A preliminary geometric structure simplification for Principal Component Analysis

Real world data are commonly geometrically nonlinear and thus are not easy to be processed by the traditional linear methods. Many existing techniques for nonlinear dimensionality reduction need careful parameter tuning and cannot be applied to real data stably and consistently. In this article we propose an efficient data preprocessing algorithm, called Curve Straightening Transformation (CST), to flatten the nonlinear geometric structure of data. Then Principal Component Analysis (PCA) and other linear projection methods are adequate to perform the dimensionality reduction task in most cases. In this aspect, the proposed CST algorithm can be regarded as a geometric preprocessing step tailored for PCA. The comprehensive experiments on both artificial and real datasets demonstrate that the proposed preprocessing algorithm is able to simplify the nonlinear geometric structures, and the flattened data are suitable for further dimensionality reduction by linear methods such as PCA. (C) 2018 Elsevier B.V. All rights reserved.