k-means handout

k-means handout - 232 Image Smnntetinn Chap “I in...

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Unformatted text preview: 232 Image Smnntetinn Chap. “I: in heuiitinnal clustering. thereare Helueters £3,133..." C; with nicanamhatz. .. .1 tax. A lean squares error measure-ten he deﬁned an 5:22 HI; —ﬂ!*l'1. ﬁ=l lrEC; Whith Measures how close the data are to their aseigned clusteta. .9. lean-aqteres clue- tcn'ng peasant-e could emitter all possible partitilata into it” clusters and select the one that minimizes D. Since this is mnnputatienully infmihle. the popular embeds ate up proximatione. One important issue is whether at nut If is knot-v11 in advance. Many algo- t'itltms expect it: as a parameter from the unenﬂthetautempt to ﬁnd the heat it“ meta-d- ing to some criterion. such Illi limping the variance of each cluster less than a speciﬁed value. Iterative K—Muns {tutoring 'I1te K-meartt algeritlun is a simple. iterative hill-climbing mhnd. It can he expressed 33: Form Krmcaiu clusters that: n eet ut'n-dhnemlurnl vectors. 1. Set it: {iteration center) to l. 2. Choose ranthtlrnlglr a setoi‘ I meant ml [IanEtI]. mgll}. 3. Fm each vector x; compute 0(151Mﬂfﬂ] let“ each k = I ..... K and assign x; to the cluster C:- with the nearest mean. It. Inclement r'r- by l and update-the means togctn the“: eel mllie]. mite]. . . ., cutie]. 5. Repeal steps 3 and-41mm C'ﬂt'c] = Cgﬁc‘+ I} For all. It. Algwit'hm ‘IllJ Ill—Means ﬂuttering- This algorithm il- guaranteed to terminate. but: it ma)r not ﬁnd the global optimum in the least squares sense. Step I may be modiﬁed to partition the net. of vectors into I random clusters and then cempate their means. Step 5 may be modiﬁed to stop alter the percentage of vector: that change clusters the given iteration is small. Figure ”1.4 “helm the application rrf the III-meant: clustering algorithm in REE space to the original football imageei‘Fig-ue Ill]. Isodtttn mutating thorium cluttering is another iterative algorithm that use” splitm-merge technique. Again assume that duet-e are lt' clusters Cl. C; ..... Cg widt moms my. n11, . . . .H‘Tx. and let I; he the covariance matrix ofchlsterltlao deﬁned next]. if the rye nre vector: of the form xl=[u1.-"31'”Iun] ...
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