Weighted kernel isomap for data visualization and pattern classification

Abstract

Dimensionality reduction is an important task in pattern recognition and data mining. Isomap is a representative of manifold learning approaches for nonlinear dimensionality reduction. However, Isomap is an unsupervised learning algorithm and has no out-of-sample ability. Kernel Isomap (KIsomap) is an improved Isomap and has a generalization property by utilizing kernel trick. At first, considering class label, a Weighted Euclidean Distance (WED) is designed. Then, WED based kernel Isomap (WKIsomap) is proposed. As a supervised learning algorithm, WKIsomap can not only be used in data visualization, but also applied to feature extraction for pattern recognition. The experimental results show that WKIsomap is more robust than Isomap and KIsomap in data visualization. Moreover, when noise is added into data, WKIsomap based classifiers are more robust to noise than KIsomap based ones. © Springer-Verlag Berlin Heidelberg 2007.