Input space versus feature space in kernel-based interval fuzzy C-Means clustering

The main property of kernel methods is that they can implicitly perform a nonlinear mapping of the input data into a high-dimensional space. This mapping allows to find a simpler structure within space without increasing the number of parameters increasing the clustering quality. Therefore, kernel methods may find better results for data arranged not linearly. Many methods presented in the literature only use point data. However, real problems need more complex representation. In this work, we propose a new kernel-based fuzzy method using feature space metric for interval-valued data. Moreover, a comparative study between input space and feature space is set up in this paper. In order to evaluate the performance of the proposed method, experiments with synthetic and real interval data set were carried out.