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# What can go wrong various schemes for prevenng this

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Unformatted text preview: lustering   Basic idea: group together similar instances   Example: 2D point paOerns   What could “similar” mean?   One op)on: small (squared) Euclidean distance K ­Means K ­Means   An itera)ve clustering algorithm   Pick K random points as cluster centers (means)   Alternate:   Assign data instances to closest mean   Assign each mean to the average of its assigned points   Stop when no points’ assignments change K ­Means Example K ­Means as Op)miza)on   Consider the total distance to the means: means points assignments   Each itera)on reduces phi   Two stages each itera)on:   Update assignments: ﬁx means c, change assignments a   Update means: ﬁx assignments a, change means c Phase I: Update Assignments   For each point, re ­assign to closest mean:   Can only decrease total distance phi! Phase II: Update Means   Move each mean to the average of its assigned points:   Also can only decrease total distance… (Why?)   Fun fact: the point y with minimum squared Euclidean distance to a set of points {x} is their mean Ini)aliza)on   K ­means is non ­determinis)c   Requires ini)al means   It does maOer what you pick!   What can go wrong?   Various schem...
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