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Similarity/Clustering 인공지능연구실 문홍구 2006. 1. 17

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2 Content What is Clustering Clustering Method Distance-based -Hierarchical -Flat Geometric embedding approach -self-organizing maps -multidimensional scaling -latent semantic indexing

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3 Formulations and Approaches Partitioning Approaches One possible goal that we can set up for a clustering algorithm is to partition the document collection into k subsets or clusters D 1,···,D k so as to minimize the intracluster distance or maximize the intracluster resemblance. Bottom-up clustering Top-down clustering

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4 Formulations and Approaches

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5 Distance based Hierarchical clustering -The tree of hierarchical clustering can be produced Bottom-up(agglomerative clustering) –start with the individual object and grouping the most similar ones –join cluster with maximum similarity Top-down(divisive clustering) –start with all the object and divides them into groups in order to maximize within-group similarity –split least coherent part in cluster

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6 Three methods in hierarchical clustering Single-link Similarity of two most similar members Complete link Similarity of two least similar members Group average Average similarity between members

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7 Single link Clustering Similarity of two most similar members => O(n 2 ) Locally Coherent close objects are in the same cluster Chaining Effect Because of following a chain of large similarities without taking into account the global context => low global cluster quality

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8 Complete link Clustering Similarity of two least similar members => O(n 3 ) The function focused on global cluster quality avoids elongated cluster a/f or b/e is tighter than a/d (tighter cluster are better than ‘straggly’ cluster)

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9 Group average agglomerative clustering Averages similarity between members The complexity of computing average similarity is O(n 2 ) Average similarities are computed at each time a new group is formed compromise between single-link and complete-link

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10 Comparison Single-link Relative efficient Long straggly clusters –Ellipsoidal cluster Loosely bound cluster Complete-link Tightly bound cluster Group average Intermediate between single and complete

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11 Distance based Flat clustering -k – means - k – means 군집방법은 계층적 군집 분석과는 달리 개체가 어느 한 군집에만 속하도록 하는 상호 배반적 군집 방법이다. 이 방법은 군집의 수를 미리 정하고, 각 개체가 어느 군집에 속 하는지를 분석하는 방법으로서 대량의 데이터의 군집분석에 유용하게 이용되는 방법이다.

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12 Distance based k – means

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13 Geometric Embedding Approaches Self - organizing maps Multidimensional scaling Latent semantic indexing ★ A different form of partition-based clustering is to identify dense regions in space.

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14 Geometric Embedding Approaches Self - organizing maps(SOMs) - Self – organizing maps are a close cousin to k-means, except that unlike k-means, which is concerned only with determining the association between clusters and documents, the SOM algorithm also embeds the clusters in a low – dimensional space right from the beginning and proceeds in as way that places related clusters close together in that space.

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15 SOM : Example SOM computed from over a million documents taken from 80 Usenet newsgroups. Light areas have a high density of documents.

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16 Geometric Embedding Approaches Multidimensional scaling (MDS) - The goal of MDS is to present documents as point in a low – dimensional space (often 2D-3D) such that the Euclidean distance between any pair of points is as close as possible to the distance between them specified by the input

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17 Geometric Embedding Approaches Latent semantic indexing (LSI) - The latent semantic indexing (LSI) method is an attempt to solve the synonymy problem while staying within the vector space model framework

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18 Latent semantic indexing (LSI) - k k-dim vector A Documents Terms U d t r DV d SVD TermDocument car auto

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19 EM algorithm A soft version of K-means clustering both cluster move towards the centroid of all three objects reach the stable final state

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20 EM algorithm(2) We want to calculate probability P(c j | vector x i ) Assume that cluster i has a normal distribution Maximum likelihood of the form

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21 Procedure of EM Expectation Step (E) Compute h ij that is expectation of z ij Maximization Step (M)

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