χ2 Metric Learning for Nearest Neighbor Classification and Its Analysis

We study the Chi-Squared (chi(2)) distance and metric learning as a problem of Large Margin Nearest Neighbor (LMNN) classification. We suggest the chi(2) metric learning algorithm, based on the LMNN approach, to learn a metric to improve the accuracy of k-nearest neighbor (kNN) classification. We show that the chi(2) distance in the transformed space is one of the Quadratic-Chi distance family members. We use a gradient descent method to get an optimal value of the linear transformation matrix of the input feature space. We also show an alternative approach of chi(2) metric learning by using a convex optimization method with relaxation. We demonstrate experimental results on the datasets mainly for domain adaptation.