A fuzzy clustering model for multivariate spatial time series

Journal of Classification

Volumn 27, Issue 1, 2010, Pages 54-88

  Coppi, Renato ^a   D'Urso, Pierpaolo ^a   Giordani, Paolo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Array of space time data; Dissimilarity measures between multivariate time trajectories; Fuzzy clustering; Spatial autocorrelation function; Spatial penalization term

Indexed keywords

EID: 77953023706     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-010-9043-y     Document Type: Article

References (49)

1. ALLENDE, H. and GALBIATI, J. (2004), "A Non-Parametric Filter for Digital Image Restoration, Using Cluster Analysis", Pattern Recognition Letters, 25, 841-847.
2. AMBROISE, C. and GOVAERT, G. (1998), "Convergence of an EM-Type Algorithm for Spatial Clustering", Pattern Recognition Letters, 19, 919-927.
3. AYALA, G., EPIFANIO, I., SIMÓ, A., and ZAPATER, V. (2006), "Clustering of Spatial Point Patterns", Computational Statistics and Data Analysis, 50, 1016-1032.
4. BEZDEK, J. C. (1974), "Cluster Validity with Fuzzy Sets", Journal of Cybernetics, 3, 58-72.
5. BEZDEK, J. C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum Press.
6. BEZDEK, J. C., KELLER, J., KRISNAPURAM, R., and PAL, N. R. (1999), Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, The Handbooks of Fuzzy Sets, 4, New York: Kluwer.
7. CHUANG, K.-S., TZENG, H.-L., CHEN, S., WU, J., and CHEN, T. J. (2006), "Fuzzy C means Clustering with Spatial Information for Image Segmentation", Computerized Medical Imaging and Graphics, 30, 9-15.
8. CINQUE, L., FORESTI, G., and LOMBARDI, L. (2004), "A Clustering Fuzzy Approach for Image Segmentation", Pattern Recognition, 37, 1797-1807.
9. COPPI, R. and D'URSO, P. (2001), "The Geometric Approach to the Comparison of Multivariate Time Trajectories", in Advances in Data Science and Classification, eds. S. Borra, R. Rocci, M. Vichi, and M. Schader, Heidelberg: Springer-Verlag, 93-100.
10. COPPI, R. and D'URSO, P. (2006), "Fuzzy Unsupervised Classification of Multivariate Time Trajectories with the Shannon Entropy Regularization", Computational Statistics and Data Analysis, 50, 1452-1477.
11. COSTANZO, G. D. (2001), "A Constrained k-means Clustering Algorithm for Classifying Spatial Units", Statistical Methods and Applications, 10, 237-256.
12. DI NOLA, A., LOIA, V., and STAIANO, A. (2002), "An Evolutionary Approach to Spatial Fuzzy C-means Clustering", Fuzzy Optimization and Decision Making, 1, 195-219.
13. DUAN, L., XU, L., GUO, F., LEE, J., and YAN, B. (2007), "A Local-Density Based Spatial Clustering Algorithm with Noise", Information Systems, 32, 978-986.
14. D'URSO, P. (2000), "Dissimilarity Measures for Time Trajectories", Journal of the Italian Statistical Society, 1-3, 1-31.
15. D'URSO, P. (2004), "Fuzzy C-means Clustering Models for Multivariate Time-Varying Data: Different Approaches", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 287-326.
16. D'URSO, P. (2005), "Fuzzy Clustering for Data Time Array with Inlier and Outlier Time Trajectories", IEEE Transactions on Fuzzy Systems, 13, 583-604.
17. EVERITT, B. S., LANDAU, S., and LEESE, M. (2001), Cluster Analysis (4th ed.), London: Arnold Press.
18. FERLIGOJ A. and BATAGELJ, V. (1982), "Clustering with Relational Constraint", Psychometrika, 47, 413-426.
19. FERLIGOJ A. and BATAGELJ, V. (1983), "Some Types of Clustering with Relational Constraint", Psychometrika, 48, 541-552.
20. FERLIGOJ A. and BATAGELJ, V. (1992), "Direct Multicriteria Clustering Algorithm", Journal of Classification, 9, 43-61.
21. GORDON, A. D. (1996), "A Survey of Constrained Classification", Computational Statistics and Data Analysis, 21, 17-29.
22. GORDON, A. D. (1999), Classification, New York: Chapman & Hall/CRC.
23. HEISER, W. J. and GROENEN, P. J. F. (1997), "Cluster Differences Scaling with a Within-Clusters Loss Component and a Fuzzy Successive Approximation Strategy to Avoid Local Minima", Psychometrika, 62, 63-83.
24. HU, T. and SUNG, S. Y. (2006), "A Hybrid EM Approach to Spatial Clustering", Computational Statistics and Data Analysis, 50, 1188-1205.
