Uncertain Graph Research Articles

DGCU: A new deep directed method based on Gaussian embedding for clustering uncertain graphs

Clustering uncertain graphs, with the aim of discovering the most reliable partitions, has many applications in real-world networks. In literature, uncertainty is applied somehow to the traditional graph clustering algorithms, so that probabilistic extensions of them are achieved. Due to the difficulty of this technique per algorithm, besides the increasing noise and sparsity followed by more graph dimensions, we propose a deep learning based method to overcome these challenges. As a preprocessing, we first generate a Probabilistic Proximity Matrix (PPM) and a Probabilistic Similarity Matrix (PSM) using the topological structures of the uncertain graph. Afterward, we benefit from Gaussian embedding to capture uncertainty beyond the efficient representation of nodes in a low-dimensional space. PPM is used to embed nodes in a Gaussian space, and PSM is utilized for embedding directed clustering in which a mutually objective function is employed to learn node embedding and clustering simultaneously. Finally, the representations can be partitioned by any deterministic graph clustering algorithm. Various experiments were accomplished on four real-world datasets. The results show more effectiveness of the proposed method than the state-of-the-art approaches in detecting co-cluster objects and well-separated clusters, also indicating high reliability with regard to the pairwise connection probabilities within the clusters.

Depression Classification Using Frequent Subgraph Mining Based on Pattern Growth of Frequent Edge in Functional Magnetic Resonance Imaging Uncertain Network.

The brain network structure is highly uncertain due to the noise in imaging signals and evaluation methods. Recent works have shown that uncertain brain networks could capture uncertain information with regards to functional connections. Most of the existing research studies covering uncertain brain networks used graph mining methods for analysis; for example, the mining uncertain subgraph patterns (MUSE) method was used to mine frequent subgraphs and the discriminative feature selection for uncertain graph classification (DUG) method was used to select discriminant subgraphs. However, these methods led to a lack of effective discriminative information; this reduced the classification accuracy for brain diseases. Therefore, considering these problems, we propose an approximate frequent subgraph mining algorithm based on pattern growth of frequent edge (unFEPG) for uncertain brain networks and a novel discriminative feature selection method based on statistical index (dfsSI) to perform graph mining and selection. Results showed that compared with the conventional methods, the unFEPG and dfsSI methods achieved a higher classification accuracy. Furthermore, to demonstrate the efficacy of the proposed method, we used consistent discriminative subgraph patterns based on thresholding and weighting approaches to compare the classification performance of uncertain networks and certain networks in a bidirectional manner. Results showed that classification performance of the uncertain network was superior to that of the certain network within a defined sparsity range. This indicated that if a better classification performance is to be achieved, it is necessary to select a certain brain network with a higher threshold or an uncertain brain network model. Moreover, if the uncertain brain network model was selected, it is necessary to make full use of the uncertain information of its functional connection.

Reliability Maximization in Uncertain Graphs

Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and fundamental problem of adding a small number of edges in the uncertain network for maximizing the reliability between a given pair of nodes. We study the <inline-formula><tex-math notation="LaTeX">$\mathbf {NP}$</tex-math></inline-formula> -hardness and the approximation hardness of our problem, and design effective, scalable solutions. Furthermore, we consider extended versions of our problem (e.g., multiple source and target nodes can be provided as input) to support and demonstrate a wider family of queries and applications, including sensor network reliability maximization and social influence maximization. Experimental results validate the effectiveness and efficiency of the proposed algorithms.

AI-aided general clinical diagnoses verified by third-parties with dynamic uncertain causality graph extended to also include classification

Artificial intelligence (AI)-aided general clinical diagnosis is helpful to primary clinicians. Machine learning approaches have problems of generalization, interpretability, etc. Dynamic Uncertain Causality Graph (DUCG) based on uncertain casual knowledge provided by clinical experts does not have these problems. This paper extends DUCG to include the representation and inference algorithm for non-causal classification relationships. As a part of general clinical diagnoses, six knowledge bases corresponding to six chief complaints (arthralgia, dyspnea, cough and expectoration, epistaxis, fever with rash and abdominal pain) were constructed through constructing subgraphs relevant to a chief complaint separately and synthesizing them together as the knowledge base of the chief complaint. A subgraph represents variables and causalities related to a single disease that may cause the chief complaint, regardless of which hospital department the disease belongs to. Verified by two groups of third-party hospitals independently, total diagnostic precisions of the six knowledge bases ranged in 96.5–100%, in which the precision for every disease was no less than 80%.

