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2008
ACM

Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm

8 years 3 months ago
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
The problem of maximizing a concave function f(x) in a simplex S can be solved approximately by a simple greedy algorithm. For given k, the algorithm can find a point x(k) on a k-dimensional face of S, such that f(x(k)) f(x) - O(1/k). Here f(x) is the maximum value of f in S. This algorithm and analysis were known before, and related to problems of statistics and machine learning, such as boosting, regression, and density mixture estimation. In other work, coming from computational geometry, the existence of -coresets was shown for the minimum enclosing ball problem, by means of a simple greedy algorithm. Similar greedy algorithms, that are special cases of the Frank-Wolfe algorithm, were described for other enclosure problems. Here these results are tied together, stronger convergence results are reviewed, and several coreset bounds are generalized or strengthened.
Kenneth L. Clarkson
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Kenneth L. Clarkson
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