Mining Maximal Cliques from an Uncertain Graph

We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < {\alpha} < 1, we present a precise definition of an {\alpha}-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of {\alpha}-maximal cliques possible within an uncertain graph. We present an algorithm to enumerate {\alpha}-maximal cliques in an uncertain graph whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.Comment: ICDE 201

Efficient Subgraph Similarity Search on Large Probabilistic Graph Databases

Many studies have been conducted on seeking the efficient solution for subgraph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework (RDF) data management. All these works assume that the underlying data are certain. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and privacy preserving purposes. Therefore, in this paper, we study subgraph similarity search on large probabilistic graph databases. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study the uncertain graphs where edges' occurrences are correlated. We formally prove that subgraph similarity search over probabilistic graphs is #P-complete, thus, we employ a filter-and-verify framework to speed up the search. In the filtering phase,we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index, PMI. PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can sort out a large number of probabilistic graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. The efficiency of our proposed solutions has been verified through extensive experiments.Comment: VLDB201

Enumeration of Maximal Cliques from an Uncertain Graph

We consider the enumeration of dense substructures (maximal cliques) from an uncertain graph. For parameter 0 ;a ;1, we define the notion of an a-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of a-maximal cliques possible within a (uncertain) graph. We present an algorithm to enumerate a-maximal cliques whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm

Shortest paths and centrality in uncertain networks

Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is #P-hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution

Mining dense substructures from large deterministic and probabilistic graphs

Graphs represent relationships. Some relationships can be represented as a deterministic graph while others can only be represented by using probabilities. Mining dense structures from graphs help us to find useful patterns in these relationships having applications in wide areas like social network analysis, bioinformatics etc. Arguably the two most fundamental dense substructures are Maximal Cliques and Maximal Bicliques. The enumeration of both these structures are central to many data mining problems. With the advent of “big data”, real world graphs have become massive. Recently systems like MapReduce have evolved to process such large data. However using these systems to mine dense substrucures in massive graphs is an open question. In this thesis, we present novel parallel algorithms using MapReduce for the enumeration of Maximal Cliques / Bicliques in large graphs. We show that our algorithms are work optimal and load balanced. Further, we present a detailed evaluation which shows that the algorithm scales to large graphs with millions of edges and tens of millions of output structures. Finally we consider the problem of Maximal Clique Enumeration in an Uncertain Graph, which is a probability distribution on a set of deterministic graphs. We define the notion of a maximal clique for an uncertain graph, give matching upper and lower bounds on the number of such structures and present a near optimal algorithm to mine all maximal cliques

Influence Analysis towards Big Social Data

Large scale social data from online social networks, instant messaging applications, and wearable devices have seen an exponential growth in a number of users and activities recently. The rapid proliferation of social data provides rich information and infinite possibilities for us to understand and analyze the complex inherent mechanism which governs the evolution of the new technology age. Influence, as a natural product of information diffusion (or propagation), which represents the change in an individual’s thoughts, attitudes, and behaviors resulting from interaction with others, is one of the fundamental processes in social worlds. Therefore, influence analysis occupies a very prominent place in social related data analysis, theory, model, and algorithms. In this dissertation, we study the influence analysis under the scenario of big social data. Firstly, we investigate the uncertainty of influence relationship among the social network. A novel sampling scheme is proposed which enables the development of an efficient algorithm to measure uncertainty. Considering the practicality of neighborhood relationship in real social data, a framework is introduced to transform the uncertain networks into deterministic weight networks where the weight on edges can be measured as Jaccard-like index. Secondly, focusing on the dynamic of social data, a practical framework is proposed by only probing partial communities to explore the real changes of a social network data. Our probing framework minimizes the possible difference between the observed topology and the actual network through several representative communities. We also propose an algorithm that takes full advantage of our divide-and-conquer strategy which reduces the computational overhead. Thirdly, if let the number of users who are influenced be the depth of propagation and the area covered by influenced users be the breadth, most of the research results are only focused on the influence depth instead of the influence breadth. Timeliness, acceptance ratio, and breadth are three important factors that significantly affect the result of influence maximization in reality, but they are neglected by researchers in most of time. To fill the gap, a novel algorithm that incorporates time delay for timeliness, opportunistic selection for acceptance ratio, and broad diffusion for influence breadth has been investigated. In our model, the breadth of influence is measured by the number of covered communities, and the tradeoff between depth and breadth of influence could be balanced by a specific parameter. Furthermore, the problem of privacy preserved influence maximization in both physical location network and online social network was addressed. We merge both the sensed location information collected from cyber-physical world and relationship information gathered from online social network into a unified framework with a comprehensive model. Then we propose the resolution for influence maximization problem with an efficient algorithm. At the same time, a privacy-preserving mechanism are proposed to protect the cyber physical location and link information from the application aspect. Last but not least, to address the challenge of large-scale data, we take the lead in designing an efficient influence maximization framework based on two new models which incorporate the dynamism of networks with consideration of time constraint during the influence spreading process in practice. All proposed problems and models of influence analysis have been empirically studied and verified by different, large-scale, real-world social data in this dissertation

Efficient Node Proximity and Node Significance Computations in Graphs

abstract: Node proximity measures are commonly used for quantifying how nearby or otherwise related to two or more nodes in a graph are. Node significance measures are mainly used to find how much nodes are important in a graph. The measures of node proximity/significance have been highly effective in many predictions and applications. Despite their effectiveness, however, there are various shortcomings. One such shortcoming is a scalability problem due to their high computation costs on large size graphs and another problem on the measures is low accuracy when the significance of node and its degree in the graph are not related. The other problem is that their effectiveness is less when information for a graph is uncertain. For an uncertain graph, they require exponential computation costs to calculate ranking scores with considering all possible worlds. In this thesis, I first introduce Locality-sensitive, Re-use promoting, approximate Personalized PageRank (LR-PPR) which is an approximate personalized PageRank calculating node rankings for the locality information for seeds without calculating the entire graph and reusing the precomputed locality information for different locality combinations. For the identification of locality information, I present Impact Neighborhood Indexing (INI) to find impact neighborhoods with nodes' fingerprints propagation on the network. For the accuracy challenge, I introduce Degree Decoupled PageRank (D2PR) technique to improve the effectiveness of PageRank based knowledge discovery, especially considering the significance of neighbors and degree of a given node. To tackle the uncertain challenge, I introduce Uncertain Personalized PageRank (UPPR) to approximately compute personalized PageRank values on uncertainties of edge existence and Interval Personalized PageRank with Integration (IPPR-I) and Interval Personalized PageRank with Mean (IPPR-M) to compute ranking scores for the case when uncertainty exists on edge weights as interval values.Dissertation/ThesisDoctoral Dissertation Computer Science 201