Cleaning up toxic waste: Removing nefarious contributions to recommendation systems

Recommendation systems are becoming increasingly important, as evidenced by the popularity of the Netflix prize and the sophistication of various online shopping systems. With this increase in interest, a new problem of nefarious or false rankings that compromise a recommendation system´s integrity has surfaced. We consider such purposefully erroneous rankings to be a form of “toxic waste,” corrupting the performance of the underlying algorithm. In this paper, we propose an adaptive reweighted algorithm as a possible approach towards correcting this problem. Our algorithm relies on finding a low-rank-plus-sparse decomposition of the recommendation matrix, where the adaptation of the weights aids in rejecting the malicious contributions. Simulations suggest that our algorithm converges fairly rapidly and produces accurate results.