A Weighted Principal Component Analysis (WPCA2) for Time Series Data

Abstract

Time series are ubiquitous in all fields of application. In some situations, the number of observations in each series is too large and so it is of paramount importance to be able to compress the series reducing thus its dimension. One very popular method for both dimensionality reduction and feature extraction is Principal Component Analysis (PCA). The classical PCA gives the same importance to all of the variables. However, in a time series context, it is frequent that some observation times are more important than others. In order to take this into account, a weighted PCA specific for time series data, which was introduced in Pinto da Costa, J., Silva, I., Silva, M.E., IASC 07 (book of abstracts): Statistics for data mining, learning and knowledge extraction, page 32 (2007), is described in this chapter. The method is applied to well-known datasets and the results are compared with those obtained by classical PCA.