In this paper we present an unsupervised differential-geometric approach for learning Riemannian metrics for dynamical models. Given a training set of models the optimal metric is selected among a family of pullback metrics induced by the Fisher information tensor through a parameterized diffeomorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then...

This paper describes an interactive tool for constrained clustering that helps users to select effective constraints efficiently during the constrained clustering process. This tool has some functions such as 2-D visual arrangement of a data set and constraint assignment by mouse manipulation. Moreover, it can execute distance metric learning and k-medoids clustering. In this paper, we show the...

Many machine learning and computer vision problems (clustering, classification) make use of a distance. Starting with [20], it has been shown that it is possible to learn a suitably parametrized distance metric. For this project, we propose a new way of learning multiple metrics for the same dataset. We propose a formulation which shares dimensions of a common low-rank space. This metric not on...

The focus of image classification through supervised distance metric learning is to find an appropriate measure of similarity between images. Although this approach is effective in the presence of large amounts of training data, classification accuracy will deteriorate when the number of training samples is small, which, unfortunately, is often the situation in several medical applications. We ...

Markov decision processes (MDPs) have been studied for many decades. Recent research in using transfer learning methods to solve MDPs has shown that knowledge learned from one MDP may be used to solve a similar MDP better. In this paper, we propose two metrics for measuring the distance between finite MDPs. Our metrics are based on the Hausdorff metric which measures the distance between two su...

Multivariate Gaussian densities are pervasive in pattern recognition and machine learning. A central operation that appears in most of these areas is to measure the difference between two multivariate Gaussians. Unfortunately, traditional measures based on the Kullback– Leibler (KL) divergence and the Bhattacharyya distance do not satisfy all metric axioms necessary for many algorithms. In this...

Multivariate Gaussian densities are pervasive in pattern recognition and machine learning. A central operation that appears in most of these areas is to measure the difference between two multivariate Gaussians. Unfortunately, traditional measures based on the Kullback–Leibler (KL) divergence and the Bhattacharyya distance do not satisfy all metric axioms necessary for many algorithms. In this ...

Instead of using a uniform metric, instance specific distance learning methods assign multiple metrics for different localities, which take data heterogeneity into consideration. Therefore, they may improve the performance of distance based classifiers, e.g., kNN. Existing methods obtain multiple metrics of test data by either transductively assigning metrics for unlabeled instances or designin...

The past decade has witnessed the rapid development of feature representation learning and distance metric learning, whereas the two steps are often discussed separately. To explore their interaction, this work proposes an end-to-end learning framework called DARI, i.e. Distance metric And Representation Integration, and validates the effectiveness of DARI in the challenging task of person veri...

The Nearest Neighbor (NN) classification/regression techniques, besides their simplicity, are amongst the most widely applied and well studied techniques for pattern recognition in machine learning. A drawback, however, is the assumption of the availability of a suitable metric to measure distances to the k nearest neighbors. It has been shown that k-NN classifiers with a suitable distance metr...