BACKGROUND: How can we obtain fast and high-quality clusters in genome scale bio-networks? Graph clustering is a powerful tool applied on bio-networks to solve various biological problems such as protein complexes detection, disease module detection, and gene function prediction. Especially, MCL (Markov Clustering) has been spotlighted due to its superior performance on bio-networks. MCL, however, is skewed towards finding a large number of very small clusters (size 1-3) and fails to detect many larger clusters (size 10+). To resolve this fragmentation problem, MLR-MCL (Multi-level Regularized MCL) has been developed. MLR-MCL still suffers from the fragmentation and, in cases, unrealistically large clusters are generated. RESULTS: In this paper, we propose PS-MCL (Parallel Shotgun Coarsened MCL), a parallel graph clustering method outperforming MLR-MCL in terms of running time and cluster quality. PS-MCL adopts an efficient coarsening scheme, called SC (Shotgun Coarsening), to improve graph coarsening in MLR-MCL. SC allows merging multiple nodes at a time, which leads to improvement in quality, time and space usage. Also, PS-MCL parallelizes main operations used in MLR-MCL which includes matrix multiplication. CONCLUSIONS: Experiments show that PS-MCL dramatically alleviates the fragmentation problem, and outperforms MLR-MCL in quality and running time. We also show that the running time of PS-MCL is effectively reduced with parallelization.

How can we estimate local triangle counts accurately in a graph stream without storing the whole graph? How to handle duplicated edges in local triangle counting for graph stream? Local triangle counting, which computes the number of triangles attached to each node in a graph, is a very important problem with wide applications in social network analysis, anomaly detection, web mining, and the like. In this article, we propose algorithms for local triangle counting in a graph stream based on edge sampling: M ascot for a simple graph, and M ulti BM ascot and M ulti WM ascot for a multigraph. To develop M ascot , we first present two naive local triangle counting algorithms in a graph stream, called M ascot -C and M ascot -A. M ascot -C is based on constant edge sampling, and M ascot -A improves its accuracy by utilizing more memory spaces. M ascot achieves both accuracy and memory-efficiency of the two algorithms by unconditional triangle counting for a new edge, regardless of whether it is sampled or not. Extending the idea to a multigraph, we develop two algorithms M ulti BM ascot and M ulti WM ascot . M ulti BM ascot enables local triangle counting on the corresponding simple graph of a streamed multigraph without explicit graph conversion; M ulti WM ascot considers repeated occurrences of an edge as its weight and counts each triangle as the product of its three edge weights. In contrast to the existing algorithm that requires prior knowledge on the target graph and appropriately set parameters, our proposed algorithms require only one parameter of edge sampling probability. Through extensive experiments, we show that for the same number of edges sampled, M ascot provides the best accuracy compared to the existing algorithm as well as M ascot -C and M ascot -A. We also demonstrate that M ulti BM ascot on a multigraph is comparable to M ascot -C on the counterpart simple graph, and M ulti WM ascot becomes more accurate for higher degree nodes. Thanks to M ascot , we also discover interesting anomalous patterns in real graphs, including core-peripheries in the web, a bimodal call pattern in a phone call history, and intensive collaboration in DBLP.

How can we estimate local triangle counts accurately in a graph stream without storing the whole graph? The local triangle counting which counts triangles for each node in a graph is a very important problem with wide applications in social network analysis, anomaly detection, web mining, etc.

How can we discover interesting patterns from time-evolving high speed data streams? How to analyze the data streams quickly and accurately, with little space overhead? High speed data stream has been receiving increasing attentions due to its wide applications such as sensors, network traffic, social networks, etc. One of the most fundamental tasks in the data stream is to find frequent items; especially, finding recently frequent items has become important in real world applications.

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is not the ground truth solution. In many problem scenarios, the system has access to certain statistics of the ground truth. For instance, in image segmentation, the area and boundary length of the object may be known. In these cases, we want to estimate the most probable solution that is consistent with such statistics, i.e., satisfies certain equality or inequality constraints. The above constrained energy minimization problem is NP-hard in general, and is usually solved using Linear Programming formulations, which relax the integrality constraints. This paper proposes a novel method that directly finds the discrete approximate solution of such problems by maximizing the corresponding Lagrangian dual. This method can be applied to any constrained energy minimization problem whose unconstrained version is polynomial time solvable, and can handle multiple, equality or inequality, and linear or non-linear constraints. One important advantage of our method is the ability to handle second order constraints with both-side inequalities with a weak restriction, not trivial in the relaxation based methods, and show that the restriction does not affect the accuracy in our cases.We demonstrate the efficacy of our method on the foreground/background image segmentation problem, and show that it produces impressive segmentation results with less error, and runs more than 20 times faster than the state-of-the-art LP relaxation based approaches.

Given a real world graph, how should we lay-out its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find clique-like communities, like the cavemen graph', and compress them. We show that the block-diagonal mental image of the cavemen graph' is the wrong paradigm, in full agreement with earlier results that real world graphs have no good cuts. Instead, we propose to envision graphs as a collection of hubs connecting spokes, with super-hubs connecting the hubs, and so on, recursively. Based on the idea, we propose the SLASHBURN method to recursively split a graph into hubs and spokes connected only by the hubs. We also propose techniques to select the hubs and give an ordering to the spokes, in addition to the basic SLASHBURN. We give theoretical analysis of the proposed hub selection methods. Our view point has several advantages: (a) it avoids the no good cuts' problem, (b) it gives better compression, and (c) it leads to faster execution times for matrix-vector operations, which are the back-bone of most graph processing tools. Through experiments, we show that SLASHBURN consistently outperforms other methods for all data sets, resulting in better compression and faster running time. Moreover, we show that SLASHBURN with the appropriate spokes ordering can further improve compression while hardly sacrificing the running time.