Fuzzy clustering of spatial binary data

Mô Dang; Gérard Govaert

Kybernetika (1998)

  • Volume: 34, Issue: 4, page [393]-398
  • ISSN: 0023-5954

Abstract

top
An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method described here applies in a binary setup a recently proposed algorithm, called Neighborhood EM, which seeks a partition that is both well clustered in the feature space and spatially regular [AmbroiseNEM1996]. This approach is derived from the EM algorithm applied to mixture models [Dempster1977], viewed as an alternate optimization method [Hathaway1986]. The criterion optimized by EM is penalized by a spatial smoothing term that favors classes having many neighbors. The resulting algorithm has a structure similar to EM, with an unchanged M-step and an iterative E-step. The criterion optimized by Neighborhood EM is closely related to a posterior distribution with a multilevel logistic Markov random field as prior [Besag1986,Geman1984]. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions [Govaert1990]. Experiments on simulated spatial binary data yield encouraging results.

How to cite

top

Dang, Mô, and Govaert, Gérard. "Fuzzy clustering of spatial binary data." Kybernetika 34.4 (1998): [393]-398. <http://eudml.org/doc/33367>.

@article{Dang1998,
abstract = {An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method described here applies in a binary setup a recently proposed algorithm, called Neighborhood EM, which seeks a partition that is both well clustered in the feature space and spatially regular [AmbroiseNEM1996]. This approach is derived from the EM algorithm applied to mixture models [Dempster1977], viewed as an alternate optimization method [Hathaway1986]. The criterion optimized by EM is penalized by a spatial smoothing term that favors classes having many neighbors. The resulting algorithm has a structure similar to EM, with an unchanged M-step and an iterative E-step. The criterion optimized by Neighborhood EM is closely related to a posterior distribution with a multilevel logistic Markov random field as prior [Besag1986,Geman1984]. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions [Govaert1990]. Experiments on simulated spatial binary data yield encouraging results.},
author = {Dang, Mô, Govaert, Gérard},
journal = {Kybernetika},
keywords = {mixture models},
language = {eng},
number = {4},
pages = {[393]-398},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fuzzy clustering of spatial binary data},
url = {http://eudml.org/doc/33367},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Dang, Mô
AU - Govaert, Gérard
TI - Fuzzy clustering of spatial binary data
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 4
SP - [393]
EP - 398
AB - An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method described here applies in a binary setup a recently proposed algorithm, called Neighborhood EM, which seeks a partition that is both well clustered in the feature space and spatially regular [AmbroiseNEM1996]. This approach is derived from the EM algorithm applied to mixture models [Dempster1977], viewed as an alternate optimization method [Hathaway1986]. The criterion optimized by EM is penalized by a spatial smoothing term that favors classes having many neighbors. The resulting algorithm has a structure similar to EM, with an unchanged M-step and an iterative E-step. The criterion optimized by Neighborhood EM is closely related to a posterior distribution with a multilevel logistic Markov random field as prior [Besag1986,Geman1984]. The application of this approach to binary data relies on a mixture of multivariate Bernoulli distributions [Govaert1990]. Experiments on simulated spatial binary data yield encouraging results.
LA - eng
KW - mixture models
UR - http://eudml.org/doc/33367
ER -

References

top
  1. Ambroise C., Approche probabiliste en classification automatique et contraintes de voisinage, PhD Thesis, Université de Technologie de Compiègne 1996 
  2. Ambroise C., Dang M. V., Govaert G., Clustering of spatial data by the EM algorithm, In: Amílcar Soares (J. Gómez-Hernandez and R. Froidevaux, eds), geoENV I – Geostatistics for Environmental Applications, Kluwer Academic Publisher 1997, pp. 493–504 (1997) 
  3. Ambroise C., Govaert G., An iterative algorithm for spatial clustering, submitte 
  4. Berry B. J. L., Essay on Commodity Flows and the Spatial Structure of the Indian Economy, Research paper 111, Departement of Geography, University of Chicago 1966 
  5. Besag J. E., Spatial analysis of dirty pictures, J. Roy. Statist. Soc. 48 (1986), 259–302 (1986) MR0876840
  6. Bezdek J. C., Castelaz P. F., 10.1109/TSMC.1977.4309659, IEEE Trans. Systems Man Cybernet. SMC-7 (1977), 2, 87–92 (1977) Zbl0359.68120DOI10.1109/TSMC.1977.4309659
  7. Celeux G., Govaert G., 10.1007/BF02616237, J. Classification 8 (1991), 157–176 (1991) Zbl0775.62150DOI10.1007/BF02616237
  8. Chalmond B., 10.1016/0031-3203(89)90011-3, Pattern Recognition 22 (1989), 6, 747–761 (1989) DOI10.1016/0031-3203(89)90011-3
  9. Dempster A. P., Laird N. M., Rubin D. B., Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. 39 (1977), 1–38 (1977) Zbl0364.62022MR0501537
  10. Geman S., Geman D., 10.1109/TPAMI.1984.4767596, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-6 (1984), 721–741 (1984) Zbl0573.62030DOI10.1109/TPAMI.1984.4767596
  11. Govaert G., Classification binaire et modéles, Rev. Statist. Appl. 38 (1990), 1, 67–81 (1990) 
  12. Hathaway R. J., 10.1016/0167-7152(86)90016-7, Statist. Probab. Lett. 4 (1986), 53–56 (1986) Zbl0585.62052MR0829432DOI10.1016/0167-7152(86)90016-7
  13. Legendre P., Constrained clustering, Develop. Numerical Ecology. NATO ASI Series G 14 (1987), 289–307 (1987) MR0913543

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.