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