Significant Subgraph Mining with Multiple Testing Correction

The problem of finding itemsets that are statistically significantly enriched in a class of transactions is complicated by the need to correct for multiple hypothesis testing. Pruning untestable hypotheses was recently proposed as a strategy for this task of significant itemset mining. It was shown to lead to greater statistical power, the discovery of more truly significant itemsets, than the standard Bonferroni correction on real-world datasets. An open question, however, is whether this strategy of excluding untestable hypotheses also leads to greater statistical power in subgraph mining, in which the number of hypotheses is much larger than in itemset mining. Here we answer this question by an empirical investigation on eight popular graph benchmark datasets. We propose a new efficient search strategy, which always returns the same solution as the state-of-the-art approach and is approximately two orders of magnitude faster. Moreover, we exploit the dependence between subgraphs by considering the effective number of tests and thereby further increase the statistical power.Comment: 18 pages, 5 figure, accepted to the 2015 SIAM International Conference on Data Mining (SDM15

Mining and analysis of real-world graphs

Networked systems are everywhere - such as the Internet, social networks, biological networks, transportation networks, power grid networks, etc. They can be very large yet enormously complex. They can contain a lot of information, either open and transparent or under the cover and coded. Such real-world systems can be modeled using graphs and be mined and analyzed through the lens of network analysis. Network analysis can be applied in recognition of frequent patterns among the connected components in a large graph, such as social networks, where visual analysis is almost impossible. Frequent patterns illuminate statistically important subgraphs that are usually small enough to analyze visually. Graph mining has different practical applications in fraud detection, outliers detection, chemical molecules, etc., based on the necessity of extracting and understanding the information yielded. Network analysis can also be used to quantitatively evaluate and improve the resilience of infrastructure networks such as the Internet or power grids. Infrastructure networks directly affect the quality of people\u27s lives. However, a disastrous incident in these networks may lead to a cascading breakdown of the whole network and serious economic consequences. In essence, network analysis can help us gain actionable insights and make better data-driven decisions based on the networks. On that note, the objective of this dissertation is to improve upon existing tools for more accurate mining and analysis of real-world networks --Abstract, page iv

Subgraph covers -- An information theoretic approach to motif analysis in networks

Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original network with a statistical null model. In this paper we propose an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information. A subgraph cover is defined to be a set of subgraphs such that every edge of the graph is contained in at least one of the subgraphs in the cover. Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers and the presented approach can be used to match networks with such models. To prove the practical value of our approach we also present a heuristic for the resulting NP-hard optimization problem and give results for several real world networks.Comment: 10 pages, 7 tables, 1 Figur

Discovery of Functional Motifs from the Interface Region of Oligomeric Proteins using Frequent Subgraph Mining

Modeling the interface region of a protein complex paves the way for understanding its dynamics and functionalities. Existing works model the interface region of a complex by using different approaches, such as, the residue composition at the interface region, the geometry of the interface residues, or the structural alignment of interface regions. These approaches are useful for ranking a set of docked conformation or for building scoring function for protein-protein docking, but they do not provide a generic and scalable technique for the extraction of interface patterns leading to functional motif discovery. In this work, we model the interface region of a protein complex by graphs and extract interface patterns of the given complex in the form of frequent subgraphs. To achieve this we develop a scalable algorithm for frequent subgraph mining. We show that a systematic review of the mined subgraphs provides an effective method for the discovery of functional motifs that exist along the interface region of a given protein complex

Kernel Functions for Graph Classification

Graphs are information-rich structures, but their complexity makes them difficult to analyze. Given their broad and powerful representation capacity, the classification of graphs has become an intense area of research. Many established classifiers represent objects with vectors of explicit features. When the number of features grows, however, these vector representations suffer from typical problems of high dimensionality such as overfitting and high computation time. This work instead focuses on using kernel functions to map graphs into implicity defined spaces that avoid the difficulties of vector representations. The introduction of kernel classifiers has kindled great interest in kernel functions for graph data. By using kernels the problem of graph classification changes from finding a good classifier to finding a good kernel function. This work explores several novel uses of kernel functions for graph classification. The first technique is the use of structure based features to add structural information to the kernel function. A strength of this approach is the ability to identify specific structure features that contribute significantly to the classification process. Discriminative structures can then be passed off to domain-specific researchers for additional analysis. The next approach is the use of wavelet functions to represent graph topology as simple real-valued features. This approach achieves order-of-magnitude decreases in kernel computation time by eliminating costly topological comparisons, while retaining competitive classification accuracy. Finally, this work examines the use of even simpler graph representations and their utility for classification. The models produced from the kernel functions presented here yield excellent performance with respect to both efficiency and accuracy, as demonstrated in a variety of experimental studies

Latent Representation and Sampling in Network: Application in Text Mining and Biology.

In classical machine learning, hand-designed features are used for learning a mapping from raw data. However, human involvement in feature design makes the process expensive. Representation learning aims to learn abstract features directly from data without direct human involvement. Raw data can be of various forms. Network is one form of data that encodes relational structure in many real-world domains. Therefore, learning abstract features for network units is an important task. In this dissertation, we propose models for incorporating temporal information given as a collection of networks from subsequent time-stamps. The primary objective of our models is to learn a better abstract feature representation of nodes and edges in an evolving network. We show that the temporal information in the abstract feature improves the performance of link prediction task substantially. Besides applying to the network data, we also employ our models to incorporate extra-sentential information in the text domain for learning better representation of sentences. We build a context network of sentences to capture extra-sentential information. This information in abstract feature representation of sentences improves various text-mining tasks substantially over a set of baseline methods. A problem with the abstract features that we learn is that they lack interpretability. In real-life applications on network data, for some tasks, it is crucial to learn interpretable features in the form of graphical structures. For this we need to mine important graphical structures along with their frequency statistics from the input dataset. However, exact algorithms for these tasks are computationally expensive, so scalable algorithms are of urgent need. To overcome this challenge, we provide efficient sampling algorithms for mining higher-order structures from network(s). We show that our sampling-based algorithms are scalable. They are also superior to a set of baseline algorithms in terms of retrieving important graphical sub-structures, and collecting their frequency statistics. Finally, we show that we can use these frequent subgraph statistics and structures as features in various real-life applications. We show one application in biology and another in security. In both cases, we show that the structures and their statistics significantly improve the performance of knowledge discovery tasks in these domains