χ2 Metric learning for nearest neighbor classification and its analysis

We study the Chi-Squared (χ²) distance and metric learning as a problem of Large Margin Nearest Neighbor (LMNN) classification. We suggest the χ² 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 χ² 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 χ² metric learning by using a convex optimization method with relaxation. We demonstrate experimental results on the datasets mainly for domain adaptation.