Online linear and quadratic discriminant analysis with adaptive forgetting for streaming classification

Abstract

AbstractAdvances in data technology have enabled streaming acquisition of real‐time information in a wide range of settings, including consumer credit, electricity consumption, and internet user behavior. Streaming data consist of transiently observed, temporally evolving data sequences, and poses novel challenges to statistical analysis. Foremost among these challenges are the need for online processing, and temporal adaptivity in the face of unforeseen changes, both smooth and abrupt, in the underlying data generation mechanism. In this paper, we develop streaming versions of two widely used parametric classifiers, namely quadratic and linear discriminant analysis. We rely on computationally efficient, recursive formulations of these classifiers. We additionally equip them with exponential forgetting factors that enable temporal adaptivity via smoothly down‐weighting the contribution of older data. Drawing on ideas from adaptive filtering, we develop an online method for self‐tuning forgetting factors on the basis of an approximate gradient scheme. We provide extensive simulation and real data analysis that demonstrate the effectiveness of the proposed method in handling diverse types of change, while simultaneously offering monitoring capabilities via interpretable behavior of the adaptive forgetting factors. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012