2026-09-18T22:32:18Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/775342022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023col_1721.1_131024
Jonathan A. Kelner.
Kishore, Shaunak
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
2013-03-01T15:27:03Z
2013-03-01T15:27:03Z
2012
2012
http://hdl.handle.net/1721.1/77534
826515141
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).
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.
by Shaunak Kishore.
S.B.
M.Eng.
18 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Mathematics.
Accelerated clustering through locality-sensitive hashing
Thesis
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Publication
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<Abstract>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.</Abstract>
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