TY - GEN
T1 - Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function
AU - Kanzawa, Yuchi
AU - Endo, Yasunori
AU - Miyamoto, Sadaaki
PY - 2008/12/30
Y1 - 2008/12/30
N2 - In this paper, the fuzzy classification functions of the entropy regularized 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 entropy regularized 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 entropy regularized 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 entropy regularized 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=57949109596&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=57949109596&partnerID=8YFLogxK
U2 - 10.1109/GRC.2008.4664765
DO - 10.1109/GRC.2008.4664765
M3 - Conference contribution
AN - SCOPUS:57949109596
SN - 9781424425129
T3 - 2008 IEEE International Conference on Granular Computing, GRC 2008
SP - 350
EP - 355
BT - 2008 IEEE International Conference on Granular Computing, GRC 2008
T2 - 2008 IEEE International Conference on Granular Computing, GRC 2008
Y2 - 26 August 2008 through 28 August 2008
ER -