Application of Linear and Nonlinear Dimensionality Reduction Methods

Abstract

Dimensionality reduction methods have proved to be important tools in exploratory analysis as well as confirmatory analysis for data mining in various fields of science and technology. Where ever applications involve reducing to fewer dimensions, feature selection, pattern recognition, clustering, dimensionality reduction methods have been used to overcome the curse of dimensionality. In particular, Principal Component Analysis (PCA) is widely used and accepted linear dimensionality reduction method which has achieved successful results in various biological and industrial applications, while demanding less computational power. On the other hand, several nonlinear dimensionality reduction methods such as kernel PCA (kPCA), Isomap and local linear embedding (LLE) have been developed. It has been observed that nonlinear methods proved to be effective only for specific datasets and failed to generalize over real world data, even at the cost of heavy computational burden to accommodate nonlinearity.