An approach to supervised distance metric learning based on difference of convex functions programming

Distance metric learning has motivated a great deal of research over the last years due to its robustness for many pattern recognition problems. In this paper, we develop a supervised distance metric learning method that aims to improve the performance of nearest-neighbor classification. Our method is inspired by the large-margin principle, resulting in an objective function based on a sum of margin violations to be minimized. Due to the use of the ramp loss function, the corresponding objective function is nonconvex, making it more challenging. To overcome this limitation, we formulate our distance metric learning problem as an instance of difference of convex functions (DC) programming. This allows us to design a more robust method than when using standard optimization techniques. The effectiveness of this method is empirically demonstrated through extensive experiments on several standard benchmark data sets.