  Memory-based collaborative filtering methods like user or item k-nearest
neighbors (kNN) are a simple yet effective solution to the recommendation
problem. The backbone of these methods is the estimation of the empirical
similarity between users/items. In this paper, we analyze the spectral
properties of the Pearson and the cosine similarity estimators, and we use
tools from random matrix theory to argue that they suffer from noise and
eigenvalues spreading. We argue that, unlike the Pearson correlation, the
cosine similarity naturally possesses the desirable property of eigenvalue
shrinkage for large eigenvalues. However, due to its zero-mean assumption, it
overestimates the largest eigenvalues. We quantify this overestimation and
present a simple re-scaling and noise cleaning scheme. This results in better
performance of the memory-based methods compared to their vanilla counterparts.
