Metric Learning based on Fast χ2 Distance for Histogram Data Classification via KNN Classifier

Data comparison is a fundamental problem in machine learning research. Since, metric learning has various applications in clustering and classification problems, it is attracted much attention in the last decades. In this paper, an appropriate metric learning method is presented to utilize in machine vision problems. Common features in machine vision are often histogram; however, metric learning methods are usually designed based on Mahalanobis distance which is not applicable in histogram features. In this study, a new metric learning method based on modified chi-squared distance (χ2) for histogram data is presented. In histogram data classification, χ2 distance is more accurate than Euclidean one; however, its computational cost is higher than Euclidean distance. In this paper, a χ2 distance approximated formulation where a part of its computations is moved into the feature extraction step in offline phase is proposed. Consequently, computational cost of feature comparison is reduced. Experiments on different datasets show that the proposed metric learning method is more accurate than the existing ones in histogram data classification. Moreover, the approximated χ2 distance increases feature comparison speed about 2.5 times without loss of accuracy.