Manifold Regularized Transfer Distance Metric Learning

The performance of many computer vision and machine learning algorithms are heavily depend on the distance metric between samples. It is necessary to exploit abundant of side information like pairwise constraints to learn a robust and reliable distance metric[2, 3]. Let D = {(xl i ,xj,yi j)} l i, j=1 denotes the labeled training set for the target task, wherein xi, x j ∈ Rd and yi j = ±1 indicates xl i and xl i are similar/dissimilar to each other. Then, a metric is usually learned to minimize the distance between the data from the same class and maximize their distance otherwise. This leads to the following loss function for learning the metric A: