An Explicit Mapping for Kernel Data Analysis and Application to Text Analysis

Kernel data analysis is now becoming standard in every application of data analysis and mining. Kernels are used to represent a mapping into a high-dimensional feature space, where an explicit form of the mapping is unknown. Contrary to this common understanding, we introduce an explicit mapping which we consider standard. 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 and we have the same formulas in every kernel methods. ( 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 an example of text mining where we use fuzzy c-means clustering and cluster centers in the high-dimensional space and visualize the centers using kernel principal component analysis.