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

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Presentation transcript:

On Mechanism in Clustering Speaker: Caiming Zhong

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

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

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

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21 Densities

22 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

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

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

25 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

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

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

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

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

42 Thanks!