A Combinatorial Approach to Assess the Separability of Clusters

Journal of Classification

Volumn 29, Issue 1, 2012, Pages 7-22

  Cerdeira, J Orestes ^a   Martins, M João ^a   Silva, Pedro C ^a  

^a INSTITUTO SUPERIOR DE AGRONOMIA   (Portugal)

Author keywords

Cluster analysis; Combinatorics; Convex hulls; Minimum spanning forests

Indexed keywords

EID: 84858449356     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-012-9098-z     Document Type: Article

References (17)

1. BIONDI, E., FEOLI, E., and ZUCCARELLO, V. (2004), "Modelling Environmental Responses of Plant Associations: A Review of Some Critical Concepts in Vegetation Study", Critical Reviews in Plant Sciences, 23, 149-156.
2. DAVIES, D. L., and BOULDIN, D. W. (1979), "A Cluster SeparationMeasure", IEEE Transactions on Pattern Analysis and Machine Intelligence, 1, 224-227.
3. DIXON, S. J., HEINRICH, N., HOLMBOE, M., SCHAEFER, M. L., REED, R R., TREVEJO, J., and BRERETON, R. G. (2009), "Use of Cluster Separation Indices and the Influence of Outliers: Application of Two New Separation Indices, the Modified Silhouette Index and the Overlap Coefficient to Simulated Data and Mouse Urine Metabolomic Profiles", Journal of Chemometrics, 23, 19-31.
4. DUNN, J. C. (1974), "Well Separated Clusters and Optimal Fuzzy Partitions", Journal of Cybernetica, 4, 95-104.
5. FISHER, R. A. (1936), "The Use of Multiple Measurements in Taxonomic Problems", Annals of Eugenics, 7, 179-188.
6. GAN, G., MA, C., and WU, J. (2007), Data Clustering: Theory, Algorithms and Applications, ASA-SIAM Series on Statistics and Applied Probability 20, Philadelphia: SIAM Press.
7. HALKIDI, M., BATISTAKIS, Y., and VAZIRGIANNIS, M. (2001), "On Clustering Validation Techniques", Journal of Intelligent Information Systems, 17, 107-145.
8. HANSEN, P., and JAUMARD, B. (1997), "Cluster Analysis and Mathematical Programming", Mathematical Programming, 79, 191-215.
9. HUTCHINSON, G. E. (1957), "Concluding Remarks", Cold Spring Harbor Symposia on Quantitative Biology, 22, 415-427.
10. KRUSKAL, J. B. (1956), "On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem", Proceedings of the American Mathematical Society, 7, 48-50.
11. MADDOX, J. F., LUYENDYK, J. P., COSMA, G. N., BREAU, A. P., BIBLE, R. H., HARRIGAN, G. G., GOODACRE, R., GANEY, P. E., CANTOR, G. H., COCKERELL, G. L., and ROTH, R. A. (2006), "Metabonomic Evaluation of Idiosyncrasy-like Liver Injury in Rats Cotreated with Ranitidine and Lipopolysaccharide", Toxicology and Applied Pharmacology, 212, 35-44.
12. PAL, N. R., and BISWAS, J. (1997), "Cluster Validation Using Graph Theoretic Concepts", Pattern Recognition, 30, 847-857.
13. ROUSSEEUW, P. J. (1987), "Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis", Journal of Computational and Applied Mathematics, 20, 53-65.
14. STANFORTH, R. W., KOLOSSOV, E., and MIRKIN, B. (2007), "A Measure of Domain of Applicability for QSAR Modelling Based on Intelligent k-means Clustering", QSAR & Combinatorial Science, 26, 837-844.
15. THORNTON, C. (1997), "Separability is a Learner's Best Friend", in Proceedings of the 4th Neural Computation and Psychology Workshop: Connectionist Representations, eds. J. A. Bullinaria, D. W. Glasspool, and G. Houghton, London: Springer, pp. 40-44.
16. WALKER, P. A., and COCKS, K. D. (1991), "HABITAT: A Procedure for Modelling a Disjoint Environmental Envelope for a Plant or Animal Species", Global Ecology and Biogeography Letters, 1, 108-118.
17. WANG, H., WINGREEN, N. S., and MUKHOPADHYAY, R. (2008), "Self-organized Periodicity of Protein Clusters in Growing Bacteria", Physical Review Letters, 101, 218101.