Center-Piece Subgraphs: Problem Definition and Fast Solutions
by Hanghang Tong and Christos Faloutsos
Given $\QN$ nodes in a social network (say, authorship network), how can we find the node/author that is the center-piece, and has direct or indirect connections to all, or most of them? For example, this node could be the common advisor, or someone who started the research area that the $\QN$ nodes belong to. Isomorphic scenarios appear in law enforcement (find the master-mind criminal, connected to all current suspects), gene regulatory networks (find the protein that participates in pathways with all or most of the given $\QN$ proteins), viral marketing and many more. Connection subgraphs is an important first step, handling the case of $\QN$=2 query nodes. Then, the connection subgraph algorithm finds the $b$ intermediate nodes, that provide a good connection between the two query nodes. Here we generalize the challenge in multiple dimensions: First, we allow more than two query nodes. Second, we allow a whole family of queries, ranging from 'OR' to 'AND', with 'softAND' in-between. Finally, we design and compare a fast approximation, and study the quality/speed trade-off. We also present experiments on the DBLP dataset. The experiments confirm that our proposed method naturally deals with multi-source queries and that the resulting subgraphs agree with our intuition. Wall-clock timing results on the DBLP dataset show that our proposed approximation achieve good accuracy for about $6:1$ speedup.
Beyond Streams and Graphs: Dynamic Tensor Analysis
by Jimeng Sun, Yufei Tao, Christos Faloutsos
How do we find patterns in author-keyword associations, evolving over time? Or in DataCubes, with product-branch-customer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule identification in numerous settings like streaming data, text, graphs, social networks and many more.However, they have only two orders, like author and keyword, in the above example. We propose to envision such higher order data as tensors, and tap the vast literature on the topic. However, these methods do not necessarily scale up, let alone operate on semi-infinite streams. Thus, we introduce the dynamic tensor analysis (DTA) method, and its variants. DTA provides a compact summary for high-order and high-dimensional data, and it also reveals the hidden correlations. Algorithmically,we designed DTA very carefully so that it is (a) scalable, (b) space efficient (it does not need to store the past) and (c) fully automatic with no need for user defined parameters. Moreover, we propose STA, a streaming tensor analysis method, which provides a fast, streaming approximation to DTA. We implemented all our methods, and applied them in two real settings, namely, anomaly detection and multi-way latent semantic indexing. We used two real, large datasets, one on network flow data (100GB over 1 month) and one from DBLP (200MB over 25 years). Our experiments show that our methods are fast, accurate and that they find interesting patterns and outliers on the real datasets.
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Pradeep Ravikumar Last modified: Fri Sep 29 00:09:44 EDT 2006