On a statistical model of cluster stability

Posted in Science on September 02, 2008


On a statistical model of cluster stability

Lecture slides:

  • ON STATISTICAL MODEL OF CLUSTER STABILITY
  • Concept
  • Motivating works
  • Clustering
  • Example: a three-cluster set partitioned into 2 and 4 clusters
  • Implication
  • Concept
  • Some probability metrics
  • Examples
  • Ky Fan metrics
  • Concentration measure index
  • Simple and Compound Metrics
  • Geometrical Algorithm
  • General algorithm. Given a probability metric dis(·, ·)
  • Klebanov’s N-distances
  • Simple distances (cont)
  • Graphical illustration
  • Graphical illustration (cont. 1) Distances between points belonging to different samples
  • Remark
  • Euclidean Minimal Spanning Tree
  • An EMST of 60 random points
  • How can an EMST be used in the cluster validation problem?
  • Graphical illustration. Stable clustering
  • Graphical illustration. Non-stable clustering
  • The two-sample MST-test (cont. 2)
  • Theorem’s application
  • Example: Calculation of Rn(S1,S2)
  • Distances from normality
  • The Kolmogorov-Smirnov Distance
  • Example : synthetic data
  • Membership Stability Algorithm
  • A family of clustering algorithms
  • Clusters correspondence problem
  • Correspondence between labels a and ß obtained for a sample S.
  • Example:The Iris Flower Dataset
  • Graph of the normalized mean value
  • Graph of the normalized quartile value
  • Histograms of the distances’ values

Author: Zeev Volkovich, Ort Braude College Of Engineering

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Tags: Science, Lectures, Computer Science, Clustering, Machine Learning, VideoLectures.Net