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CHAPTER 14 Clustering and Unsupervised Classification CLASSIFICATION A. Dermanis

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m = x 1N1N i x i C T = S T 1N1N i x i S T = (x – m i )(x – m i ) T x i S i = (x – m i )(x – m i ) T C i = S i 1ni1ni m i = x x i 1ni1ni Clustering = dividing of N pixels into K classes ω 1, ω 2, …, ω K global mean Clustering total scatter matrix: mean of class ω i : scatter matrix of class ω i : total covariance matrix: covariance matrix of class ω i : A. Dermanis

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S ex = n i (m i – m)(m i – m) T i i x i S in = S i = (x – m i )(x – m i ) T i Clustering criteria overall compactness of the clusters internal scatter matrix degree of distinction between the clusters external scatter matrix Optimal algorithm: S in = min and S ex = max (simultaneously) Problem: How many clusters ? (K = ?) Extreme choice: K = N (each pixel a different class) k = {x k } Extreme choice: K = 1 (all pixels in a single class) S in = S T, S ex = 0 S T = S in + S ex = constant m k = x k, S k = 0, S in = S k = 0 = min, S ex = S T =max k A. Dermanis

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FE D CB AGGLOMERATIVE DIVISIVE A Hierarchical Clustering Agglomerative clustering: Unifying at each step the two closest clusters Divisive clustering : Dividing at each step the most disperse cluster into two new clusters Needed: Unification criteria. Division criteria and procedures. A. Dermanis

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ABD FE D CB AGGLOMERATIVE DIVISIVE A Hierarchical Clustering CEF A. Dermanis

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Distance between two clusters (alternatives): mean distance: minimum distance: maximum distance: Used in agglomerative and divisive clustering A. Dermanis

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The K-means or migrating means algorithm A. Dermanis

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The K-means or migrating means algorithm Step 0: Selection of K = 3 pixels as initial positions of means A. Dermanis

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Step 1: Assignment each pixels to the cluster of its closest mean Calculation of the new means for each cluster The K-means or migrating means algorithm A. Dermanis

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Step 2: Assignment each pixels to the cluster of its closest mean Calculation of the new means for each cluster The K-means or migrating means algorithm A. Dermanis

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Step 3: Assignment each pixels to the cluster of its closest mean Calculation of the new means for each cluster The K-means or migrating means algorithm A. Dermanis

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Step 4: Assignment each pixels to the cluster of its closest mean All pixels remain in the same cluster. Means remain the same. Termination of the algorithm ! The K-means or migrating means algorithm A. Dermanis

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The Isodata Algorithm A variant of the K means algorithm. In each step one of 3 additional procedures can be used: A variant of the K means algorithm. In each step one of 3 additional procedures can be used: ELIMINATION 1. Cluster ELIMINATION UNIFICATION 2. Cluster UNIFICATION DIVISION 3. Cluster DIVISION Eliminate clusters with very few pixels Unify pairs of clusters Very close to each other Divide large clusters which are elongated Into two clusters A. Dermanis

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The Isodata Algorithm ELIMINATION 1. Cluster ELIMINATION Eliminate clusters with very few pixels A. Dermanis

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The Isodata Algorithm UNIFICATION 2. Cluster UNIFICATION Unify pairs of clusters Very close to each other A. Dermanis

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The Isodata Algorithm DIVISION 3. Cluster DIVISION Divide large clusters which are elongated Into two clusters A. Dermanis

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The unification process The division process The Isodata Algorithm m2m2 m1m1 m 2 +kσ 2 m2–kσ2m2–kσ2 A. Dermanis

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K-means: 5 classes K-means: 7 classesK-means: 9 classes K-means: 3 classes Examples of classifiction using the K-mean algorithm Examples of classifiction using the K-mean algorithm A. Dermanis

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ISODATA : 3 classes ISODATA : 5 classes ISODATA : 7 classesISODATA : 9 classes Examples of classifiction using the ISODATA algorithm Examples of classifiction using the ISODATA algorithm A. Dermanis

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