Applying the Possibilistic c-Means Algorithm in Kernel-Induced Spaces

被引:27
作者
Filippone, Maurizio [1 ]
Masulli, Francesco [2 ]
Rovetta, Stefano [2 ]
机构
[1] Univ Glasgow, Dept Comp Sci, Glasgow G12 8QQ, Lanark, Scotland
[2] Univ Genoa, Dept Comp & Informat Sci, I-16146 Genoa, Italy
关键词
Kernel methods; outlier detection; possibilistic clustering; regularization; SUPPORT;
D O I
10.1109/TFUZZ.2010.2043440
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In this paper, we study a kernel extension of the classic possibilistic c-means. In the proposed extension, we implicitly map input patterns into a possibly high-dimensional space by means of positive semidefinite kernels. In this new space, we model the mapped data by means of the possibilistic clustering algorithm. We study in more detail the special case where we model the mapped data using a single cluster only, since it turns out to have many interesting properties. The modeled memberships in kernel-induced spaces yield a modeling of generic shapes in the input space. We analyze in detail the connections to one-class support vector machines and kernel density estimation, thus, suggesting that the proposed algorithm can be used in many scenarios of unsupervised learning. In the experimental part, we analyze the stability and the accuracy of the proposed algorithm on some synthetic and real datasets. The results show high stability and good performances in terms of accuracy.
引用
收藏
页码:572 / 584
页数:13
相关论文
共 26 条
[1]  
AIZERMAN MA, 1965, AUTOMAT REM CONTR+, V25, P821
[2]  
[Anonymous], 1973, Pattern Classification and Scene Analysis
[3]  
[Anonymous], 2007, Uci machine learning repository
[4]   THEORY OF REPRODUCING KERNELS [J].
ARONSZAJN, N .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAY) :337-404
[5]   A possibilistic approach to clustering - Comments [J].
Barni, M ;
Cappellini, V ;
Mecocci, A .
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 1996, 4 (03) :393-396
[6]   Support vector clustering [J].
Ben-Hur, A ;
Horn, D ;
Siegelmann, HT ;
Vapnik, V .
JOURNAL OF MACHINE LEARNING RESEARCH, 2002, 2 (02) :125-137
[7]  
Bezdek J. C., 1981, Pattern recognition with fuzzy objective function algorithms
[8]   LIBSVM: A Library for Support Vector Machines [J].
Chang, Chih-Chung ;
Lin, Chih-Jen .
ACM TRANSACTIONS ON INTELLIGENT SYSTEMS AND TECHNOLOGY, 2011, 2 (03)
[9]  
FILIPPONE M, 2007, LECT NOTES COMPUTER
[10]   A survey of kernel and spectral methods for clustering [J].
Filippone, Maurizio ;
Camastra, Francesco ;
Masulli, Francesco ;
Rovetta, Stefano .
PATTERN RECOGNITION, 2008, 41 (01) :176-190