This proposal is a fundamental research project whose main goal is to provide new theoretical frameworks and algorithms for automatically learning metrics from data. Based on the saying “Birds of a feather flock together”, metrics play a crucial role in a large set of learning methods, such as the widely used k-nearest neighbors, kernel-based methods in classification or the k-Means algorithm in clustering.
Since manually tuning metrics for a given real-world problem is often difficult and tedious, our objective is to automatically acquire knowledge from training data to optimize good metrics. This requires to formally define the notion of goodness that would allow us to ensure theoretical guarantees (i) on the generalization ability of the metric (i.e. do the properties optimized over the training set still hold on new data ?) and (ii)on the generalization capability of a classifier using that metric (i.e. can we derive upper bounds on the generalization error of the classifier ?). The metric learning algorithms developed in this project will be used to deal with an application in energy management in collaboration with Schneider Electric.