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Social tagging recommendation is an urgent and useful enabling technology for Web 2.0. In this paper, we present a systematic study of low-order tensor decomposition approach that are specifically targeted at the very sparse data problem in tagging recommendation problem. Low-order polynomials have low functional complexity, are uniquely capable of enhancing statistics and also avoids overfitting than traditional tensor decompositions such as Tucker and Parafac decompositions. We perform extensive experiments on several datasets and compared with 6 existing methods. Experimental results demonstrate that our approach outperforms existing approaches.

Algorithms defining similarities between objects of an information network are important to many IR tasks. SimRank algorithm and its variations are popularly used in many applications. Many fast algorithms are also developed. In this note, we first reformulate them as random walks on the network and express them using forward and backward transition probability in a matrix form. Second, we show that P-Rank (SimRank is just the special case of PRank) has a unique solution of ee T when decay factor c is equal to 1. We also show that SimFusion algorithm is a special case of P-Rank algorithm and prove that the similarity matrix of SimFusion is the product of PageRank vector. Our experiments on the web datasets show that for P-Rank the decay factor c doesn't seriously affect the similarity accuracy and accuracy of P-Rank is also higher than SimFusion and SimRank. SIMRANK AND P-RANK ALGORITHMSSimRank[1] is a method of measuring linkage-based similarity between objects in a graph that models the object-to-object relationships for a particular domain. The intuition behind SimRank similarity is that two objects are similar if they are linked by the similar objects. However, SimRank only consider in-link information on the information network but in fact out-link information is also useful for the similarity calculation on the real network. Thus, P-Rank[2] extends SimRank intuition and consider both out-link and in-link information. The intuition of P-Rank is that "two objects are similar if (1) they are linked by the similar objects; and (2) they link the similar objects."We proceed to present the formula to compute P-Rank. Given a graph G(V, E) consisting of a set of nodes V and a set of links E, the P-Rank similarity between objects a and b, denoted as S(a,b), is computed recursively as follows: | ( )|| ( )| 1 1 | ( 1 1 ( ) ( ( ), ( )) + | ( ) || ( ) | ( , ) (1-) ( ( ), ( )) | ( )|| ( )|

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