Intelligent diagnosis system for jaundice based on dynamic uncertain causality graph

Intelligent diagnosis system for jaundice based on dynamic uncertain causality graph

Intelligent diagnosis system for jaundice based on dynamic uncertain causality graph

Intelligent diagnosis system for jaundice based on dynamic uncertain causality graph

Uncertain graph generating approach based on differential privacy for preserving link relationship of social networks

Uncertain graph generating approach based on differential privacy for preserving link relationship of social networks

Stable structural clustering in uncertain graphs

The uncertain graph is widely used to model and analyze graph data in which the relation between objects is uncertain. We here study the structural clustering in uncertain graphs. As an important method in graph clustering, structural clustering can not only discover the densely connected core vertices, but also the hub vertices and the outliers. We propose a new clustering model named stable structural clustering, to solve the problem existing in previous models that the mined core vertex is a ‘real’ core one in only a small amount of possible worlds of the uncertain graph. Specifically, we first propose the concept of probability core reliability which measures the probability of a vertex being a core vertex in the uncertain graph. On the basis of probability core reliability, we propose the definition of stable core vertex and formulate the stable structural clustering problem. Comparing with other structural clustering models, the proposed stable structural clustering performs better in crucial indicators that reflect the quality of clustering. We develop two algorithms to calculate stable core vertex, a precise dynamic programming based algorithm and a sampling based algorithm with some effective pruning techniques, based on which we give our structural clustering algorithm. Extensive experiments show that comparing with other structural clustering algorithms in uncertain graphs, the stable structural clustering algorithms proposed can get better clustering to a certain extent.

Efficient computation of target-oriented link criticalness centrality in uncertain graphs

We challenge the problem of efficiently identifying critical links that substantially degrade network performance if they do not function under a realistic situation where each link is probabilistically disconnected, e.g., unexpected traffic accident in a road network and unexpected server down in a communication network. To solve this problem, we utilize the bridge detection technique in graph theory and efficiently identify critical links in case the node reachability is taken as the performance measure.To be more precise, we define a set of target nodes and a new measure associated with it, Target-oriented latent link Criticalness Centrality (TCC), which is defined as the marginal loss of the expected number of nodes in the network that can reach, or equivalently can be reached from, one of the target nodes, and compute TCC for each link by use of detected bridges. We apply the proposed method to two real-world networks, one from social network and the other from spatial network, and empirically show that the proposed method has a good scalability with respect to the network size and the links our method identified possess unique properties. They are substantially more critical than those obtained by the others, and no known measures can replace the TCC measure.

Iterative learning control for consensus of second-order multi-agent systems with interval uncertain topologies

Abstract This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.

EGG+: A graph grammar formalism with uncertain structure processing mechanism

Abstract Extended from string grammars, graph grammar is a 2D formal method, which could specify the syntax structures of visual programming languages intuitively yet formally. However, the graph matching conditions in most graph grammars are too strict in specified applications, influencing the flexibility and fault tolerant capability of graph grammar. To solve the problems, this paper introduces an uncertain structure processing mechanism into graph grammar formalism and proposes a new graph grammar named EGG+. Different from traditional graph grammars, EGG+ defines a class of special edges named uncertain edges to specify the uncertain relationships between graphical elements. Each graph with uncertain edge is defined an uncertain graph, as a prototype of a set of graphical structures. By the new terms and definitions, EGG+ productions are divided into two categories: certain productions and uncertain productions, where certain productions specify the structures with strict matching requirements and uncertain productions are used to ignore specified syntactical errors during derivation and reduction, providing fault tolerant capability for the accessible non-isomorphic structures. Moreover, a redex searching algorithm with polynomial time complexity is designed for the convenience of grammatical application in the new formalism.

