Parametric PCA for unsupervised metric learning

In pattern recognition, the problem of quantifying a suitable similarity measure between different objects in a collection is a challenging task, especially in cases where the standard Euclidean distance is not a reasonable choice. In this context, dimensionality reduction algorithms are powerful tools for unsupervised metric learning. In this paper, we propose a framework to build dimensionality reduction methods for unsupervised metric learning based on the mapping of local neighborhoods of the KNN graph to a parametric feature space, defined in terms of a statistical model. By incorporating a non-Euclidean metric based on the Bhattacharyya coefficient, we define the parametric kernel matrix, a surrogate for the covariance matrix of the parametric feature vectors. Inspired by PCA, we use the eigenvalues of the parametric kernel matrix to learn features for the original data. Numerical experiments with real datasets show that Parametric PCA is capable of producing better defined clusters and also more discriminant features in comparison to regular PCA, kernel PCA, sparse PCA, robust PCA and manifold learning algorithms, making the proposed method a promising alternative for unsupervised metric learning. © 2020 Elsevier B.V.