Web Mining and Social Networking: Techniques and ... - tud.ttu.ee

172 8 Web Mining and Recommendation SystemsCosine-based SimilarityIn this case, two items are treated as two vectors in the form of m-dimensional user space.The similarity between two items i and j is formulated as the cosine of the angle between twovectors:where ”·” denotes the dot product of two vectors.Correlation-based Similaritysim(i, j)=cos ( −→ −→ )−→ −→ i · ji , j =∥ −→ i ∥ 2 × ∥ −→ j ∥ (8.1)2In this case, similarity between two items i and j is computed by the Pearson correlation corr ijcoefficient. To calculate it, the user set who co-rated both item i and j are chosen. Let the userset be U the the correlation coefficient is defined by( )( )∑ u∈U Ru,i − R i Ru, j − R jsim(i, j)=corr ij =( ) 2 ( )(8.2)2√∑ u∈U Ru,i − R i ∑u∈U Ru, j − R jwhere R u,i denotes the rating score on item i by user u, R i is the average rating of the ith item.Adjusted Cosine SimilarityIn the case of cosine-based similarity computation, one possible problem existed in the calculationis that the difference in rating score between different users are not fully taken intoconsideration, which brings in the biased weights to the users who always made higher ratingscores. To overcome such rating score bias, an adjust cosine-based similarity is introducedto offset the impact of relative rating score difference by subtracting the corresponding useraverage from each co-rated item pair. Thus the similarity between two item i and j is given by( )( )∑ u∈U Ru,i − R u Ru, j − R usim(i, j)=( ) 2 ( )(8.3)2√∑ u∈U Ru,i − R u ∑u∈U Ru, j − R uwhere R u is the average score of the uth user’s rating.Prediction ComputationAfter defining the similarity measures, they can be used to compute the prediction or recommendationscores. Here, the authors of [218] proposed two methods, namely weighted sumand regression.Weighted SumThe weighted sum scheme is to calculate the final rating score of an item i for the target useru by averaging the sum of the total rating scores of items that are similar to item i given bythe user. And each rating is weighted by the corresponding similarity s ij between item i andj. The predicted rating score of item i is defined by