We study the retrieval task that ranks a set of objects for a given query in the pair wise preference learning framework. Recently researchers found out that raw features (e.g. words for text retrieval) and their pair wise features which describe relationships between two raw features (e.g. word synonymy or polysemy) could greatly improve the retrieval precision. However, most existing methods can not scale up to problems with many raw features (e.g. English vocabulary), due to the prohibitive computational cost on learning and the memory requirement to store a quadratic number of parameters. In this paper, we propose to learn a sparse representation of the pair wise features under the preference learning framework using the L1 regularization. Based on stochastic gradient descent, an online algorithm is devised to enforce the sparsity using a mini-batch shrinkage strategy. On multiple benchmark datasets, we show that our method achieves better performance with fast convergence, and takes much less memory on models with millions of parameters.
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