Re: Fuzzy c-means initialisation

Warren Sarle (
Thu, 21 May 1998 17:01:26 +0200 (MET DST)

Jose Manuel Benitez Sanchez <> wrote on
1998/04/27 in Message-ID <>:
|> By the way, the reference for the Mountain Method is:
|> @Article{Yager:ieee-smc:94,
|> author = {Ronald R. Yager and D.P.~Filev},
|> title = {Approximate Clustering Via the Mountain Method},
|> journal = IEEE Trans. on Systems, Man, and Cybernetics,
|> year = 1994,
|> volume = 24,
|> number = 8,
|> pages = {1279--1284}
|> }

The Mountain Method is basically a crude form of kernel density
estimation (often called Parzen windows in the engineering literature),
which has been widely used in statistics and pattern recognition since
the 1950s. There are many clustering methods that use kernel density
estimation and that are much more effective and efficient than this
mountain method. Here are some related references:

Barnett, V., ed. (1981), _Interpreting Multivariate Data_, New York:
John Wiley & Sons, Inc.

Girman, C.J. (1994), "Cluster Analysis and Classification Tree
Methodology as an Aid to Improve Understanding of Benign Prostatic
Hyperplasia," Ph.D. thesis, Chapel Hill, NC: Department of
Biostatistics, University of North Carolina.

Gitman, I. (1973), "An Algorithm for Nonsupervised Pattern
Classification," IEEE Transactions on Systems, Man, and Cybernetics,
SMC-3, 66-74.

Hartigan, J.A. and Hartigan, P.M. (1985), "The Dip Test of
Unimodality," Annals of Statistics_ 13, 70-84.

Hartigan, P.M. (1985), "Computation of the Dip Statistic to Test for
Unimodality," Applied Statistics, 34, 320-325.

Huizinga, D. H. (1978), "A Natural or Mode Seeking Cluster Analysis
Algorithm," Technical Report 78-1, Behavioral Research Institute, 2305
Canyon Blvd., Boulder, Colorado 80302.

Koontz, W.L.G. and Fukunaga, K. (1972a), "A Nonparametric
Valley-Seeking Technique for Cluster Analysis," IEEE Transactions on
Computers, C-21, 171-178.

Koontz, W.L.G. and Fukunaga, K. (1972b), "Asymptotic Analysis of a
Nonparametric Clustering Technique," IEEE Transactions on Computers,
C-21, 967-974.

Koontz, W.L.G., Narendra, P.M., and Fukunaga, K. (1976), "A
Graph-Theoretic Approach to Nonparametric Cluster Analysis," IEEE
Transactions on Computers, C-25, 936-944.

Minnotte, M.C. (1992), "A Test of Mode Existence with
Applications to Multimodality," Ph.D. thesis, Rice University,
Department of Statistics.

Mizoguchi, R. and Shimura, M. (1980), "A Nonparametric Algorithm for
Detecting Clusters Using Hierarchical Structure," IEEE Transactions on
Pattern Analysis and Machine Intelligence, PAMI-2, 292-300.

Mueller, D.W. and Sawitzki, G. (1991), "Excess mass estimates and tests
for multimodality," JASA 86, 738-746.

Polonik, W. (1993), "Measuring Mass Concentrations and Estimating
Density Contour Clusters--An Excess Mass Approach," Technical Report,
Beitraege zur Statistik Nr. 7, Universitaet Heidelberg.

SAS Institute Inc. (1993), _SAS/STAT Software: The MODECLUS Procedure_,
SAS Technical Report P-256, Cary, NC: SAS Institute Inc.

Silverman, B.W. (1986), _Density Estimation_, New York: Chapman and

Tukey, P.A. and Tukey, J.W. (1981), "Data-Driven View Selection;
Agglomeration and Sharpening," in Barnett (1981).

Wong, M.A. (1982), "A Hybrid Clustering Method for Identifying
High-Density Clusters," Journal of the American Statistical
Association, 77, 841-847.

Wong, M.A. and Lane, T. (1983), "A _k_th Nearest Neighbor Clustering
Procedure," _Journal of the Royal Statistical Society_, Series B, 45,

Wong, M.A. and Schaack, C. (1982), "Using the _k_th Nearest Neighbor
Clustering Procedure to Determine the Number of Subpopulations,"
_American Statistical Association 1982 Proceedings of the Statistical
Computing Section_, 40-48.


Warren S. Sarle SAS Institute Inc. The opinions expressed here SAS Campus Drive are mine and not necessarily (919) 677-8000 Cary, NC 27513, USA those of SAS Institute.