Algorithmic robustness for semi-supervised (ε, γ, τ)-good metric learning

Abstract

Using the appropriate metric is crucial for the performance of most of machine learning algorithms. For this reason, a lot of effort has been put into distance and similarity learning. However, it is worth noting that this research field lacks theoretical guarantees that can be expected on the generalization capacity of the classifier associated to a learned metric. The theoretical framework of (ε, γ, τ)-good similarity functions [1] provides means to relate the properties of a similarity function and those of a linear classifier making use of it. In this paper, we extend this theory to a method where the metric and the separator are jointly learned in a semi-supervised way, setting that has not been explored before. We furthermore prove the robustness of our algorithm, which allows us to provide a generalization bound for this approach. The behavior of our method is illustrated via some experimental results.