SimRank Similarity Research Articles

Construction of implicit social network and recommendation between users and items via the ISR-RRM algorithm

To alleviate the challenges posed by privacy protection, sparse data, cold-start problem and weak interpretation, in this paper, we investigate how to uncover the implicit “social relationships” for user/item pairs and create recommendation relationships between users and items in the recommendation systems with no explicit trust relationships. Firstly, according to complex network theory, a recommendation system is presented by a heterogeneous network with five various types of subnets. Secondly, a novel algorithm ISimRank-ISR is designed based on the improved SimRank similarity index, which mainly integrates common and non-common behavior information, as well as attribute information for exploring the implicit social relations, and generates two types of social subnets. Further, introducing these implicit social relations into the nonnegative matrix factorization (NMF) model, another novel algorithm INMF-RRM is proposed to reconstruct the user-item rating subnet. Then, the integration of the above two algorithms derives an algorithm ISR-RRM to create recommendation relationships for the recommendation task. Finally, numerical experiments on two Movielens datasets are conducted to verify the feasibility and effectiveness of the three new algorithms mentioned above, and we come to the following conclusions. (1) The ISimRank-ISR algorithm provides an in-depth exploration of the implicit social relationships for user/item pairs. (2) The INMF-RRM algorithm has convergence properties. (3) To perform better and obtain more accurate recommendations, with the ISR-RRM algorithm, there are optimal parameters achieved. (4) Compared with the other seven benchmark algorithms, the ISR-RRM algorithm shows excellent performance, and its RMSE and MAE are reduced by a maximum of 14.75% and 8.05%, respectively. Additionally, it is more effective in alleviating the cold-start problem.

Efficient index-free SimRank similarity search in large graphs by discounting path lengths

Link-based similarity search aims to find similar nodes for a given query node in a graph, which arises in numerous applications, including web spam detection, social network analysis and web search. Among existing methods, SimRank is a well-known similarity model, which provides an effective and trustful function for similarity search. A large amount of techniques on SimRank similarity search are devoted recently, which compute the similarity scores by traversing the paths between query and candidate nodes. However, the number of paths increases exponentially as path length increases, which makes the computation expensive and cannot support fast similarity search over large graphs. In this paper, we propose an efficient index-free SimRank similarity search approach, namely DisSim, which reduces the computational cost by discounting path length. We observe that SimRank could rapidly converge at a stable state and the results change little after a few of iterations. Based on the fast convergence, the similarity between nodes is defined as the SimRank score at the second iteration. For the computation of DisSim, we divide the similarity into one-step and two-step first-meeting probabilities. The one-step first-meeting probabilities are computed by path traverses from query to candidate nodes, which reduces computational cost by skipping unnecessary nodes. And the two-step first-meeting probabilities are computed by integrating the repeated parts of the paths. For further speeding up query processing, we develop a pruning algorithm, which prunes unpromising path traverses by setting a threshold, and the accuracy loss under threshold is given through mathematical analysis. Extensive experiments on real graphs demonstrate the performance of DisSim through comparing with the state-of-the-art algorithms.

Improving NMF-based community discovery using distributed robust nonnegative matrix factorization with SimRank similarity measure

Nonnegative matrix factorization (NMF) has become a powerful model for community discovery in complex networks. Existing NMF-based methods for community discovery often factorize the corresponding adjacent matrix of complex networks to obtain its community indicator matrix. However, the adjacent matrix cannot represent the global structure feature of complex networks very well, and this leads to the performance degradation of community discovery. Besides, most of existing methods are not robust and scalable enough, so they are not effective to deal with complex networks with noises and large scales. Aiming at these problems above, in this paper we propose a method for community discovery using distributed robust NMF with SimRank similarity measure. This method selects SimRank measure to construct the feature matrix, which can more accurately represent the global structure feature of complex networks. To improve the robustness, we select $$\ell _{2,1}$$ norm instead of the widely used Frobenius norm to construct its NMF-based community discovery model. In addition, to improve the scalability, we implement its key components by using MapReduce distributed computing framework, including computing SimRank feature matrix and iteratively solving the NMF-based model for community discovery. We conduct extensive experiments on several typical complex networks. The results show that our method has better performance and robustness than other representative NMF-based methods for community discovery. Moreover, our method presents good scalability and hence can be used to discover communities in the large-scale complex networks.

