Accelerated clustering through locality-sensitive hashing
Author(s)
Kishore, Shaunak
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Jonathan A. Kelner.
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We obtain improved running times for two algorithms for clustering data: the expectation-maximization (EM) algorithm and Lloyd's algorithm. The EM algorithm is a heuristic for finding a mixture of k normal distributions in Rd that maximizes the probability of drawing n given data points. Lloyd's algorithm is a special case of this algorithm in which the covariance matrix of each normally-distributed component is required to be the identity. We consider versions of these algorithms where the number of mixture components is inferred by assuming a Dirichlet process as a generative model. The separation probability of this process, [alpha], is typically a small constant. We speed up each iteration of the EM algorithm from O(nd2k) to O(ndk log 3(k/a))+nd 2 ) time and each iteration of Lloyd's algorithm from O(ndk) to O(nd(k/a). 39) time.
Description
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 18).
Date issued
2012Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science., Mathematics.