Unformatted text preview: 232 Image Smnntetinn Chap. “I: in heuiitinnal clustering. thereare Helueters £3,133..." C; with nicanamhatz. .. .1
tax. A lean squares error measureten he deﬁned an 5:22 HI; —ﬂ!*l'1. ﬁ=l lrEC; Whith Measures how close the data are to their aseigned clusteta. .9. leanaqteres clue
tcn'ng peasante 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 knotv11 in advance. Many algo
t'itltms expect it: as a parameter from the unenﬂthetautempt to ﬁnd the heat it“ metad ing to some criterion. such Illi limping the variance of each cluster less than a speciﬁed
value. Iterative K—Muns {tutoring 'I1te Kmeartt algeritlun is a simple. iterative
hillclimbing mhnd. It can he expressed 33: Form Krmcaiu clusters that: n eet ut'ndhnemlurnl 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 updatethe means togctn the“: eel mllie]. mite]. . . .,
cutie]. 5. Repeal steps 3 and41mm 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 IIImeant: clustering algorithm in REE space to the original football
imageei‘Figue Ill]. Isodtttn mutating thorium cluttering is another iterative algorithm that use”
splitmmerge technique. Again assume that duete 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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 Fall '06
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 Image processing

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