TY - GEN

T1 - Indefinite kernel fuzzy c-means clustering algorithms

AU - Kanzawa, Yuchi

AU - Endo, Yasunori

AU - Miyamoto, Sadaaki

PY - 2010

Y1 - 2010

N2 - This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each datum and each cluster center in the feature space is non-negative, instead of subtracting the minimal eigenvalue of the given kernel matrix as its preprocess. This derivation follows the manner in which the non-Euclidean relational fuzzy c-means algorithm is derived from the original relational fuzzy c-means one. The second proposed method produces the memberships by solving the optimization problem in which the constraint of non-negative memberships is added to the one of K-sFCM. This derivation follows the manner in which the non-Euclidean fuzzy relational clustering algorithm is derived from the original relational fuzzy c-means one. Through a numerical example, the proposed algorithms are discussed.

AB - This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each datum and each cluster center in the feature space is non-negative, instead of subtracting the minimal eigenvalue of the given kernel matrix as its preprocess. This derivation follows the manner in which the non-Euclidean relational fuzzy c-means algorithm is derived from the original relational fuzzy c-means one. The second proposed method produces the memberships by solving the optimization problem in which the constraint of non-negative memberships is added to the one of K-sFCM. This derivation follows the manner in which the non-Euclidean fuzzy relational clustering algorithm is derived from the original relational fuzzy c-means one. Through a numerical example, the proposed algorithms are discussed.

KW - Indefinite kernel

KW - Kernel fuzzy c-means

KW - Non-Euclidean fuzzy relational clustering

KW - Non-Euclidean relational fuzzy c-means

UR - http://www.scopus.com/inward/record.url?scp=79956276305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956276305&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-16292-3_13

DO - 10.1007/978-3-642-16292-3_13

M3 - Conference contribution

AN - SCOPUS:79956276305

SN - 3642162916

SN - 9783642162916

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

SP - 116

EP - 128

BT - Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings

T2 - 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010

Y2 - 27 October 2010 through 29 October 2010

ER -