A note on the strong polynomiality of convex quadratic programming
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Inferring Web communities from link topology
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On power-law relationships of the Internet topology
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Stable distributions, pseudorandom generators, embeddings and data stream computation
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Maximizing the spread of influence through a social network
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Non-negative Matrix Factorization with Sparseness Constraints
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AutoPart: parameter-free graph partitioning and outlier detection
PKDD '04 Proceedings of the 8th European Conference on Principles and Practice of Knowledge Discovery in Databases
Graphs over time: densification laws, shrinking diameters and possible explanations
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Mining compressed frequent-pattern sets
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Neighborhood Formation and Anomaly Detection in Bipartite Graphs
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
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Group formation in large social networks: membership, growth, and evolution
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Fast computation of low-rank matrix approximations
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A Generalized Divergence Measure for Nonnegative Matrix Factorization
Neural Computation
Modeling relationships at multiple scales to improve accuracy of large recommender systems
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Evolutionary spectral clustering by incorporating temporal smoothness
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Relational learning via collective matrix factorization
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Colibri: fast mining of large static and dynamic graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
ACM Computing Surveys (CSUR)
On compressing social networks
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Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Detecting fraudulent personalities in networks of online auctioneers
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OddBall: spotting anomalies in weighted graphs
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II
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Matrix factorization is a very powerful tool to find graph patterns, e.g. communities, anomalies, etc. A recent trend is to improve the usability of the discovered graph patterns, by encoding some interpretation-friendly properties (e.g., non-negativity, sparseness, etc) in the factorization. Most, if not all, of these methods are tailored for the task of community detection.We propose NrMF, a non-negative residual matrix factorization framework, aiming to improve the interpretation for graph anomaly detection. We present two optimization formations and their corresponding optimization solutions. Our method can naturally capture abnormal behaviors on graphs. We further generalize it to admit sparse constrains in the residual matrix. The effectiveness and efficiency of the proposed algorithms are analyzed, showing that our algorithm (i) leads to a local optima; and (ii) scales to large graphs. The experimental results on several data sets validate its effectiveness as well as efficiency. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 5: 3–15, 2012, © 2012 Wiley Periodicals, Inc. (Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053. It is continuing through participation in the Anomaly Detection at Multiple Scales (ADAMS) program sponsored by the U.S. Defense Advanced Research Projects Agency (DARPA) under Agreement Number W911NF-11-C-0200. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.)