Figure 2

Relationship between signed similarity and Jaccard similarity (The results shown here are for the Movielens dataset). (a) The cumulative probability distributions of three similarities (i.e. Jaccard similarity (in black), positive similarity (in red) and negative similarity (in blue)) and probability density distribution in inset. They all roughly follow exponential distributions. The straight lines represent the least square fitting of the data points. (b,c) Present correlation between Jaccard similarity (s ^Jacc) and positive similarity (s ⁺), negative similarity (s ⁻), respectively. The solid lines are average Jaccard similarity with respect to different signed similarity values (positive similarity (red line), negative similarity (blue line)) and error bar for the statistical standard deviation over different Jaccard similarity values. In general, Jaccard similarity increases along positive similarity increases, while almost remains unchanged when negative similarity rises. The scatter in the red and blue boxes indicate the cases that signed similarity is nonzero but Jaccard similarity is zero.