Graph Mining Problem Research Articles

Deep Network Embedding for Graph Representation Learning in Signed Networks.

Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a given network. The vast majority of existing network embedding algorithms, however, are only designed for unsigned networks, and the signed networks containing both positive and negative links, have pretty distinct properties from the unsigned counterpart. In this paper, we propose a deep network embedding model to learn the low-dimensional node vector representations with structural balance preservation for the signed networks. The model employs a semisupervised stacked auto-encoder to reconstruct the adjacency connections of a given signed network. As the adjacency connections are overwhelmingly positive in the real-world signed networks, we impose a larger penalty to make the auto-encoder focus more on reconstructing the scarce negative links than the abundant positive links. In addition, to preserve the structural balance property of signed networks, we design the pairwise constraints to make the positively connected nodes much closer than the negatively connected nodes in the embedding space. Based on the network representations learned by the proposed model, we conduct link sign prediction and community detection in signed networks. Extensive experimental results in real-world datasets demonstrate the superiority of the proposed model over the state-of-the-art network embedding algorithms for graph representation learning in signed networks.

Motif Counting Beyond Five Nodes

Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets.

Edge distance graph kernel and its application to small molecule classification

Graph classification is an important problem in graph mining with various applications in different fields. Kernel methods have been successfully applied to this problem, recently producing promising results. A graph kernel that mostly specifies classification performance has to be defined in order to apply kernel methods to a graph classification problem. Although there are various previously proposed graph kernels, the problem is still worth investigating, as the available kernels are far from perfect. In this paper, we propose a new graph kernel based on a recently proposed concept called edge distance-k graphs. These new graphs are derived from the original graph and have the potential to be used as novel graph descriptors. We propose a method to convert these graphs into a multiset of strings that is further used to compute a kernel for graphs. The proposed graph kernel is then evaluated on various data sets in comparison to a recently proposed group of graph kernels. The results are promising, both in terms of performance and computational requirements.

Supergraph based periodic pattern mining in dynamic social networks

In dynamic networks, periodically occurring interactions express especially significant meaning. However, these patterns also could occur infrequently, which is why it is difficult to detect while working with mass data. To identify such periodic patterns in dynamic networks, we propose single pass supergraph based periodic pattern mining SPPMiner technique that is polynomial unlike most graph mining problems. The proposed technique stores all entities in dynamic networks only once and calculate common sub-patterns once at each timestamps. In this way, it works faster. The performance study shows that SPPMiner method is time and memory efficient compared to others. In fact, the memory efficiency of our approach does not depend on dynamic network’s lifetime. By studying the growth of periodic patterns in social networks, the proposed research has potential implications for behavior prediction of intellectual communities.

Fast hierarchy construction for dense subgraphs

Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed by two smaller dense subgraphs). Peeling algorithms ( k -core, k -truss, and nucleus decomposition) have been effective to locate many dense subgraphs. However, constructing a hierarchical representation of density structure, even correctly computing the connected k -cores and k -trusses, have been mostly overlooked. Keeping track of connected components during peeling requires an additional traversal operation, which is as expensive as the peeling process. In this paper, we start with a thorough survey and point to nuances in problem formulations that lead to significant differences in runtimes. We then propose efficient and generic algorithms to construct the hierarchy of dense subgraphs for k -core, k -truss, or any nucleus decomposition. Our algorithms leverage the disjoint-set forest data structure to efficiently construct the hierarchy during traversal. Furthermore, we introduce a new idea to avoid traversal. We construct the subgraphs while visiting neighborhoods in the peeling process, and build the relations to previously constructed subgraphs. We also consider an existing idea to find the k -core hierarchy and adapt for our objectives efficiently. Experiments on different types of large scale real-world networks show significant speedups over naive algorithms and existing alternatives. Our algorithms also outperform the hypothetical limits of any possible traversal-based solution.

Top-k overlapping densest subgraphs

Finding dense subgraphs is an important problem in graph mining and has many practical applications. At the same time, while large real-world networks are known to have many communities that are not well-separated, the majority of the existing work focuses on the problem of finding a single densest subgraph. Hence, it is natural to consider the question of finding the top-kdensest subgraphs. One major challenge in addressing this question is how to handle overlaps: eliminating overlaps completely is one option, but this may lead to extracting subgraphs not as dense as it would be possible by allowing a limited amount of overlap. Furthermore, overlaps are desirable as in most real-world graphs there are vertices that belong to more than one community, and thus, to more than one densest subgraph. In this paper we study the problem of finding top-koverlapping densest subgraphs, and we present a new approach that improves over the existing techniques, both in theory and practice. First, we reformulate the problem definition in a way that we are able to obtain an algorithm with constant-factor approximation guarantee. Our approach relies on using techniques for solving the max-sum diversification problem, which however, we need to extend in order to make them applicable to our setting. Second, we evaluate our algorithm on a collection of benchmark datasets and show that it convincingly outperforms the previous methods, both in terms of quality and efficiency.

