arXiv subjects

Arlei Silva

Publications and source records attributed to Arlei Silva.

23 records · Page 2Linked to original sources

arXiv2017

Spectral Algorithms for Temporal Graph Cuts

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce the sparsest and normalized cut problems in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, multiplex graphs, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend our formulation to dynamic graph signals, where cuts also capture node values, as graph wavelets. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.

cs.SI↗

arXiv2016

Outlier Detection from Network Data with Subnetwork Interpretation

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why the network is exceptional, expressed in the form of subnetwork, is also equally important. In this paper, we develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that mostly discriminate it from nearby regular samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery and we show that it converges to a global optimum. Evaluation on various real-world network datasets demonstrates that our algorithm not only outperforms baselines in both network and high dimensional setting, but also discovers highly relevant and interpretable local subnetworks, further enhancing our understanding of anomalous networks.

cs.AI↗

arXiv2016

Graph Wavelets via Sparse Cuts: Extended Version

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a both compact and accurate manner. However, how to discover wavelet bases that capture the geometry of the data with respect to the signal as well as the graph structure remains an open question. In this paper, we study the problem of computing graph wavelet bases via sparse cuts in order to produce low-dimensional encodings of data-driven bases. This problem is connected to known hard problems in graph theory (e.g. multiway cuts) and thus requires an efficient heuristic. We formulate the basis discovery task as a relaxation of a vector optimization problem, which leads to an elegant solution as a regularized eigenvalue computation. Moreover, we propose several strategies in order to scale our algorithm to large graphs. Experimental results show that the proposed algorithm can effectively encode both the graph structure and signal, producing compressed and accurate representations for vertex values in a wide range of datasets (e.g. sensor and gene networks) and significantly outperforming the best baseline.

cs.DS↗

arXiv2016

Prediction-based Online Trajectory Compression

Recent spatio-temporal data applications, such as car-shar\-ing and smart cities, impose new challenges regarding the scalability and timeliness of data processing systems. Trajectory compression is a promising approach for scaling up spatio-temporal databases. However, existing techniques fail to address the online setting, in which a compressed version of a trajectory stream has to be maintained over time. In this paper, we introduce ONTRAC, a new framework for map-matched online trajectory compression. ONTRAC learns prediction models for suppressing updates to a trajectory database using training data. Two prediction schemes are proposed, one for road segments via a Markov model and another for travel-times by combining Quadratic Programming and Expectation Maximization. Experiments show that ONTRAC outperforms the state-of-the-art offline technique even when long update delays (4 mininutes) are allowed and achieves up to 21 times higher compression ratio for travel-times. Moreover, our approach increases database scalability by up to one order of magnitude.

cs.DB↗

arXiv2012

Mining Attribute-structure Correlated Patterns in Large Attributed Graphs

In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph induced by a particular attribute set. Existing methods are not able to extract relevant knowledge regarding how vertex attributes interact with dense subgraphs. Structural correlation pattern mining combines aspects of frequent itemset and quasi-clique mining problems. We propose statistical significance measures that compare the structural correlation of attribute sets against their expected values using null models. Moreover, we evaluate the interestingness of structural correlation patterns in terms of size and density. An efficient algorithm that combines search and pruning strategies in the identification of the most relevant structural correlation patterns is presented. We apply our method for the analysis of three real-world attributed graphs: a collaboration, a music, and a citation network, verifying that it provides valuable knowledge in a feasible time.

cs.DB↗