cluster

cluster - Unsupervised Clustering Unsupervised Clustering...

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Unformatted text preview: Unsupervised Clustering Unsupervised Clustering PR , ANN, & ML 2 Unsupervised Clustering x Training samples are not labeled x May not know b how many classes b a prior probability b state-conditional probability x Automatic discovery of structures b Intuitively, objects in the same class stick together and form clusters P i ( ) ϖ p x i ( | ) ϖ PR , ANN, & ML 3 x Locating groups (clusters) having similar measurements Given x x x unlabelled partition in to C clusters n C ℵ = ℵ ℵ ℵ { , ,..., }( ) , ,..., 1 2 1 2 Unsupervised Clustering (cont) PR , ANN, & ML 4 Similarity Measure x Need a similarity measurement s( x,x ’) b (e.g., distance between x and x ’ ) d d d d q | d t q q k k d k y x y x y x y x y x y x Σ y x y x y x y x ⋅ = ⋅ =-- = ≥- =- = ∑ ) , ( features) binary (for y Commonalit ) , ( product inner Normalized ) ( ) ( ) , ( Distance s Mahalanobi 1 , ) | ( ) , ( Metric Minkowski 1 1 1 PR , ANN, & ML 5 Similarity Measure (cont.) x How to set the threshold? b Too large all samples assigned into a single class b Too small each sample in its own class x How to properly weight each feature? b How do brightness of a fish and length of a fish relate? b How to scale (or normalize) different measures? PR , ANN, & ML 6 Axis Scaling PR , ANN, & ML 7 Axis Scaling (cont.) PR , ANN, & ML 8 PR , ANN, & ML 9 Threshold PR , ANN, & ML 10 Criteria for Clustering x A criterion function for clustering ∑ ∑∑ ℵ ∈ = ℵ ∈ =- = i i x i i c i x i n J x m m x 1 | | 1 2 ∑ ∑ ∑ = ℵ ∈ ℵ ∉- = c i x x i i i n J 1 ' 2 | ' | 1 x x PR , ANN, & ML 11 x Within and Between group variance b minimize and maximize the trace and determinant of the appropriate scatter matrix b trace : square of the scattering radius b determinant : square of the scattering volume ∑ ∑ ∑ ∑∑ ℵ ∈ = ℵ ∈ = ℵ ∈ =-- = =-- = x c i t i B x i i c i x t W n n n i i x m m m m m S x m m x m x S i i i i 1 ) )( ( 1 ) )( ( 1 1 Criteria for Clustering (cont.) PR , ANN, & ML...
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This note was uploaded on 08/06/2008 for the course CS 290I taught by Professor Wang during the Spring '07 term at UCSB.

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cluster - Unsupervised Clustering Unsupervised Clustering...

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