MiMAG: mining coherent subgraphs in multi-layer graphs with edge labels

Detecting dense subgraphs such as cliques or quasi-cliques is an important graph mining problem. While this task is established for simple graphs, today's applications demand the analysis of more complex graphs: In this work, we consider a frequently observed type of graph where edges represent different types of relations. These multiple edge types can also be viewed as different "layers" of a graph, which is denoted as a "multi-layer graph". Additionally, each edge might be annotated by a label characterizing the given relation in more detail. By simultaneously exploiting all this information, the detection of more interesting subgraphs can be supported. We introduce the multi-layer coherent subgraph model, which defines clusters of vertices that are densely connected by edges with similar labels in a subset of the graph layers. We avoid redundancy in the result by selecting only the most interesting, non-redundant subgraphs for the output. Based on this model, we introduce the best-first search algorithm MiMAG. In thorough experiments, we demonstrate the strengths of MiMAG in comparison with related approaches on synthetic as well as real-world data sets.

Person instance graphs for mono-, cross- and multi-modal person recognition in multimedia data: application to speaker identification in TV broadcast

This work introduces a unified framework for mono-, cross- and multi-modal person recognition in multimedia data. Dubbed person instance graph models the person recognition task as a graph mining problem: i.e., finding the best mapping between person instance vertices and identity vertices. Practically, we describe how the approach can be applied to speaker identification in TV broadcast. Then, a solution to the above-mentioned mapping problem is proposed. It relies on integer linear programming to model the problem of clustering person instances based on their identity. We provide an in-depth theoretical definition of the optimization problem. Moreover, we improve two fundamental aspects of our previous related work: the problem constraints and the optimized objective function. Finally, a thorough experimental evaluation of the proposed framework is performed on a publicly available benchmark database. Depending on the graph configuration (i.e., the choice of its vertices and edges), we show that multiple tasks can be addressed interchangeably (e.g., speaker diarization, supervised or unsupervised speaker identification), significantly outperforming state-of-the-art mono-modal approaches.

Graph Mining Sub Domains and a Framework for Indexing – A Graphical Approach

Graphs are one of the popular models for effective representation of complex structured huge data and the similarity search for graphs has become a fundamental research problem in Graph Mining. In this paper initially, the preliminary graph related basic theorems are brushed and showcased on with various research sub domains such as Graph Classification, Graph Searching, Graph Indexing, and Graph Clustering. These are discussed with few of the most dominant algorithms in their respective sub domains. Finally a model is proposed along with various algorithms with their future projection.

Semantic Based Graph Mining Technology for Automatic Service Semantic Link Network Navigation

To reduce the user's cognitive load and make sense of complex interlinked service data for realizing advanced service application, an approach to Service Semantic Link Network (S-SLN) navigation was proposed. S emantic based g raph m ining t echnology was employed as an effective solution for automatic service navigation . As one of the most important navigation tools, related service nodes recommendation was mapped as a basic graph mining problem. The closely related service nodes linked by different relations to form a sub-graph of S-SLN, which service nodes and links with different type and weight represent different service scenarios and relationship to the maximum extent such that sub-graph of S-SLN can improve or speed up user’s navigation decisions by providing the most probable related Web service and links which are most likely to be of interest. The experimental results and analysis shows that the proposed approach is efficient, feasible and practical.

Spectral counting of triangles via element-wise sparsification and triangle-based link recommendation

Triangle counting is an important problem in graph mining. The clustering coefficient and the transitivity ratio, two commonly used measures effectively quantify the triangle density in order to quantify the fact that friends of friends tend to be friends themselves. Furthermore, several successful graph-mining applications rely on the number of triangles in the graph. In this paper, we study the problem of counting triangles in large, power-law networks. Our algorithm, SparsifyingEigenTriangle, relies on the spectral properties of power-law networks and the Achlioptas–McSherry sparsification process. SparsifyingEigenTriangle is easy to parallelize, fast, and accurate. We verify the validity of our approach with several experiments in real-world graphs, where we achieve at the same time high accuracy and considerable speedup versus a straight-forward exact counting competitor. Finally, our contributions include a simple method for making link recommendations in online social networks based on the number of triangles as well as a procedure for estimating triangles using sketches.

