Kernel entropy principal component analysis using Parzen estimator

Abstract

Clustering is the task of dividing data objects into meaningful groups named as clusters such that objects in the same cluster are similar and objects form different clusters are dissimilar. It is an important unsupervised technique more and more frequently adopted by several research communities. In this paper we introduce an enhanced kernel-based method for data transformation. The method is founded on the maximum entropy principle through the kernel entropy principal component analysis. Incorporating the kernel method, the input space can be implicitly mapped into a high-dimensional feature space. Therefore the nonlinear patterns turn linear. The key measure is Shannon's entropy estimated via the inertia provided by the contribution of each object in data. As a result, the proposed method uses kernel mapping function to map data before performing entropy principal component analysis. Then data could be reduced into lower dimension of valuable extracted features. This has a major effect on the fast search of center clusters based on the local densities. The method performs very well our clustering algorithm.