On Locally Linear Classification by Pairwise Coupling

Feng Chen, Chang-Tien Lu, Arnold P. Boedihardjo

Abstract: Locally linear classification by pairwise coupling addresses a nonlinear classification problem by three basic phases: decompose the classes of complex concepts into linearly separable subclasses, learn a linear classifier for each pair, and combine pairwise classifiers into a single classifier. A number of methods have been proposed in this framework. However, these methods have two major deficiencies: 1) lack of systematic evaluation of this framework; 2) naive application of clustering algorithms to generate subclasses. This paper proves the equivalence between three popular combination schemas under general settings, defines several global criterion functions for measuring the goodness of subclasses, and presents a supervised greedy clustering algorithm to optimize the proposed criterion functions. Extensive experiments were conducted to validate the effectiveness of the proposed techniques.