Abstract
This paper proposes a fuzzy partitioning subspace clustering algorithm that minimizes a variant of the FCM cost function with a weighted Euclidean distance and a penalty term. To this aim it considers the framework of proximal optimization. It establishes the expression of the proximal operator for the considered cost function and derives PFSCM, an algorithm combining proximal descent and alternate optimization. Experiments show the relevance of the proposed approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agrawal, R., Gehrke, J., Gunopulos, D., Raghavan, P.: Automatic subspace clustering of high dimensional data for data mining applications. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 94–105. ACM (1998)
Bach, F., Jenatton, R., Mairal, J., Obozinski, G., et al.: Convex optimization with sparsity-inducing norms. In: Optimization for Machine Learning, pp. 19–53 (2012)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell (1981)
Borgelt, C.: Fuzzy subspace clustering. In: Fink, A., Lausen, B., Seidel, W., Ultsch, A. (eds.) Advances in Data Analysis, Data Handling and Business Intelligence. Studies in Classification, Data Analysis, and Knowledge Organization, pp. 93–103. Springer, Heidelberg (2010)
Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing. In: Bauschke, H.H., Burachik, R.S., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer Optimization and Its Applications, vol. 49, pp. 185–212. Springer, New York (2011)
Keller, A., Klawonn, F.: Fuzzy clustering with weighting of data variables. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 8(06), 735–746 (2000)
Klawonn, F., Höppner, F.: What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier. In: Berthold, M., Lenz, H.-J., Bradley, E., Kruse, R., Borgelt, C. (eds.) IDA 2003. LNCS, vol. 2810, pp. 254–264. Springer, Heidelberg (2003)
Moreau, J.J.: Fonctions convexes duales et points proximaux dans un espace hilbertien. CR Acad. Sci. Paris Sér. A Math. 255, 2897–2899 (1962)
Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 123–231 (2013)
Qiu, X., Qiu, Y., Feng, G., Li, P.: A sparse fuzzy c-means algorithm based on sparse clustering framework. Neurocomputing 157, 290–295 (2015)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Series B (Methodological) 58, 267–288 (1996)
Vidal, R.: A tutorial on subspace clustering. IEEE Signal Proces. Mag. 28(2), 52–68 (2010)
Wang, D., Ding, C., Li, T.: K-subspace clustering. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009, Part II. LNCS, vol. 5782, pp. 506–521. Springer, Heidelberg (2009)
Witten, D.M., Tibshirani, R.: A framework for feature selection in clustering. J. Am. Stat. Assoc. 105, 713–726 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Guillon, A., Lesot, MJ., Marsala, C., Pal, N.R. (2016). Proximal Optimization for Fuzzy Subspace Clustering. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_56
Download citation
DOI: https://doi.org/10.1007/978-3-319-40596-4_56
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40595-7
Online ISBN: 978-3-319-40596-4
eBook Packages: Computer ScienceComputer Science (R0)