SimRank on Uncertain Graphs

SimRank is a similarity measure between vertices in a graph. Recently, many algorithms have been proposed to efficiently evaluate SimRank similarities. However, the existing algorithms either overlook uncertainty in graph structures or depends on an unreasonable assumption. In this paper, we study SimRank on uncertain graphs. Following the random-walk-based formulation of SimRank on deterministic graphs and the possible world model of uncertain graphs, we first define random walks on uncertain graphs and show that our definition of random walks satisfies Markov’s property. We formulate our SimRank measure based on random walks on uncertain graphs. We discover a critical difference between random walks on uncertain graphs and random walks on deterministic graphs, which makes all existing SimRank computation algorithms on deterministic graphs inapplicable to uncertain graphs. For SimRank computation, we consider computing both single-pair SimRank and single-source top- $K$ SimRank. We propose three algorithms, namely the sampling algorithm with high efficiency, the two-phase algorithm with comparable efficiency and higher accuracy, and a speeding-up algorithm with much higher efficiency. Meanwhile, we present an optimized algorithm for efficient computing the single-source top- $K$ SimRank. The experimental results verify the effectiveness of our SimRank measure and the efficiency of the proposed SimRank computation algorithms.

SimRank similarity preserving projection for shape‐based 3D model auto‐annotation

We present a new dimensionality reduction method, called SimRank similarity preserving projection (SSPP), that finds a subspace preserving semantic similarity among data represented with SimRank similarity on a bipartite graph. The relationship between 3D models and keywords in a tagged 3D model dataset is represented with bipartite graph. For shape‐based 3D model auto‐annotation, we try to capture the relationship of tagged 3D models by SSPP. Experimental results show that our method outperforms the baseline and previous methods.

Probesim

Single-source and top- k SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these two types of queries, but very few can efficiently support similarity search over large dynamic graphs, due to either significant preprocessing time or large space overheads. This paper presents ProbeSim , an index-free algorithm for single-source and top- k SimRank queries that provides a non-trivial theoretical guarantee in the absolute error of query results. ProbeSim estimates SimRank similarities without precomputing any indexing structures, and thus can naturally support real-time SimRank queries on dynamic graphs. Besides the theoretical guarantee, ProbeSim also offers satisfying practical efficiency and effectiveness due to non-trivial optimizations. We conduct extensive experiments on a number of benchmark datasets, which demonstrate that our solutions outperform the existing methods in terms of efficiency and effectiveness. Notably, our experiments include the first empirical study that evaluates the effectiveness of SimRank algorithms on graphs with billion edges, using the idea of pooling.

Efficient top-k simrank-based similarity join

SimRank is a popular and widely-adopted similarity measure to evaluate the similarity between nodes in a graph. It is time and space consuming to compute the SimRank similarities for all pairs of nodes, especially for large graphs. In real-world applications, users are only interested in the most similar pairs. To address this problem, in this paper we study the top-k SimRank-based similarity join problem, which finds k most similar pairs of nodes with the largest SimRank similarities among all possible pairs. To the best of our knowledge, this is the first attempt to address this problem. We encode each node as a vector by summarizing its neighbors and transform the calculation of the SimRank similarity between two nodes to computing the dot product between the corresponding vectors. We devise an efficient two-step framework to compute top- k similar pairs using the vectors. For large graphs, exact algorithms cannot meet the high-performance requirement, and we also devise an approximate algorithm which can efficiently identify top- k similar pairs under user-specified accuracy requirement. Experiments on both real and synthetic datasets show our method achieves high performance and good scalability.

Assessing single-pair similarity over graphs by aggregating first-meeting probabilities

Link-based similarity plays an important role in measuring similarities between nodes in a graph. As a widely used link-based similarity, SimRank scores similarity between two nodes as the first-meeting probability of two random surfers. However, due to the large scale of graphs in real-world applications and dynamic change characteristic, it is not viable to frequently update the whole similarity matrix. Also, people often only concern about the similarities of a small subset of nodes in a graph. In such a case, the existing approaches need to compute the similarities of all node-pairs simultaneously, suffering from high computation cost.In this paper, we propose a new algorithm, Iterative Single-Pair SimRank (ISP), based on the random surfer-pair model to compute the SimRank similarity score for a single pair of nodes in a graph. To avoid computing similarities of all other nodes, we introduce a new data structure, position matrix, to facilitate computation of the first-meeting probabilities of two random surfers, and give two optimization techniques to further enhance their performance. In addition, we theoretically prove that the time cost of ISP is always less than the original algorithm SimRank. Comprehensive experiments conducted on both synthetic and real datasets demonstrate the effectiveness and efficiency of our approach.