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Collaborative filtering is the de facto standard for analyzing users’ activities and building recommendation systems for items. In this work we develop Sliced Anti-symmetric Decomposition (SAD), a new model for collaborative filtering based on implicit feedback. In contrast to traditional techniques where a latent representation of users (user vectors) and items (item vectors) are estimated, SAD introduces one additional la- tent vector to each item, using a novel three-way tensor view of user-item interactions. This new vector extends user-item preferences calculated by standard dot products to general inner products, producing interactions between items when evaluating their relative preferences. SAD reduces to state-of-the-art (SOTA) collaborative filtering models when the vector collapses to 1, while in this paper we allow its value to be estimated from data. The proposed SAD model is simple, resulting in an efficient group stochastic gradient descent (SGD) algorithm. We demonstrate the efficiency of SAD in both simulated and real world datasets containing over 1M user-item interactions. By comparing SAD with seven alternative SOTA collaborative filtering models, we show that SAD is able to more consistently estimate personalized preferences.

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