Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
High-Dimensional Shape Fitting in Linear Time
Discrete & Computational Geometry
Matrix approximation and projective clustering via volume sampling
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
How to get close to the median shape
Proceedings of the twenty-second annual symposium on Computational geometry
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Coresets forWeighted Facilities and Their Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Efficient subspace approximation algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Adaptive sampling and fast low-rank matrix approximation
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near-optimal private approximation protocols via a black box transformation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Data reduction for weighted and outlier-resistant clustering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and hardness for subspace approximation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Column subset selection via sparse approximation of SVD
Theoretical Computer Science
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We give a randomized bi-criteria algorithm for the problem of finding a k-dimensional subspace that minimizesthe Lp-error for given points, i.e., p-th root of the sum of p-th powers of distances to given points,for any p ≥ 1. Our algorithm runs in time Õ (mn · pk3 (k/ε)2p) andproduces a subset of size Õ (pk2 (k/ε)2p) from the given points such that, withhigh probability, the span of these points gives a (1+ε)-approximation to the optimal k-dimensionalsubspace. We also show a dimension reduction type of result for this problem where we can efficiently find asubset of size Õ (pk2(p+1) + (k/ε)p+2) such that, with high probability, theirspan contains a k-dimensional subspace that gives (1+ε)-approximation to the optimum. We prove similarresults for the corresponding projective clustering problem where we need to find multiple k-dimensional subspaces.