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Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

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  • ter Braak, Cajo J.F.
  • Kourmpetis, Yiannis
  • Kiers, Henk A.L.
  • Bink, Marco C.A.M.

Abstract

Let be a given nn square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the nK fuzzy memberships matrix is found by least-squares approximation of the off-diagonal elements of by inner products of rows of . By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix . Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster model.

Suggested Citation

  • ter Braak, Cajo J.F. & Kourmpetis, Yiannis & Kiers, Henk A.L. & Bink, Marco C.A.M., 2009. "Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3183-3193, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3183-3193
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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Mooijaart, Ab & van der Heijden, Peter G. M. & van der Ark, L. Andries, 1999. "A least squares algorithm for a mixture model for compositional data," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 359-379, June.
    3. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    4. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    5. Sato-Ilic, Mika & Sato, Yoshiharu, 2000. "Asymmetric aggregation operator and its application to fuzzy clustering model," Computational Statistics & Data Analysis, Elsevier, vol. 32(3-4), pages 379-394, January.
    6. Nowicki K. & Snijders T. A. B., 2001. "Estimation and Prediction for Stochastic Blockstructures," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1077-1087, September.
    7. Peter D. Hoff, 2005. "Bilinear Mixed-Effects Models for Dyadic Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 286-295, March.
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    Cited by:

    1. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    2. Andrei Prodan & Henk Brand & Sultan Imangaliyev & Evgeni Tsivtsivadze & Fridus van der Weijden & Ad de Jong & Armand Paauw & Wim Crielaard & Bart Keijser & Enno Veerman, 2016. "A Study of the Variation in the Salivary Peptide Profiles of Young Healthy Adults Acquired Using MALDI-TOF MS," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-15, June.

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