Dynamic Uncertain Causality Graph Applied to the Intelligent Evaluation of a Shale-Gas Sweet Spot

Shale-gas sweet-spot evaluation as a critical part of shale-gas exploration and development has always been the focus of experts and scholars in the unconventional oil and gas field. After comprehensively considering geological, engineering, and economic factors affecting the evaluation of shale-gas sweet spots, a dynamic uncertainty causality graph (DUCG) is applied for the first time to shale-gas sweet-spot evaluation. A graphical modeling scheme is presented to reduce the difficulty in model construction. The evaluation model is based on expert knowledge and does not depend on data. Through rigorous and efficient reasoning, it guarantees exact and efficient diagnostic reasoning in the case of incomplete information. Multiple conditional events and weighted graphs are proposed for specific problems in shale-gas sweet-spot evaluation, which is an extension of the DUCG that defines only one conditional event for different weighted function events and relies only on the experience of a single expert. These solutions make the reasoning process and results more objective, credible, and interpretable. The model is verified with both complete data and incomplete data. The results show that compared with other methods, this methodology achieves encouraging diagnostic accuracy and effectiveness. This study provides a promising auxiliary tool for shale-gas sweet spot evaluation.

Effective and efficient aggregation on uncertain graphs

Large-scale graphs are widely used to model the entities and their complex relations. Uncertain graphs are adopted when the relations between entities contain some uncertainty. However, the inherent uncertainties, which are embedded underlying the data and structure of the graphs derived from various sources introduce difficulties on data analysis. To understand the underlying characteristics of large graphs, graph aggregation techniques are critical. However, the existing graph aggregation techniques are designed for deterministic graphs therefore are not applicable on uncertain graphs. In this paper, we provide the first attempt on addressing the aggregation problem on uncertain graphs. To deal with the computation complexity of the aggregation problem, we propose a heuristic-based aggregation algorithm for uncertain graphs and some optimization methods to improve its efficiency in real world implementation. Besides the optimization, to further speed up the process, we design a parallel aggregation implementation approach. The intensive evaluations on the two datasets, DBLP and Flickr, demonstrate that our proposed algorithms are able to produce high quality aggregation results within reasonable operation time and the parallel implementation accelerates the aggregation by up to 82 times compared with the baseline algorithm.

The Application of Dynamic Uncertain Causality Graph Based Diagnosis and Treatment Unification Model in the Intelligent Diagnosis and Treatment of Hepatitis B

Although hepatitis B is widespread, it is hard to cure. This paper presents a new and more accurate model for the diagnosis and treatment of hepatitis B. Based on previous research, the diagnosis and treatment modes were combined into one. By adding more influencing factors and risk factors, the overall diagnosis and treatment model will be further expanded, and a richer and more detailed overall diagnosis and treatment model will be constructed. Reverse logic gates are used in the model to improve the accuracy of the treatment planning. The new unified model is more accurate in subdividing diagnosis results, and it is more flexible and accurate in providing dynamic treatment plans. The prediction process and the static diagnosis process of the model are symmetric, and the related sub-graph is symmetric in structure. In addition, an algorithm for predicting the response probability of treatment scheme is developed, so as to predict the subsequent treatment effects of the current treatment scheme, such as the probability of drug resistance. The results show that this method is more accurate than other available systems, and it has encouraging diagnostic accuracy and effectiveness, which provides a promising help for doctors in diagnosing hepatitis B.

Community Search in Spatial Uncertain Network

Community search is to explore valuable target community structure from a large social network. In real community, every point has a geographic location information, and many edges are uncertain. Such a network is called spatial uncertain network. In order to meet the existing needs, this paper studies the community search in the spatial uncertain network so that the searched communities can be relatively close in the geographical location and the relationship between each other is also very close. Based on the spatial uncertain graph, this paper proposes K-R-τ community, and proposes a linear algorithm and a two-dimensional algorithm for community search in the spatial uncertain network. A large number of experiments are carried out on several real datasets, and the results show that the algorithm proposed in this paper is effective and accurate.

