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We study the problem of similarity learning and its application to imageretrieval with large-scale data. The similarity between pairs of images can bemeasured by the distances between their high dimensional representations, andthe problem of learning the appropriate similarity is often addressed bydistance metric learning. However, distance metric learning requires thelearned metric to be a PSD matrix, which is computational expensive and notnecessary for retrieval ranking problem. On the other hand, the bilinear modelis shown to be more flexible for large-scale image retrieval task, hence, weadopt it to learn a matrix for estimating pairwise similarities under theregression framework. By adaptively updating the target matrix in regression,we can mimic the hinge loss, which is more appropriate for similarity learningproblem. Although the regression problem can have the closed-form solution, thecomputational cost can be very expensive. The computational challenges comefrom two aspects: the number of images can be very large and image featureshave high dimensionality. We address the first challenge by compressing thedata by a randomized algorithm with the theoretical guarantee. For the highdimensional issue, we address it by taking low rank assumption and applyingalternating method to obtain the partial matrix, which has a global optimalsolution. Empirical studies on real world image datasets (i.e., Caltech andImageNet) demonstrate the effectiveness and efficiency of the proposed method.

Similarity Learning via Adaptive Regression and Its Application to Image Retrieval