Partial Graph Research Articles

Self-Guided Partial Graph Propagation for Incomplete Multiview Clustering.

In this work, we study a more realistic challenging scenario in multiview clustering (MVC), referred to as incomplete MVC (IMVC) where some instances in certain views are missing. The key to IMVC is how to adequately exploit complementary and consistency information under the incompleteness of data. However, most existing methods address the incompleteness problem at the instance level and they require sufficient information to perform data recovery. In this work, we develop a new approach to facilitate IMVC based on the graph propagation perspective. Specifically, a partial graph is used to describe the similarity of samples for incomplete views, such that the issue of missing instances can be translated into the missing entries of the partial graph. In this way, a common graph can be adaptively learned to self-guide the propagation process by exploiting the consistency information, and the propagated graph of each view is in turn used to refine the common self-guided graph in an iterative manner. Thus, the associated missing entries can be inferred through graph propagation by exploiting the consistency information across all views. On the other hand, existing approaches focus on the consistency structure only, and the complementary information has not been sufficiently exploited due to the data incompleteness issue. By contrast, under the proposed graph propagation framework, an exclusive regularization term can be naturally adopted to exploit the complementary information in our method. Extensive experiments demonstrate the effectiveness of the proposed method in comparison with state-of-the-art methods. The source code of our method is available at the https://github.com/CLiu272/TNNLS-PGP.

Simple and Efficient Partial Graph Adversarial Attack: A New Perspective

Simple and Efficient Partial Graph Adversarial Attack: A New Perspective

Conditions for chainability of inverse limits on [0,1] with interval-valued functions

For an inverse sequence on [0,1] with interval-valued functions, we establish necessary conditions on the bonding functions for chainability of the inverse limit space. We also characterize chainability of the inverse limit in this setting in terms of properties of the bonding functions fi and the induced functions Fn:[0,1]→G′(f1,…,fn−1). The properties, in both cases, are related to how triods arise in the partial graphs associated with the inverse sequence when each graph G(fi) is chainable.

Absent Multiview Semisupervised Classification.

With the advent of vast data collection ways, data are often with multiple modalities or coming from multiple sources. Traditional multiview learning often assumes that each example of data appears in all views. However, this assumption is too strict in some real applications such as multisensor surveillance system, where every view suffers from some data absent. In this article, we focus on how to classify such incomplete multiview data in semisupervised scenario and a method called absent multiview semisupervised classification (AMSC) has been proposed. Specifically, partial graph matrices are constructed independently by anchor strategy to measure the relationships among between each pair of present samples on each view. And to obtain unambiguous classification results for all unlabeled data points, AMSC learns view-specific label matrices and a common label matrix simultaneously. AMSC measures the similarity between pair of view-specific label vectors on each view by partial graph matrices, and consider the similarity between view-specific label vectors and class indicator vectors based on the common label matrix. To characterize the contributions of different views, the p th root integration strategy is adopted to incorporate the losses of different views. By further analyzing the relation between the p th root integration strategy and exponential decay integration strategy, we develop an efficient algorithm with proved convergence to solve the proposed nonconvex problem. To validate the effectiveness of AMSC, comparisons are made with some benchmark methods on real-world datasets and in the document classification scenario as well. The experimental results demonstrate the advantages of our proposed approach.

A Robust Framework for One-Shot Key Information Extraction via Deep Partial Graph Matching.

Text field labelling plays a key role in Key Information Extraction (KIE) from structured document images. However, existing methods ignore the field drift and outlier problems, which limit their performance and make them less robust. This paper casts the text field labelling problem into a partial graph matching problem and proposes an end-to-end trainable framework called Deep Partial Graph Matching (dPGM) for the one-shot KIE task. It represents each document as a graph and estimates the correspondence between text fields from different documents by maximizing the graph similarity of different documents. Our framework obtains a strict one-to-one correspondence by adopting a combinatorial solver module with an extra one-to-(at most)-one mapping constraint to do the exact graph matching, which leads to the robustness of the field drift problem and the outlier problem. Finally, a large one-shot KIE dataset named DKIE is collected and annotated to promote research of the KIE task. This dataset will be released to the research and industry communities. Extensive experiments on both the public and our new DKIE datasets show that our method can achieve state-of-the-art performance and is more robust than existing methods.

