Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:C1L-B
Session:
Number:C1L-B1
An Explict Mapping for Kernel Data Analysis and Application to c-Means Clustering
Sadaaki Miyamoto, Keisuke Sawazaki,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
Kernel data analysis is now becoming standard in many applications of data analysis. An implicit mapping into a high-dimensional feature space is first assumed, in other words, an explicit form of the mapping is unknown but their inner product should be known. Contrary to this common assumption, we introduce an explicit mapping which is standard in a sense. The reason why we use this mapping is as follows. (1) the use of this mapping does not lose any fundamental information in kernel data analysis. (2) We have the same formulas in every kernel methods with and without this explicit mapping. (2) Usually the derivation becomes simpler by using this mapping. (3) New applications of the kernel methods become possible using this mapping. As an application we consider fuzzy c-means clustering and principal component analysis. A typical numerical example is shown to observe the effectiveness of the present method.