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

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