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Mathematical Problems in Engineering
Volume 2015, Article ID 352849, 12 pages
Research Article

Chi-Squared Distance Metric Learning for Histogram Data

1Laboratory of Spatial Information Processing, School of Computer and Information Engineering, Henan University, Kaifeng 475004, China
2Department of Information Engineering, Shengda Trade Economics and Management College of Zhengzhou, Zhengzhou 451191, China

Received 11 December 2014; Revised 25 March 2015; Accepted 27 March 2015

Academic Editor: Davide Spinello

Copyright © 2015 Wei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 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.