Clustered low rank approximation of graphs in information science applications

In this paper we present a fast and accurate procedure called clusteredlow rank matrix approximation for massive graphs. The procedure involvesa fast clustering of the graph and then approximates e ...

[1]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[2]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

[4]  Andrew B. Kahng,et al.  New spectral methods for ratio cut partitioning and clustering , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  Dorothea Wagner,et al.  Between Min Cut and Graph Bisection , 1993, MFCS.

[6]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  G. W. Stewart,et al.  Matrix algorithms , 1998 .

[8]  G. Stewart Matrix Algorithms, Volume II: Eigensystems , 2001 .

[9]  Hongyuan Zha,et al.  Structure and Perturbation Analysis of Truncated SVDs for Column-Partitioned Matrices , 2000, SIAM J. Matrix Anal. Appl..

[10]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[11]  Jon Kleinberg,et al.  The link prediction problem for social networks , 2003, CIKM '03.

[12]  Michael I. Jordan,et al.  Learning Spectral Clustering , 2003, NIPS.

[13]  Ben Taskar,et al.  Link Prediction in Relational Data , 2003, NIPS.

[14]  Alexander Thomasian,et al.  CSVD: Clustering and Singular Value Decomposition for Approximate Similarity Search in High-Dimensional Spaces , 2003, IEEE Trans. Knowl. Data Eng..

[15]  Inderjit S. Dhillon,et al.  Concept Decompositions for Large Sparse Text Data Using Clustering , 2004, Machine Learning.

[16]  Efstratios Gallopoulos,et al.  CLSI: A Flexible Approximation Scheme from Clustered Term-Document Matrices , 2005, SDM.

[17]  Jon M. Kleinberg,et al.  Group formation in large social networks: membership, growth, and evolution , 2006, KDD '06.

[18]  Benno Schwikowski,et al.  Graph-based methods for analysing networks in cell biology , 2006, Briefings Bioinform..

[19]  Petros Drineas,et al.  FAST MONTE CARLO ALGORITHMS FOR MATRICES II: COMPUTING A LOW-RANK APPROXIMATION TO A MATRIX∗ , 2004 .

[20]  George Karypis,et al.  Multilevel algorithms for partitioning power-law graphs , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[21]  Inderjit S. Dhillon,et al.  Weighted Graph Cuts without Eigenvectors A Multilevel Approach , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  David Liben-Nowell,et al.  The link-prediction problem for social networks , 2007 .

[23]  Christos Faloutsos,et al.  Fast direction-aware proximity for graph mining , 2007, KDD '07.

[24]  Francesco Masulli,et al.  A survey of kernel and spectral methods for clustering , 2008, Pattern Recognit..

[25]  Jure Leskovec,et al.  Statistical properties of community structure in large social and information networks , 2008, WWW.

[26]  Christos Boutsidis,et al.  Clustered subset selection and its applications on it service metrics , 2008, CIKM '08.

[27]  Mark Tygert,et al.  A Randomized Algorithm for Principal Component Analysis , 2008, SIAM J. Matrix Anal. Appl..

[28]  Yin Zhang,et al.  Scalable proximity estimation and link prediction in online social networks , 2009, IMC '09.

[29]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[30]  Christos Boutsidis,et al.  An improved approximation algorithm for the column subset selection problem , 2008, SODA.

[31]  James T. Kwok,et al.  Clustered Nyström Method for Large Scale Manifold Learning and Dimension Reduction , 2010, IEEE Transactions on Neural Networks.

[32]  Shirish Tatikonda,et al.  A Survey of Graph Mining Techniques for Biological Datasets , 2010, Managing and Mining Graph Data.

[33]  Nagarajan Natarajan,et al.  Scalable Affiliation Recommendation using Auxiliary Networks , 2011, TIST.

[34]  Nathan Halko,et al.  Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions , 2009, SIAM Rev..

[35]  Yin Zhang,et al.  Clustered embedding of massive social networks , 2012, SIGMETRICS '12.