Fast linear discriminant analysis using binary bases

  • Authors:

  • Feng Tang;Hai Tao

  • Affiliations:

  • Department of Computer Engineering, University of California, Santa Cruz, CA, USA;Department of Computer Engineering, University of California, Santa Cruz, CA, USA

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2007

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Abstract

Linear Discriminant Analysis (LDA) is a widely used technique for pattern classification. It seeks the linear projection of the data to a low dimensional subspace where the data features can be modelled with maximal discriminative power. The main computation in LDA is the dot product between LDA base vector and the data point which involves costly element-wise floating point multiplications. In this paper, we present a fast linear discriminant analysis method called binary LDA (B-LDA), which possesses the desirable property that the subspace projection operation can be computed very efficiently. We investigate the LDA guided non-orthogonal binary subspace method to find the binary LDA bases, each of which is a linear combination of a small number of Haar-like box functions. We also show that B-LDA base vectors are nearly orthogonal to each other. As a result, in the non-orthogonal vector decomposition process, the computationally intensive pseudo-inverse projection operator can be approximated by the direct dot product without causing significant distance distortion. This direct dot product projection can be computed as a linear combination of the dot products with a small number of Haar-like box functions which can be efficiently evaluated using the integral image. The proposed approach is applied to face recognition on ORL and FERET dataset. Experiments show that the discriminative power of binary LDA is preserved and the projection computation is significantly reduced.