Hamiltonian-Based Clustering: Algorithms for Static and Dynamic Clustering in Data Mining and Image Processing

The large amount of data available for analysis and management raises the need for defining, determining, and extracting meaningful information from the data. Hence in scientific, engineering, and economics studies, the practice of clustering data arises naturally when sets of data have to be divided into subgroups with the aim of possibly deducting common features for data belonging to the same subgroup. For instance, the innovation scoreboard [1] (see Figure 1) allows for the classification of the countries into four main clusters corresponding to the level of innovation defining the “leaders,” the “followers,” the “trailing,” and the “catching up” countries. Many other disciplines may require or take advantage of a clustering of data, from market research [2] to gene expression analysis [3], from biology to image processing [4][7]. Therefore, several clustering techniques have been developed (for details see “Review of Clustering Algorithms”).

[1]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[2]  Patrik D'haeseleer,et al.  How does gene expression clustering work? , 2005, Nature Biotechnology.

[3]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[4]  R. Fisher THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[5]  James C. Bezdek,et al.  Generalized clustering networks and Kohonen's self-organizing scheme , 1993, IEEE Trans. Neural Networks.

[6]  Joshua Zhexue Huang,et al.  Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values , 1998, Data Mining and Knowledge Discovery.

[7]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[8]  Sudipto Guha,et al.  CURE: an efficient clustering algorithm for large databases , 1998, SIGMOD '98.

[9]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[10]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[11]  S. Lang Complex Analysis , 1977 .

[12]  Miin-Shen Yang,et al.  Alternative c-means clustering algorithms , 2002, Pattern Recognit..

[13]  Daniel A. Keim,et al.  An Efficient Approach to Clustering in Large Multimedia Databases with Noise , 1998, KDD.

[14]  Ickjai Lee,et al.  AMOEBA: HIERARCHICAL CLUSTERING BASED ON SPATIAL PROXIMITY USING DELAUNATY DIAGRAM , 2000 .

[15]  Mehdi Hatamian,et al.  Optical character recognition by the method of moments , 1987 .

[16]  Girish N. Punj,et al.  Cluster Analysis in Marketing Research: Review and Suggestions for Application , 1983 .

[17]  George Karypis,et al.  C HAMELEON : A Hierarchical Clustering Algorithm Using Dynamic Modeling , 1999 .

[18]  Olga Sourina,et al.  Automatic clustering and boundary detection algorithm based on adaptive influence function , 2008, Pattern Recognit..

[19]  Petra Perner,et al.  Data Mining - Concepts and Techniques , 2002, Künstliche Intell..

[20]  Hadar I. Avi-Itzhak,et al.  High Accuracy Optical Character Recognition Using Neural Networks with Centroid Dithering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Cheng-Yuan Liou,et al.  Handprinted Character Recognition Based on Spatial Topology Distance Measurement , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Tarantola Stefano,et al.  European Innovation Scoreboard 2006 - Comparative Analysis of Innovation Performance , 2007 .

[23]  Yin Bai,et al.  A New Approach to Hierarchical Clustering Using Partial Least Squares , 2006, 2006 International Conference on Machine Learning and Cybernetics.

[24]  Yuli B. Rudyak On Thom spectra, orientability, and cobordism , 1998 .

[25]  Tian Zhang,et al.  BIRCH: an efficient data clustering method for very large databases , 1996, SIGMOD '96.

[26]  Theodosios Pavlidis,et al.  Direct Gray-Scale Extraction of Features for Character Recognition , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Nei Kato,et al.  A Handwritten Character Recognition System Using Directional Element Feature and Asymmetric Mahalanobis Distance , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  David Tall,et al.  Complex Analysis: The Hitchhiker's Guide to the Plane , 1983 .

[29]  Georgios C. Anagnostopoulos,et al.  Ellipsoid ART and ARTMAP for incremental clustering and classification , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).