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Collaborative Filtering is one of the most widely used approaches in recommendation systems which predicts user preferences by learning past user-item relationships. In recent years, item-oriented collaborative filtering methods came into prominence as they are more scalable compared to useroriented methods. Item-oriented methods discover itemitem relationships from the training data and use these relations to compute predictions. In this paper, we propose a novel item-oriented algorithm, Random Walk Recommender, that first infers transition probabilities between items based on their similarities and models finite length random walks on the item space to compute predictions. This method is especially useful when training data is less than plentiful, namely when typical similarity measures fail to capture actual relationships between items. Aside from the proposed prediction algorithm, the final transition probability matrix computed in one of the intermediate steps can be used as an item similarity matrix in typical item-oriented approaches. Thus, this paper suggests a method to enhance similarity matrices under sparse data as well. Experiments on MovieLens data show that Random Walk Recommender algorithm outperforms two other item-oriented methods in different sparsity levels while having the best performance difference in sparse datasets.

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FundamentalThe following problem is considered: Given an undirected, connected graph G, find a spanning tree in G such that the sum of the lengths of the fundamental cycles (with respect to this tree) is minimum. This problem, besides being interesting in its own right, is useful in a variety of situations It is shown that this problem is NP-complete. A number of polynomial-time, heuristic algorithms which yield "good" suboptimal solutions are presented and their performances are discussed. Finally, it is shown that for regular graphs of order n the expected value of the total length of a minimum fundamentalcycle set does not exceed O(n2).

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