Cross language text classification is an important learning task in natural language processing. A critical challenge of cross language learning lies in that words of different languages are in disjoint feature spaces. In this paper, we propose a two-step representation learning method to bridge the feature spaces of different languages by exploiting a set of parallel bilingual documents. Specifically, we first formulate a matrix completion problem to produce a complete parallel document-term matrix for all documents in two languages, and then induce a cross-lingual document representation by applying latent semantic indexing on the obtained matrix. We use a projected gradient descent algorithm to solve the formulated matrix completion problem with convergence guarantees. The proposed approach is evaluated by conducting a set of experiments with cross language sentiment classification tasks on Amazon product reviews. The experimental results demonstrate that the proposed learning approach outperforms a number of comparison cross language representation learning methods, especially when the number of parallel bilingual documents is small.
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