Clustering. Sandrien van Ommen
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1 Clustering Sandrien van Ommen
2 Overview Why clustering When clustering Types of clustering Dialects Distances Dutch towns Buldialect Conclusion
3 Why clustering To find similarity in your data T-test & Anova = means Correlation & regression = effect size Chi-square = frequencies PCA = summarizing data Clustering = grouping data on basis of similarity
4 Example
5 When clustering Market research: determining populations Biology: group gene families Social Network Analysis Linguistics: Dialect differences/-areas neighborhoods in semantics/syntax/phonology Language models
6 Types of clustering Agglomerative- / Divisive clustering Soft (disjunctive)- / Hard clustering Hierarchical- /Non- hierarchical (flat) clustering Single-link vs. Complete-link clustering
7 Types of Clustering Agglomerative Divisive
8 Types of clustering Soft Hard
9 Types of Clustering Hierarchical Flat X6 X5 X7 X1 X2 X10 X3 X9 X4 X8
10 Types of Clustering Single-link Complete-link
11 Types of Clustering Single link: d k[ij] = min(d ki ; d kj ) Complete link: d k[ij] = max(d ki ; d kj ) UPGMA (unweighted pair group method using arithmetic averages): d k[ij] = (( n i / (n i + n j )) x d ki ) + ((n j / (n i + n j )) x d kj ) WPGMA (weighted): d k[ij] = ( 1/2 x d ki ) + ( 1/2 x d kj )
12 Types of Clustering Group average, centroids, medoids
13 Types of Clustering Centroids: UPGMC d k[ij] = (( n i / (n i + n j )) x d ki ) + ((n j / (n i + n j )) x d kj ) - ((n i x n j ) / ( n i + n j ) 2 x d ij ) WPGMC d k[ij] = ( 1/2 x d ki ) + ( 1/2 x d kj ) (1/4 x d ij )
14 Types of Clustering Flat: K-means L1 The EM algorithm (soft, iterative) Make use of centroids (or medoids)
15 Dialects Clustering = grouping data based on similarity Similarity is calculated based on distance s(x,y) = 1 / ( 1 + d(x,y) ) for grouping dialects: calculate distances Sequence comparison (pronunciation distance) Average pronunciation distance between villages
16 Dialects Sequence comparison: Levenshtein Distance Based on string-changing operations Deletions, insertions, substitions Weight assigned to each operation Calculation of the minimum cost
17 Dialects Hamming Distance: Levenshtein Distance:
18 Distance Matrix
19 Alignment
20 Example 5 Dutch towns Data collected, transcribed, distances computed
21 Example Group-average agglomerative Clustering
22 Example (Dendrogram)
23 Example MultiDimensional Scaling (MDS)
24 Dialects The data: from project: Buldialect: Measuring linguistic unity and diversity in Europe Levenshtein Distance: What is the minimum cost? Deletions/insertions Substitutions Vowel-vowel and consonant-consonant alignment 156 word pronunciations 197 villages in Bulgaria
25 Buldialect Dialect distances between villages = Average of all distances in pronunciation Many objects! Distances in pronunciation -> distances between villages (n x (n-1)) / 2 = values -> (197 x (197-1))/2 = distance values
26 Buldialect Let s try some of the different methods Single link Complete link UPGMA WPGMA (MDS)
27 Ways to view results Dendrograms Maps
28 Single-link Dendrogram Space contracting Unequally sized clusters Outliers visible
29 Single-link
30 Single-link
31 Complete-link Dendrogram Space dilating Balanced clustering Clusters often not easy to interpret
32 Complete-link
33 UPGMA Dendrogram Space conserving d k[ij] = (( n i / (n i + n j )) x d ki ) + ((n j / (n i + n j )) x d kj ) Linkage between groups Averages instead of extreme values Number of elements in cluster taken into account
34 UPGMA
35 UPGMA
36 WPGMA Dendrogram Space conserving d k[ij] = ( 1/2 x d ki ) + ( 1/2 x d kj ) Linkage within groups Number of elements not taken into account
37 WPGMA
38 WPGMA
39 MultiDimensional Scaling What is MDS? No clustering A different way to visualize dialect areas Allows insight in dialect-similarities Less sensitive to changes in data Dimensions
40 MultiDimensional Scaling
41 Conclusion Clustering shows similarity in data Useful for exploratory data analysis or data-grouping (dialect areas) Know your data! Clustering always has output Choose your method carefully Questions?
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