25. HWANG, H., DE SARBO, W. S., and TAKANE Y. (2007), "Fuzzy Clusterwise Generalized Structured Component Analysis", Psychometrika, 72, 181-198.
26. KONTOS, D. and MEGALOOIKONOMOU, V. (2005), "Fast and Effective Characterization for Classification and Similarity Searches of 2D and3D Spatial Region Data", Pattern Recognition, 38, 1831-1846.
27. KROOSHOF, P. W. T., TRAN, T. N., POSTMA, G. J., MELSSEN, W. J., and BUYDENS, L. M. C. (2006), "Effects of Including Spatial Information in Clustering Multivariate Image Cata", Trends in Analytical Chemistry, 25, 1067-1080.
28. LAWSON, A. B., SIMEON, S., KULLDORFF, M., BIGGERI, A., and MAGNANI, C. (2007), "Line and Point Cluster Models for Spatial Health Data", Computational Statistics and Data Analysis, 51, 6027-6043.
29. LEFKOVITCH, L. P. (1980), "Conditional Clustering", Biometrics, 36, 43-58.
30. LIEW, A. W. C., LEUNG, S. H., and LAU, W. H. (2000), "Fuzzy Image ClusteringIncorporating Spatial Continuity", IEE Proceedings of Visual Image Signal Process, 147, 185-192.
31. LIEW, A. W. C., LEUNG, S. H., and LAU, W. H. (2003), "Segmentation of Color Lip Images by Spatial Fuzzy Clustering", IEEE Transactions on Fuzzy Systems, 11, 542-549.
32. LIEW, A. W. C. and YAN, H. (2003), "An Adaptive Spatial Fuzzy Clustering Algorithm for 3-D MR image Segmentation", IEEE Transactions on Medical Imaging, 22, 1063-1075.
33. MACQUEEN, J. B. (1967), "Some Methods for Classifilcation and Analysis of Multivariate Observations", in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 2, 281-297.
34. MARÇAL, A. R. S. and CASTRO, L. (2005), "Hierarchical Clustering of Multispectral Images Using Combined Spectral and Spatial Criteria", IEEE Geoscience and Remote Sensing Letters, 2, 59-63.
35. MAHARAJ, E. A. (2000), "Clusters of Time Series", Journal of Classification, 17, 298-314.
36. MCBRATNEY, A. B. and MOORE, A. W. (1985), "Application of Fuzzy Sets to Climatic Classification", Agricultural and Forest Meteorology, 35, 165-185.
37. MOLENAAR, M. and Cheng, T. (2000), "Fuzzy Spatial Objects and Their Dynamics", ISPRS Journal of Photogrammetry and Remote Sensing, 55, 164-175.
38. MORAN, P. A. P. (1950), "A Test for the Serial Independence of Residuals", Biometrika 37, 178-181.
39. MURTAGH, F. (1985), "A Survey of Algorithms for Contiguity-Constrained Clustering and Related Problems", Computer Journal, 28, 82-88.
40. NG, R. T. and HAN, J. (2002), "CLARANS: A Method for Clustering Objects for Spatial Data Mining", IEEE Transactions on Knowledge and Data Engineering, 14, 1003-1016.
41. PERMUTER, H., FRANCOS, J., and JERMYN, I. (2006), "A Study of Gaussian Mixture Models of Color and Texture Features for Image Classification and Segmentation", Pattern Recognition, 39, 695-166.
42. PHAM, D. L. (2001), "Spatial Models for Fuzzy Clustering", Computer Vision and Image Understandin, 84, 285-297.
43. PHAM, D. L. and PRINCE, J. L. (1999), "Adaptive Fuzzy Segmentation of Magnetic Resonance Images", IEEE Transactions on Medical Imaging 18, 737-752.
44. PILEVAR, A. H. and SUKUMAR, M. (2005), "GCHL: A Grid-Clustering Algorithm for High-dimensional Very Large Spatial Data Bases", Pattern Recognition Letters, 26, 999-1010.
45. SMOUSE, P. E. and PEAKALL, R. (1999), "Spatial Autocorrelation Analysis of Individual Multiallele and Multilocus Genetic Structure", Heredity, 82, 561-573.
46. TOLIAS, Y. A. and PANAS, S. M. (1998), "On Applying Spatial Constraints in Fuzzy Image Clustering Using a Fuzzy Rule-based System", IEEE Signal Processing Letters, 5, 245-247.
47. TOLIAS, Y. A. and PANAS, S. M. (1998), "Image Segmentation by a Fuzzy Clustering Algorithm Using Adaptive Spatially Constrained Membership Functions", IEEE Transactions on Systems, Man, and Cybernetics A, 28, 359-369.
48. TRAN, T. N., WEHRENS, R., and BUYDENS, M. C. (2005), "Clustering Multispectral Images: A Tutorial", Chemometrics and Intelligent Laboratory Systems, 77, 3-17.
49. XIA, Y., FENG, D., WANG, T., ZHAO, R,. and ZHANG, Y. (2007), "Image Segmentation by Clustering of Spatial Patterns", Pattern Recognition Letters, 28, 1548-1555.