Grouping objects so that objects in the same group are more similar to each other than to objects of other groups.
Cluster analysis
Cluster analysis
Grouping objects so that objects in the same group are more similar to each other than to objects of other groups.
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Linkage:
single([2,3], [4]) = 1 complete([2,3], [4]) = 2 centroid([2,3], [4]) = 1.5
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Linkage:
single([2,3], [4]) = 1 complete([2,3], [4]) = 2 centroid([2,3], [4]) = 1.5
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Linkage:
single([2,3,4], [8]) = 4, single([8], [11]) = 3 complete([2,3,4], [8]) = 6, complete([8], [11]) = 3 centroid([2,3,4], [8]) = 5, centroid([8], [11]) = 3
Agglomerative Hierarchical Clustering
Clusters: 2
Input: 2, 8, 4, 11, 3
Linkage:
single([2,3,4], [8]) = 4, single([8], [11]) = 3 complete([2,3,4], [8]) = 6, complete([8], [11]) = 3 centroid([2,3,4], [8]) = 5, centroid([8], [11]) = 3
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
Initial centroids: A=2, B=4
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
Initial centroids: A=2, B=4
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
New centroids: A=2.5, B=7.5
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
New centroids: A=2.5, B=7.5
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
K-means
Clusters: 2
Input: 2, 8, 4, 11, 2
Centroids/membership is stable
Clustering in two dimensions
Euclidian distance
\(d_\epsilon(X,Y) = \sqrt{\big|X_0 - Y_0\big|^2 + \big|X_1 - Y_1\big|^2 + ... + \big|X_n - Y_n\big|^2}\)
p-norm
\(d_p(X, Y) = \bigg(\big|X_0 - Y_0\big|^2 + \big|X_1 - Y_1\big|^2 + ... + \big|X_n - Y_n\big|^2\bigg)^{1/p}\)
- Manhattan (\(p=1\))
- Euclidian (\(p=2\)) -Chebyshev (\(p=∞\))
Other: Levenstein-Damerau (strings), graph distances