Clustered embedding of massive social networks

Song, Han Hee; Savas, Berkant; Cho, Tae Won; Dave, Vacha; Lu, Zhengdong; Dhillon, Inderjit S.; Zhang, Yin; Qiu, Lili

doi:10.1145/2254756.2254796

Cited by 13 publications

(18 citation statements)

References 41 publications

(25 reference statements)

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“…There are a number of benefits of clustered low rank approximation compared to spectral regular low-rank approximation: (1) the clustered low-rank approximation preserves important structural information of a network by extracting a certain amount of information from all of the clusters; (2) it has been shown that the clustered low-rank approximation achieves a lower relative error than the truncated SVD with the same amount of memory [25]; (3) it also has been shown that even a sequential implementation of clustered low rank approximation [25] is faster than state-of-the-art algorithms for low-rank matrix approximation [20]; (4) improved accuracy of clustered low-rank approximation contributes to improved performance of end tasks, e.g., prediction of new links in social networks [26] and group recommendation to community members [29].…”

Section: Clustered Low-rank Approximationmentioning

confidence: 99%

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Parallel Clustered Low-Rank Approximation of Graphs and Its Application to Link Prediction

Sui

Lee

Whang

et al. 2013

Lecture Notes in Computer Science

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Abstract. Social network analysis has become a major research area that has impact in diverse applications ranging from search engines to product recommendation systems. A major problem in implementing social network analysis algorithms is the sheer size of many social networks, for example, the Facebook graph has more than 900 million vertices and even small networks may have tens of millions of vertices. One solution to dealing with these large graphs is dimensionality reduction using spectral or SVD analysis of the adjacency matrix of the network, but these global techniques do not necessarily take into account local structures or clusters of the network that are critical in network analysis. A more promising approach is clustered low-rank approximation: instead of computing a global low-rank approximation, the adjacency matrix is first clustered, and then a low-rank approximation of each cluster (i.e., diagonal block) is computed. The resulting algorithm is challenging to parallelize not only because of the large size of the data sets in social network analysis, but also because it requires computing with very diverse data structures ranging from extremely sparse matrices to dense matrices. In this paper, we describe the first parallel implementation of a clustered low-rank approximation algorithm for large social network graphs, and use it to perform link prediction in parallel. Experimental results show that this implementation scales well on large distributed-memory machines; for example, on a Twitter graph with roughly 11 million vertices and 63 million edges, our implementation scales by a factor of 86 on 128 processes and takes less than 2300 seconds, while on a much larger Twitter graph with 41 million vertices and 1.2 billion edges, our implementation scales by a factor of 203 on 256 processes with a running time about 4800 seconds.

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Section: Clustered Low-rank Approximationmentioning

confidence: 99%

“…Link prediction is the problem of predicting formation of new links in networks that evolve over time. This problem arises in applications such as friendship recommendation in social networks [26], affiliation recommendation [29], and prediction of author collaborations in scientific publications [23].…”

Section: Link Prediction In Social Networkmentioning

confidence: 99%

Parallel Clustered Low-Rank Approximation of Graphs and Its Application to Link Prediction

Sui

Lee

Whang

et al. 2013

Lecture Notes in Computer Science

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“…A few examples are information retrieval using latent semantic indexing [11,4], link prediction, and affiliation recommendation in social networks [26,22,27,35,34,36,32]. A particular interest in network applications is to analyze network features as centrality, communicability, and betweenness.…”

Section: Motivationmentioning

confidence: 99%

“…In a recent publication Savas and Dhillon [30] introduced a first approach to clustered low rank approximation of graphs (square matrices) in information science applications. Their approach has proven to perform exceptionally well in a number of applications [34,32,36]. Subsequently a multilevel clustering approach was developed in order to speed up the computation of the dominant eigenvalues and eigenvectors of massive graphs [33].…”

Section: Principal Angles Assume We Have a Truncated Svd Approximatimentioning

confidence: 99%

Clustered Matrix Approximation

Savas¹,

Dhillon²

2016

SIAM J. Matrix Anal. & Appl.

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Abstract. In this paper we develop a novel clustered matrix approximation framework, first showing the motivation behind our research. The proposed methods are particularly well suited for problems with large scale sparse matrices that represent graphs and/or bipartite graphs from information science applications. Our framework and resulting approximations have a number of benefits: (1) the approximations preserve important structure that is present in the original matrix; (2) the approximations contain both global-scale and local-scale information; (3) the procedure is efficient both in computational speed and memory usage; and (4) the resulting approximations are considerably more accurate with less memory usage than truncated SVD approximations, which are optimal with respect to rank. The framework is also quite flexible as it may be modified in various ways to fit the needs of a particular application. In the paper we also derive a probabilistic approach that uses randomness to compute a clustered matrix approximation within the developed framework. We further prove deterministic and probabilistic bounds of the resulting approximation error. Finally, in a series of experiments we evaluate, analyze, and discuss various aspects of the proposed framework. In particular, all the benefits we claim for the clustered matrix approximation are clearly illustrated using real-world and large scale data.

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“…We use eight different real-world networks from [1], [19], [24]. The networks are presented in Table 1.…”

Section: Datasetsmentioning

confidence: 99%

Overlapping community detection using seed set expansion

Whang

Gleich

Dhillon

2013

Proceedings of the 22nd ACM International Conference on Conference on Information &Amp; Knowledge Management - CIKM '13

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149

151

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Community detection is an important task in network analysis. A community (also referred to as a cluster) is a set of cohesive vertices that have more connections inside the set than outside. In many social and information networks, these communities naturally overlap. For instance, in a social network, each vertex in a graph corresponds to an individual who usually participates in multiple communities. One of the most successful techniques for finding overlapping communities is based on local optimization and expansion of a community metric around a seed set of vertices. In this paper, we propose an efficient overlapping community detection algorithm using a seed set expansion approach. In particular, we develop new seeding strategies for a personalized PageRank scheme that optimizes the conductance community score. The key idea of our algorithm is to find good seeds, and then expand these seed sets using the personalized PageRank clustering procedure. Experimental results show that this seed set expansion approach outperforms other state-of-the-art overlapping community detection methods. We also show that our new seeding strategies are better than previous strategies, and are thus effective in finding good overlapping clusters in a graph.

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Clustered embedding of massive social networks

Cited by 13 publications

References 41 publications

Parallel Clustered Low-Rank Approximation of Graphs and Its Application to Link Prediction

Parallel Clustered Low-Rank Approximation of Graphs and Its Application to Link Prediction

Clustered Matrix Approximation

Overlapping community detection using seed set expansion

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