This paper tackles the efficiency problem of making recommendations in the context of large user and item spaces. In particular, we address the problem of learning binary codes for collaborative filtering, which enables us to efficiently make recommendations with time complexity that is independent of the total number of items. We propose to construct binary codes for users and items such that the preference of users over items can be accurately preserved by the Hamming distance between their respective binary codes. By using two loss functions measuring the degree of divergence between the training and predicted ratings, we formulate the problem of learning binary codes as a discrete optimization problem. Although this optimization problem is intractable in general, we develop effective relaxations that can be efficiently solved by existing methods. Moreover, we investigate two methods to obtain the binary codes from the relaxed solutions. Evaluations are conducted on three public-domain data sets and the results suggest that our proposed method outperforms several baseline alternatives.
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