Nonstationary linear discriminant analysis

摘要

Changes in population distributions over time are common in many applications. However, the vast majority of statistical learning theory takes place under the assumption that all points in the training data are identically distributed (and independent), that is, non-stationarity of the data is disregarded. In this paper, a version of the classic Linear Discriminant Analysis (LDA) classification rule is proposed for nonstationary data, using a linear-Gaussian state space model. This Nonstationary LDA (NSLDA) classification rule is based on the Kalman Smoother algorithm to estimate the evolving population parameters. In case the dynamics of the system are not fully known, a combination of the Expectation-Maximization (EM) algorithm and the Kalman Smoother is employed to simultaneously estimate population and statespace equation parameters. Performance is assessed in a set of numerical experiments using simulated data, where the average error rates obtained by NSLDA are compared to the error produced by a naive application of LDA to the pooled nonstationary data. Results demonstrate the promise of the proposed NSLDA classification rule.