Chi-Squared Distance Metric Learning for Histogram Data

Abstract

Learning a proper distance metric for histogram data plays a crucial role in many computer vision tasks. The chi-squared distance is a nonlinear metric and is widely used to compare histograms. In this paper, we show how to learn a general form of chi-squared distance based on the nearest neighbor model. In our method, the margin of sample is first defined with respect to the nearest hits (nearest neighbors from the same class) and the nearest misses (nearest neighbors from the different classes), and then the simplex-preserving linear transformation is trained by maximizing the margin while minimizing the distance between each sample and its nearest hits. With the iterative projected gradient method for optimization, we naturally introduce the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="script">l</mml:mi></mml:mrow><mml:mrow><mml:mn>2,1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>norm regularization into the proposed method for sparse metric learning. Comparative studies with the state-of-the-art approaches on five real-world datasets verify the effectiveness of the proposed method.