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Assume these two steps are each done once for i

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Unformatted text preview: n cluster k)   K ­means is a special case of a general procedure known as the Expecta)on Maximiza)on (EM) algorithm.   EM is known to converge.   Number of itera*ons could be large.   G = Σk Gk   Reassignment monotonically decreases G since each vector is assigned to the closest centroid.   But in prac*ce usually isn t Introduc)on to Informa)on Retrieval Sec. 16.4 Introduc)on to Informa)on Retrieval Sec. 16.4 Convergence of K ­Means Time Complexity   Recomputa*on monotonically decreases each Gk since (mk is number of members in cluster k):   Σ (di – a)2 reaches minimum for:   Σ –2(di – a) = 0   Σ di = Σ a   mK a = Σ di   a = (1/ mk) Σ di = ck   K ­means typically converges quickly   Compu*ng distance between two docs is O(M) where M is the dimensionality of the vectors.   Reassigning clusters: O(KN) distance computa*ons, or O(KNM).   Compu*ng centroids: Each doc gets added once to some centroid:...
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