vinusankars / Input-Sparsity-Time-Low-Rank-Approximation-via-Ridge-Leverage-Score-Sampling

Cohen, Michael B., Cameron Musco, and Christopher Musco. "Input sparsity time low-rank approximation via ridge leverage score sampling." Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2017.

Input-Sparsity-Time-Low-Rank-Approximation-via-Ridge-Leverage-Score-Sampling

The approximation method in sparse_time_approx.py is analyzed using analyze_sparse_time_approx.py. $\| A - (C C^{+} A)_{k} \|_{F}^{2} \leq (1 + \epsilon) \| A - A_{k} \|_F^{2}$ , where C represents a matrix generated by sub-sampling columns from A and $C_{k}$ represents the k-rank approximation of C. The following results (plots the lower bounds for $(1+\epsilon)$ ) are plotted using the analyze_sparse_time_approx.py script.

$k vs (1+$\epsilon$)$ $# Columns vs (1+$\epsilon$)$

vinusankars / Input-Sparsity-Time-Low-Rank-Approximation-via-Ridge-Leverage-Score-Sampling

Input-Sparsity-Time-Low-Rank-Approximation-via-Ridge-Leverage-Score-Sampling

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