Dimensionality reduction by using PCA with differential penalty to latent variables

Abstract

Dimensionality reduction is an important technique as a preprocessing of high-dimensional data. We extended principal component analysis (PCA) by introducing the differential penalty of the latent variables with each class, as smoothed PCA. A nonlinear extension to this method by kernel methods was proposed. We applied it to the data in which the observation is in transition with time and p >> n data.