Counting triangles in real-world networks using projections

Triangle counting is an important problem in graph mining. Two frequently used metrics in complex network analysis that require the count of triangles are the clustering coefficients and the transitivity ratio of the graph. Triangles have been used successfully in several real-world applications, such as detection of spamming activity, uncovering the hidden thematic structure of the web and link recommendation in online social networks. Furthermore, the count of triangles is a frequently used network statistic in exponential random graph models. However, counting the number of triangles in a graph is computationally expensive. In this paper, we propose the EigenTriangle and EigenTriangleLocal algorithms to estimate the number of triangles in a graph. The efficiency of our algorithms is based on the special spectral properties of real-world networks, which allow us to approximate accurately the number of triangles. We verify the efficacy of our method experimentally in almost 160 experiments using several Web Graphs, social, co-authorship, information, and Internet networks where we obtain significant speedups with respect to a straightforward triangle counting algorithm. Furthermore, we propose an algorithm based on Fast SVD which allows us to apply the core idea of the EigenTriangle algorithm on graphs which do not fit in the main memory. The main idea is a simple node-sampling process according to which node i is selected with probability $${\frac{d_i}{2m}}$$ where d i is the degree of node i and m is the total number of edges in the graph. Our theoretical contributions also include a theorem that gives a closed formula for the number of triangles in Kronecker graphs, a model of networks which mimics several properties of real-world networks.

Learning block-preserving graph patterns and its application to data mining

Recently, due to the rapid growth of electronic data having graph structures such as HTML and XML texts and chemical compounds, many researchers have been interested in data mining and machine learning techniques for finding useful patterns from graph-structured data (graph data). Since graph data contain a huge number of substructures and it tends to be computationally expensive to decide whether or not such data have given structural features, graph mining problems face computational difficulties. Let ${\mathcal{C}}$ be a graph class which satisfies a connected hereditary property and contains infinitely many different biconnected graphs, and for which a special kind of the graph isomorphism problem can be computed in polynomial time. In this paper, we consider learning and mining problems for ${\mathcal{C}}$ . Firstly, we define a new graph pattern, which is called a block preserving graph pattern (bp-graph pattern) for ${\mathcal{C}}$ . Secondly, we present a polynomial time algorithm for deciding whether or not a given bp-graph pattern matches a given graph in ${\mathcal{C}}$ . Thirdly, by giving refinement operators over bp-graph patterns, we present a polynomial time algorithm for finding a minimally generalized bp-graph pattern for ${\mathcal{C}}$ . Outerplanar graphs are planar graphs which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many pharmacologic chemical compounds are known to be represented by outerplanar graphs. The class of connected outerplanar graphs ${\mathcal{O}}$ satisfies the above conditions for ${\mathcal{C}}$ . Next, we propose two incremental polynomial time algorithms for enumerating all frequent bp-graph patterns with respect to a given finite set of graphs in ${\mathcal{O}}$ . Finally, by reporting experimental results obtained by applying the two graph mining algorithms to a subset of the NCI dataset, we evaluate the performance of the two graph mining algorithms.

A graph-based approach to systematically reconstruct human transcriptional regulatory modules

A major challenge in studying gene regulation is to systematically reconstruct transcription regulatory modules, which are defined as sets of genes that are regulated by a common set of transcription factors. A commonly used approach for transcription module reconstruction is to derive coexpression clusters from a microarray dataset. However, such results often contain false positives because genes from many transcription modules may be simultaneously perturbed upon a given type of conditions. In this study, we propose and validate that genes, which form a coexpression cluster in multiple microarray datasets across diverse conditions, are more likely to form a transcription module. However, identifying genes coexpressed in a subset of many microarray datasets is not a trivial computational problem. We propose a graph-based data-mining approach to efficiently and systematically identify frequent coexpression clusters. Given m microarray datasets, we model each microarray dataset as a coexpression graph, and search for vertex sets which are frequently densely connected across [theta m] datasets (0 < or = theta < or = 1). For this novel graph-mining problem, we designed two techniques to narrow down the search space: (1) partition the input graphs into (overlapping) groups sharing common properties; (2) summarize the vertex neighbor information from the partitioned datasets onto the 'Neighbor Association Summary Graph's for effective mining. We applied our method to 105 human microarray datasets, and identified a large number of potential transcription modules, activated under different subsets of conditions. Validation by ChIP-chip data demonstrated that the likelihood of a coexpression cluster being a transcription module increases significantly with its recurrence. Our method opens a new way to exploit the vast amount of existing microarray data accumulation for gene regulation study. Furthermore, the algorithm is applicable to other biological networks for approximate network module mining. http://zhoulab.usc.edu/NeMo/.