Uncertain Graph Neural Networks for Facial Action Unit Detection

Capturing the dependencies among different facial action units (AU) is extremely important for the AU detection task. Many studies have employed graph-based deep learning methods to exploit the dependencies among AUs. However, the dependencies among AUs in real world data are often noisy and the uncertainty is essential to be taken into consideration. Rather than employing a deterministic mode, we propose an uncertain graph neural network (UGN) to learn the probabilistic mask that simultaneously captures both the individual dependencies among AUs and the uncertainties. Further, we propose an adaptive weighted loss function based on the epistemic uncertainties to adaptively vary the weights of the training samples during the training process to account for unbalanced data distributions among AUs. We also provide an insightful analysis on how the uncertainties are related to the performance of AU detection. Extensive experiments, conducted on two benchmark datasets, i.e., BP4D and DISFA, demonstrate our method achieves the state-of-the-art performance.

Shortest path problem on uncertain networks: An efficient two phases approach

Finding the shortest path on uncertain transportation networks is a great challenge in theory and practice. There are several resources of uncertainty in the transportation networks such as traffic congestion, weather conditions, vehicle accidents, repairing roads, etc. A natural way to model uncertain networks is utilizing graphs with uncertain edges, that is, the weight of each edge, as the traveling time, may vary in an interval. In this paper, we not only discuss the theoretical aspect of this issue, but also propose a practical approach to find the shortest path on uncertain graphs. The approach has two phases; a preprocessing phase and a query phase. In the preprocessing phase, we construct a general map that contains all the edges that may lie on some shortest path, and in the query phase, when the weights are determined certainly, we find the shortest path using the map. Finally, we demonstrate the effectiveness of the proposed algorithm on both random generated graphs and real-world networks. Also, we compare it with other shortest path algorithms in the uncertainty context and shows its efficiency.

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.

Core Decomposition on Uncertain Graphs Revisited

Core decomposition on uncertain graphs is a fundamental problem in graph analysis. Given an uncertain graph G, the core decomposition problem is to determine all (k, \eta)-cores in G, where a (k, \eta)-core is a maximal subgraph of G such that each node has an \eta-degree no less than k within the subgraph. The state-of-the-art algorithm for solving this problem is based on a peeling technique which iteratively removes nodes with the smallest \eta-degrees and also dynamically updates their neighbors' \eta-degrees. Unfortunately, we find that such a peeling algorithm with the dynamical \eta-degree updating technique is incorrect due to the inaccuracy of the recursive floating-point number division operations involved in the dynamical updating procedure. To solve this problem, we propose a bottom-up algorithm based on an on-demand computational strategy. To further improve the efficiency, we also develop a more-efficient top-down algorithm with several nontrivial optimization techniques. Both of our algorithms do not involve any floating-point number division operations, thus the correctness can be guaranteed. We conduct extensive experiments to evaluate our algorithms using five large real-life datasets. The results show that our algorithms are at least three orders of magnitude faster than the existing exact algorithms on large uncertain graphs.

Efficient Top-k Vulnerable Nodes Detection in Uncertain Graphs

Uncertain graphs have been widely used to model complex linked data in many applications, such as guaranteed-loan networks and power grids. In these networks, a node usually has a certain chance of default due to self-factors or the influence from upstream nodes. For regulatory authorities, it is critical to efficiently identify the vulnerable nodes, i.e., nodes with high default risks, such that they could pay more attention to these nodes for the purpose of risk management. In this paper, we propose and investigate the top-k vulnerable nodes detection problem in uncertain graphs. We formally define the model and prove it hardness. A sampling-based approach is first proposed. Rigorous theoretical analysis is conducted to bound the quality of returned results. Novel optimization techniques and a bottom-k sketch based approach are further developed to scale for large networks. We demonstrate the performance of proposed techniques on 3 real financial networks and 5 benchmark networks. Moreover, to further verify the advantages of our model, we integrate the proposed techniques with our loan risk control system, which is deployed in the collaborated bank. Particularly, we show that our proposed model can better estimate the default risks of enterprises compared to the state-of-the-art techniques.