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SODA
2010
ACM

Coresets and Sketches for High Dimensional Subspace Approximation Problems

12 years 5 months ago
Coresets and Sketches for High Dimensional Subspace Approximation Problems
We consider the problem of approximating a set P of n points in Rd by a j-dimensional subspace under the p measure, in which we wish to minimize the sum of p distances from each point of P to this subspace. More generally, the Fq( p)-subspace approximation problem asks for a j-subspace that minimizes the sum of qth powers of p-distances to this subspace, up to a multiplicative factor of (1 + ). We develop techniques for subspace approximation, regression, and matrix approximation that can be used to deal with massive data sets in high dimensional spaces. In particular, we develop coresets and sketches, i.e. small space representations that approximate the input point set P with respect to the subspace approximation problem. Our results are: ? A dimensionality reduction method that can be applied to Fq( p)-clustering and shape fitting problems, such as those in [8, 15]. ? The first strong coreset for F1( 2)-subspace approximation in high-dimensional spaces, i.e. of size polynomial in t...
Dan Feldman, Morteza Monemizadeh, Christian Sohler
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Dan Feldman, Morteza Monemizadeh, Christian Sohler, David P. Woodruff
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