Sparse Bayesian similarity learning based on posterior distribution of data

Abstract

A major challenge in similarity/distance learning is attaining a strong measure which is close to human notions<br><br>of similarity. This paper shows why the consideration of data distribution can yield a more effective similarity<br><br>measure. In addition, the current work both introduces a new scalable similarity measure based on the posterior<br><br>distribution of data and develops a practical algorithm that learns the proposed measure from the data. To<br><br>address scalability in this algorithm, the observed data are assumed to have originated from low dimensional<br><br>latent variables that are close to several subspaces. Other advantages of the currently proposed method include:<br><br>(1) Providing a principled way to combine metrics in computing the similarity between new instances, unlike<br><br>local metric learning methods. (2) Automatically identifying the real dimension of latent subspaces, by defining<br><br>appropriate priors over the parameters of the system via a Bayesian framework. (3) Finding a better projection to<br><br>low dimensional subspaces, by learning the noise of the latent variables on these subspaces. The present method<br><br>is evaluated on various real datasets obtained from applications, such as face verification, handwritten digit<br><br>and spoken letter recognition, network intrusion detection, and image classification. The experimental results<br><br>confirm that the proposed method significantly outperforms other state-of-the-art metric learning methods on<br><br>both small and large-scale datasets.