Erratum: inverting a sum of matrices
SIAM Review
Dimensionality reduction for similarity searching in dynamic databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Inferring Web communities from link topology
Proceedings of the ninth ACM conference on Hypertext and hypermedia : links, objects, time and space---structure in hypermedia systems: links, objects, time and space---structure in hypermedia systems
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Correlating synchronous and asynchronous data streams
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Automatic multimedia cross-modal correlation discovery
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Streaming pattern discovery in multiple time-series
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Mining compressed frequent-pattern sets
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Neighborhood Formation and Anomaly Detection in Bipartite Graphs
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
SIAM Journal on Computing
Group formation in large social networks: membership, growth, and evolution
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
Evolutionary spectral clustering by incorporating temporal smoothness
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
GraphScope: parameter-free mining of large time-evolving graphs
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Random walk with restart: fast solutions and applications
Knowledge and Information Systems
Learning patterns in the dynamics of biological networks
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
JCCM: Joint Cluster Communities on Attribute and Relationship Data in Social Networks
ADMA '09 Proceedings of the 5th International Conference on Advanced Data Mining and Applications
Fast and scalable algorithms for semi-supervised link prediction on static and dynamic graphs
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
A model for automatic generation of multi-partite graphs from arbitrary data
WAIM'10 Proceedings of the 2010 international conference on Web-age information management
Correlating financial time series with micro-blogging activity
Proceedings of the fifth ACM international conference on Web search and data mining
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Non-negative residual matrix factorization: problem definition, fast solutions, and applications
Statistical Analysis and Data Mining
Multi-level Low-rank Approximation-based Spectral Clustering for image segmentation
Pattern Recognition Letters
MultiAspectForensics: mining large heterogeneous networks using tensor
International Journal of Web Engineering and Technology
Sparse functional representation for large-scale service clustering
ICSOC'12 Proceedings of the 10th international conference on Service-Oriented Computing
A regularized graph layout framework for dynamic network visualization
Data Mining and Knowledge Discovery
Dynamix: anonymity on dynamic social structures
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
Mining most frequently changing component in evolving graphs
World Wide Web
Discovering descriptive rules in relational dynamic graphs
Intelligent Data Analysis - Dynamic Networks and Knowledge Discovery
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Low-rank approximations of the adjacency matrix of a graph are essential in finding patterns (such as communities) and detecting anomalies. Additionally, it is desirable to track the low-rank structure as the graph evolves over time, efficiently and within limited storage. Real graphs typically have thousands or millions of nodes, but are usually very sparse. However, standard decompositions such as SVD do not preserve sparsity. This has led to the development of methods such as CUR and CMD, which seek a non-orthogonal basis by sampling the columns and/or rows of the sparse matrix. However, these approaches will typically produce overcomplete bases, which wastes both space and time. In this paper we propose the family of Colibri methods to deal with these challenges. Our version for static graphs, Colibri-S, iteratively finds a non-redundant basis and we prove that it has no loss of accuracy compared to the best competitors (CUR and CMD), while achieving significant savings in space and time: on real data, Colibri-S requires much less space and is orders of magnitude faster (in proportion to the square of the number of non-redundant columns). Additionally, we propose an efficient update algorithm for dynamic, time-evolving graphs, Colibri-D. Our evaluation on a large, real network traffic dataset shows that Colibri-D is over 100 times faster than the best published competitor (CMD).