<title>Principal curves for nonlinear feature extraction and classification</title>

Abstract

We present an improved unbiased algorithm for determining principal curves in high dimensional spaces, and then propose two novel applications of principal curve to feature extraction and pattern classification--the Principal Curve Feature Extractor (PCFE) and the Principal Curve Classifier (PCC). The PCFE extracts features from a subset of principal curves computed via the principal components of the input data. With its flexible partitioning choice and non- parametric nature, the PCFE is capable of modeling nonlinear data effectively. The PCC is a general non-parametric classification method that involves computing a principal curve template for each class during the training phase. In the test or application phase, an unlabeled data point is assigned the class label of the nearest principal curve template. PCC performs well for non-gaussian distributed data and data with low local intrinsic dimensionality. Experiments comparing the PCC to established classification methods are performed on selected benchmarks from the UC Irvine machine learning database and the PROBEN1 benchmark dataset, to highlight situations where PCC is advantageous for feature extraction, data characterization, and classification.