class15 - Last time . Clustering vs. Classication...

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Last time . .. Clustering vs. Classifcation Clustering: unsupervised learning Classifcation: supervised learning Classifcation: Classes are human-defned and input to the learning algorithm. Clustering: Clusters are inFerred From the data without human input. However, there are many ways oF in±uencing the outcome oF clustering: number oF clusters, similarity measure, representation oF documents, . . .
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Issues for clustering Representation for clustering Document representation Vector space? Normalization? Need a notion of similarity/distance How many clusters? Fixed a priori? Completely data driven? Avoid “trivial” clusters - too large or small In an application, if a cluster's too large, then for navigation purposes you've wasted an extra user click without whittling down the set of documents much. Flat clustering: K-means Objective/partitioning criterion: minimize the average squared difference from the centroid Assumes documents are real-valued vectors. Clusters based on centroids (aka the center of gravity or mean) of points in a cluster, w : We try to ±nd the minimum average squared difference by iterating two steps: reassignment : assign each vector to its closest centroid recomputation : recompute each centroid as the average of the vectors that were assigned to it in reassignment
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K-means Pick seeds Reassign clusters Compute centroids x x Reassign clusters x x Compute centroids Reassign clusters Converged! Convergence Why should the K-means algorithm ever reach a fxed point ? A state in which clusters don’t change. K-means is a special case of a general procedure known as the Expectation Maximization (EM) algorithm. EM is known to converge. Number of iterations could be large. But in practice usually isn’t
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Convergence of K-Means /%*0#% '""1#%. 3 -. .32 "* ! 8 3 9 : 0 ;1 0 <( 3 = > ;.32 "$%& -44 1 0 3 = 8 9 : 3 8 3 ?%-. Convergence of K-means 3 .4#(% : , 3 4. #20;%& "* 0%0; 3 <= ! ) 6-7 8 ! ) 6-79: ! ) 9 4 - ! , 2 ) ! - 9 5;< , 3 ) 9 ( 3 2 +0%-#. 3614(-556 ("#$%&'%. >24(?56
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This note was uploaded on 01/21/2011 for the course CSCP 689 taught by Professor James during the Spring '10 term at Texas A&M.

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class15 - Last time . Clustering vs. Classication...

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