ii) two deterministic algorithms for selecting rows from matrices with orthonormal columns, building upon the sparse representation theorem for decompositions of the identity that appeared in [1].