Joint Semi-supervised Similarity Learning for Linear Classification

The importance of metrics in machine learning has attracted a growing interest for distance and similarity learning. We study here this problem in the situation where few labeled data (and potentially few unlabeled data as well) is available, a situation that arises in several practical contexts. We also provide a complete theoretical analysis of the proposed approach. It is indeed worth noting that the metric learning 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

$$(\epsilon , \gamma , \tau )$$

-good similarity functions [

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] has been one of the first attempts to draw a link between 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, and provide a theoretical analysis of this joint learning via Rademacher complexity. Experiments performed on standard datasets show the benefits of our approach over state-of-the-art methods.