Chapter16
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- ひろき うるしはた
- 5 years ago
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1 16 Flat Clustering (cluster) 16.1 (unsupervised learning) ( ) (distance measure)
2 (flat clustering) (hierarchical clustering) (hard) (soft) (Latent semantic indexing) ( ) (16.1 ) (16.2 ) (16.3 ) 2 K-means(16.4 ) expectation maximization(em) (16.5 ) K-means EM K-means 16.1 Clustering in information retrieval (cluster hypothesis) < > 1 14 (contiguity hypothesis)
3 ( ) 16.2 jaguar 3 OS Vivisimo ( cluster results 16.2 jaguar Clustered results cat
4 Scatter-Gather Scatter-Gather Scatter-Gather New York Times 8 (scattered) 3 International Stories (gather) (scattered) Trinidad 16.3 Open Directory( ( ) Scatter-Gather ( 16.1 ) Columbia NewsBlaster
5 4 car car automobile car (automobile vehicle ) recall 226 (12.10) d d d (113 ) (18 )
6 7.1.6 (130 ) 16.2 Problem statement (i) D={d1,...,dN} (ii) K (iii) (objective function) 3 ( )γ:d->{1,...,k} γ K K-means China Chinese Beijing Mao UK London Britain Queen (6 ) (the la ) (the la ) < > ( partitional (17 ) ) 0 1
7 (exhaustive) (nonexhaustive) (exclusive) Cardinality - The number of clusters K (cardinality) K K-means K K K 16.3 Scatter-Gather 1990 K=10 (seed) 16.3 Evaluation of clustering ( ) ( ) (internal criterion)
8 gold standard( ) gold standard (8 140 ) gold standard (external criterion) 16.2 jaguar car animal operating system 3 gold standard 4 (purity) (normalized mutual information) Rand index false-positive false-negative F (F measure) N (16.1) Ω = {ω1,ω2,...,ωk} C = {c1,c2,...,cj} (16.1) ωk ωk cj cj Figure 16.4 Purity as an external evaluation criterion for cluster quality. Majority class and number of members of the majority class for the three clusters are: x, 5 (cluster 1); o, 4 (cluster 2); and, 3 (cluster 3). Purity is (1/17) ( )
9 Table 16.2# The four external evaluation measures applied to the clustering in Figure (normalized mutual information, NMI) (16.2) (cf ) (16.3) (16.4) P(ωk) P(cj) P(ωk cj) ωk cj (16.4) (16.3) (MLE) ( ) H 5 (91 ) (16.5) (16.6) 2 (16.3) I(Ω;C) I(Ω;C) 0 Ωexact
10 Ωexact (exercise 16.7) K=N one-document (16.2) [H(Ω)+H(C)]/2 H(Ω) K = N logn NMI NMI [H(Ω)+H(C)]/2 I(Ω;C) (exercise 16.8) NMI 0 1 N(N-1)/2 2 true-positive true-negative 2 false-positive 2 false-negative 2 Rand index(ri) (accuracy) ( ) 16.4 RI TP+FP "positive" 1 x 2 o 3 x true positive
11 FP=40-20=20 FN TN (contingency table) RI (20+72)/( )=0.68 RI FP FN F (f measure) β>1 FN FP recall P = 20/40 = 0.5 R = 20/44 = β = 1 F1 = 0.48 β = 5 F5 = F
12 16.4 K-means K-means 2 (6 121 ) ω μ 14 Rocchio (269 ) K-means Rocchio residual sum of square( 2 ) RSS 2 (16.7) RSS K-means N RSS 2 K-means K RSS K-means (364 )
13 16.5 K-means IR K-2 in R^2 K-means 9
14 I ( γ) μ λ (exercise16.5) RSS RSS θ θ K-means RSS RSS RSS RSSk (16.8) (16.9) x_m, v_m m 0 (16.10) RSSk RSSk RSS
15 K-means (outlier) RSS 1 (singleton cluster) K-means d2 d5 K-means {{d1,d2,d3}, {d4,d5,d6}} d2 d3 {{d1,d2,d4,d5}, {d3,d6}} K=2 (exercise 16.11) (i) (ii) (iii) kmeans K i ik( i=5 i=10) ( Buckshot ) i ( i=10) 16.6
16 K-means? θ(m) θ(knm) θ(nm) I θ(iknm) K-means 17 I K-means I Θ(...) M 2 M K-means - - k ( k=1000) ( 16.6 ) medoid K-means K-medoid medoid medoid Cluster cardinality in K-means 16.2 K K K RSSmin(k) K RSS RSSmin (k) K (exercise16.13) k=n(n ) 0
17 RSSmin(k) K i ( ) RSS i RSS RSSmin(k) K RSSmin(k) RSS 16.8 k=4 k=9 2 1 K( 4 9) 16.8 K-means RSSmin 1203 Reuters-RCV1 RSSmin China, Germany, Russia, Sports K=4 Reuters 2 K 2 (distortion) (K-means RSS) (model complexity) K-means K (16.11)
18 λ λ λ=0 K=N (16.11) λ 2 K λ K λ K K (16.11) AIC AIC (16.12) K -L(K) K q(k) ( ) ( ) AIC 2 K-means AIC (16.13) (16.13) (16.11) λ=2m (16.12) (16.13) K-means K q(k)=km L(k)=-(1/2)RSS (exercise 16.16) AIC AIC
19 16.8 M= MK > RSS (RSSmin(1) < 5000 ) K=1 K=4 ( 4 China, Germany, Russia, Suports) K=1 λ (16.11) (16.13) 16.5 Model-based clustering K-means EM K-means K-means K 1 model-based clustering K-means exp(-rss) ( ) K-means RSS Θ K-means Θ={μ1,...,μk} D Θ L(D Θ) 2 L(D Θ) 12 (218 ) 13.1 (245 ) Θ Θ P(d ωk;θ)
20 Chinese cars China automobiles kmeans 2 K-means 17 K-means ( 16.3 ) ( ) expectation maximizeation algorithm EM EM L (D Θ) EM 11.3 (204 ) 13.3 (243 ) (16.14) Θ={Θ1,...,Θk} Θk=(αk,q1k,...,qMk) qmk=p(um=1 ωk) P(Uk=1 ωk) k tm αk ωk d d ωk (16.15) αk ωk qmk M ( )
21 EM L(D Θ) Θ EM k-means (exception step) (maxmization step) k-means EM αk qmk qm αk (16.16) I(tm in dn) tm dn 1 0 rnk dn k ( ) 13.3(248 ) qmk αk (16.17) (16.14) (16.15) dn ωk 13.3 ( ) EM (ri1=1.00) 6 2 (ri1=0.00) EM 25 1 α /11= sugar 7 8 ( r81=0)
22 6 7 sweet 2 25 (25 qsweet,1=0) K-means EM EM EM K-means K-means EM 16.3 EM (a) EM (b)
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