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On Mechanism in Clustering

On Mechanism in Clustering. Speaker: Caiming Zhong 04-02-2010. Outline. Some main components of a clustering algorithm A mechanism: Adaptive (Autonomous) scheme, or framework K-Means: single prototype for one cluster

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On Mechanism in Clustering

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  1. On Mechanism in Clustering Speaker: Caiming Zhong 04-02-2010

  2. Outline • Some main components of a clustering algorithm • A mechanism: Adaptive (Autonomous) scheme, or framework • K-Means: single prototype for one cluster • Affinity Propagation • Multi-prototype based autonomy • Potential topics

  3. Main components of a clustering algorithm • Distance metric (Similarity measure) • Objective function • Clustering scheme

  4. Main components of a clustering algorithm (cont.) • Distance metric (Similarity measure) • Cornerstone for a clustering algorithm. • Euclidean distance is the most used, but doesn’t work some time.

  5. Euclidean vs. Geodesic

  6. Main components of a clustering algorithm (cont.) • A similarity measure is not always a metric • Conventional similarity measures

  7. Main components of a clustering algorithm (cont.) • Special similarity measures • Point symmetry distance

  8. Main components of a clustering algorithm (cont.) • Special similarity measures • Path-based distance (minmax diatance)

  9. Densities

  10. Main components of a clustering algorithm (cont.) • Objective Function • What objective function to be optimized? • K-Means: MSE, compactness • Path-based: connectivity • Point symmetry: Symmetry

  11. Main components of a clustering algorithm (cont.) • Clustering framework • Split-and-merge • Agglomerative • Divisive • Partitioning • Density connectivity • …

  12. A mechanism: Autonomous framework • Generally a clustering process of clustering scheme stops when a certain criterion is satisfied. • The criterion is usually user-specified parameters. • The number of clusters • The number of iterations • If the criterion is not a specific threshold, but convergence (the stable state is achieved), we can say “Autonomous framework”

  13. A mechanism: Autonomous framework (cont.) • K-Means is a typical autonomous framework • Repeatedly move prototypes (representative points of a cluster), until no prototype changed • Affinity propagation

  14. A mechanism: Autonomous framework (cont.) • A multi-prototype clustering algorithm

  15. Potential topics • Apply existing mechanisms onto Graph (K-MST Graph) , in breeding. • Improve the existing mechanisms. • Exploit new mechanism.

  16. References • R. XU, D. WUNSCH, Survey of clustering algorithms. IEEE Transactions on Neural Networks, 2005. • M. Su, C. Chou, A modified version of the K-means algorithm with a distance based on cluster symmetry, IEEE Transactions on PAMI, 2001. • S, Bandyopadhyay, S. Saha, GAPS: A clustering method using a new point symmetry-based distance measure, Pattern Recognition, 2007. • B. Fischer, J. Buhmann, Path-Based Clustering for Grouping of Smooth Curves and Texture Segmentation, IEEE Transactions PAMI, 2003.

  17. References (cont.) • H. Chang, D. Yeung, Robust path-based spectral clustering,Pattern recognition, 2008. • B. Frey, D. Dueck, Clustering by passing messages between data points,Science, 2007. • M. Liu, X. Jiang, AC. Kot, A multi-prototype clustering algorithm, Pattern Recognition, 2009.

  18. Thanks!

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