TY - GEN

T1 - Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function

AU - Kanzawa, Yuchi

AU - Endo, Yasunori

AU - Miyamoto, Sadaaki

PY - 2008/12/31

Y1 - 2008/12/31

N2 - In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

AB - In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

UR - http://www.scopus.com/inward/record.url?scp=58049085676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049085676&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-88269-5-12

DO - 10.1007/978-3-540-88269-5-12

M3 - Conference contribution

AN - SCOPUS:58049085676

SN - 3540882685

SN - 9783540882688

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 122

EP - 133

BT - Modeling Decisions for Artificial Intelligence - 5th International Conference, MDAI 2008, Proceedings

T2 - 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008

Y2 - 30 October 2008 through 31 October 2008

ER -