As an important tool for information filtering in the era of socialized web,recommender systems have witnessed rapid development in the last decade. Asbenefited from the better interpretability, neighborhood-based collaborativefiltering techniques, such as item-based collaborative filtering adopted byAmazon, have gained a great success in many practical recommender systems.However, the neighborhood-based collaborative filtering method suffers from therating bound problem, i.e., the rating on a target item that this methodestimates is bounded by the observed ratings of its all neighboring items.Therefore, it cannot accurately estimate the unobserved rating on a targetitem, if its ground truth rating is actually higher (lower) than the highest(lowest) rating over all items in its neighborhood. In this paper, we addressthis problem by formalizing rating estimation as a task of recovering a scalarrating function. With a linearity assumption, we infer all the ratings byoptimizing the low-order norm, e.g., the $l_1/2$-norm, of the second derivativeof the target scalar function, while remaining its observed ratings unchanged.Experimental results on three real datasets, namely Douban, Goodreads andMovieLens, demonstrate that the proposed approach can well overcome the ratingbound problem. Particularly, it can significantly improve the accuracy ofrating estimation by 37% than the conventional neighborhood-based methods.
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