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

  • Authors:
  • Christoforos Anagnostopoulos;Dimitris K. Tasoulis;Niall M. Adams;Nicos G. Pavlidis;David J. Hand

  • Affiliations:
  • Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK;Winton Capital Management Ltd, 1-5 St Mary Abbot's Place, London W8 6LS, UK;Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK;Lancaster University Management School, Lancaster LA1 4YX, UK;Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

  • Venue:
  • Statistical Analysis and Data Mining
  • Year:
  • 2012

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Abstract

Advances 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 © 2012 Wiley Periodicals, Inc.