ISOMAP-KL: a parametric approach for unsupervised metric learning

Unsupervised metric learning consists in building data-specific similarity measures without information of the class labels. Dimensionality reduction (DR) methods have shown to be a powerful mathematical tool for uncovering the underlying geometric structure of data. Manifold learning algorithms are capable of finding a more compact representation for data in the presence of non-linearities. However, one limitation is that most of them are pointwise methods, in the sense that they are not robust to the presence of outliers and noise in data. In this paper, we present ISOMAP-KL, a parametric patch-based algorithm that uses the KL-divergence between local Gaussian distributions learned from neighborhood systems along the KNN graph. We use this non-Euclidean measure to compute the weights and define the entropic KNN graph, whose shortest paths approximate the geodesic distances between patches of points in a parametric feature space. Results obtained in several datasets show that the proposed method is capable of improving the classification accuracy in comparison to other DR methods.