Modeling Appearances with Low-Rank SVM

Several authors have noticed that the common representation of images as vectors is sub-optimal. The process of vectorization eliminates spatial relations between some of the nearby image measurements and produces a vector of a dimension which is the product of the measurements\´ dimensions. It seems that images may be better represented when taking into account their structure as a 2D (or multi-D) array. Our work bears similarities to recent work such as 2DPCA or Coupled Subspace Analysis in that we treat images as 2D arrays. The main difference, however, is that unlike previous work which separated representation from the discriminative learning stage, we achieve both by the same method. Our framework, "low-rank separators ", studies the use of a separating hyperplane which are constrained to have the structure of low-rank matrices. We first prove that the low-rank constraint provides preferable generalization properties. We then define two "low-rank SVM problems" and propose algorithms to solve these. Finally, we provide supporting experimental evidence for the framework.