Incomplete Graph Learning via Partial Graph Convolutional Network

Incomplete Graph Learning via Partial Graph Convolutional Network

Multi-hop community question answering based on multi-aspect heterogeneous graph

Community question answering aims to connect queries and answers based on users' community behaviors, find the most relevant solutions for newly raised questions, and improve community activity. Existing research mainly focuses on the single-hop method, which relies on a particular feature for simple question answering. However, multi-hop question answering, which depends on multi-step reasoning to solve complex questions, still faces the destitute adaptability caused by various entity features and complex entity correlations. In this work, we put forward a Multi-Hop Community Question-Answering method called MHCQA, that combines the multi-aspect features of community entities, constrains the answer retrieval process from different perspectives and improves the adaptability of multi-hop answer retrieval. Firstly, we utilize phrases for representing the semantic features of question-answering and fuse them with entity constitution properties through heterogeneous graphs to effectively indicate the diverse relationships among entities in communities. At the same time, we bring a dynamic heterogeneous network construction strategy to improve the efficiency of feature representation. Secondly, we enhance heterogeneous graph attention networks for efficiently computing local entity similarities to find relevant answers to questions based on partial graphs. Finally, we propose a multi-constraint multi-hop community question-answering method, which optimizes answer retrieval from three aspects: the hop count, the number of answers, and the relevance of responses, to improve the scene adaptability of multi-hop answer retrieving. Abundant experiments on realistic corpus (Quora, Math, Super User, and Stack Overflow) illustrate that MHCQA improves the multi-hop question answering error rate by about 2 % and is about 11 % ahead of the baselines in terms of operating efficiency. Given our present literature survey, MHCQA is a promising research idea for automatic answering services in online question-answering communities.

Multi-channel Partial Graph Integration Learning of Partial Multi-omics Data for Cancer Subtyping

Background: The appearance of cancer subtypes with different clinical significance fully reflects the high heterogeneity of cancer. At present, the method of multi-omics integration has become more and more mature. However, in the practical application of the method, the omics of some samples are missing. Objective: The purpose of this study is to establish a depth model that can effectively integrate and express partial multi-omics data to accurately identify cancer subtypes. Methods: We proposed a novel partial multi-omics learning model for cancer subtypes, MPGIL (Multichannel Partial Graph Integration Learning). MPGIL has two main components. Firstly, it obtains more lateral adjacency information between samples within the omics through the multi-channel graph autoencoders based on high-order proximity. To reduce the negative impact of missing samples, the weighted fusion layer is introduced to replace the concatenate layer to learn the consensus representation across multi-omics. Secondly, a classifier is introduced to ensure that the consensus representation is representative of clustering. Finally, subtypes were identified by K-means. Results: This study compared MPGIL with other multi-omics integration methods on 16 datasets. The clinical and survival results show that MPGIL can effectively identify subtypes. Three ablation experiments are designed to highlight the importance of each component in MPGIL. A case study of AML was conducted. The differentially expressed gene profiles among its subtypes fully reveal the high heterogeneity of cancer. Conclusion: MPGIL can effectively learn the consistent expression of partial multi-omics datasets and discover subtypes, and shows more significant performance than the state-of-the-art methods.

USAGE : Uncertain flow graph and spatio-temporal graph convolutional network-based saturation attack detection method

With the development of Software-Defined Networking (SDN), its security problems have attached interests from academia. The saturation attack targeted at the SDN switch is one of the most destructive problems in SDN. The saturation attack can destroy SDN networks by depleting the computation and storage resources of SDN switches. Currently, graph neural networks have already been used for detecting saturation attacks in SDN. When constructing the graph based on K-Nearest Neighbors (KNN) algorithm, the number of edges in the graph is fixed. That may fail on accurately representing the relationship among different nodes. In addition, when using the Graph Convolutional Network (GCN) to detect saturation attack against SDN, only a partial graph structure and node features will be learned, causing the flow graph nodes information cannot be fully utilized. To overcome these issues, in this work, we propose USAGE, an uncertain flow graph and spatio-temporal graph neural network-based saturation attack detection method. More specifically, USAGE designs the CRAM algorithm and EGG model. The CRAM algorithm is proposed to generate an uncertain flow graph for each network traffic flow, which can represent the uncertain relationship among different nodes. EGG is a spatio-temporal graph convolutional network model, which is proposed to detect saturation attacks. The evaluation results demonstrate that USAGE can generate a better graph than KNN and achieve high detection performance. Meanwhile, USAGE outperforms other methods in terms of TPR, TNR, accuracy, precision, recall, F-score, confusion matrix, ROC curves, and PR curves.

Measuring the Privacy Leakage via Graph Reconstruction Attacks on Simplicial Neural Networks (Student Abstract)

In this paper, we measure the privacy leakage via studying whether graph representations can be inverted to recover the graph used to generate them via graph reconstruction attack (GRA). We propose a GRA that recovers a graph's adjacency matrix from the representations via a graph decoder that minimizes the reconstruction loss between the partial graph and the reconstructed graph. We study three types of representations that are trained on the graph, i.e., representations output from graph convolutional network (GCN), graph attention network (GAT), and our proposed simplicial neural network (SNN) via a higher-order combinatorial Laplacian. Unlike the first two types of representations that only encode pairwise relationships, the third type of representation, i.e., SNN outputs, encodes higher-order interactions (e.g., homological features) between nodes. We find that the SNN outputs reveal the lowest privacy-preserving ability to defend the GRA, followed by those of GATs and GCNs, which indicates the importance of building more private representations with higher-order node information that could defend the potential threats, such as GRAs.

A massively parallel evolutionary algorithm for the partial Latin square extension problem

The partial Latin square extension problem is to fill as many as possible empty cells of a partially filled Latin square. This problem is a useful model for a wide range of applications in diverse domains. This paper presents the first massively parallel evolutionary algorithm for this computationally challenging problem based on a transformation of the problem to partial graph coloring. The algorithm features the following original elements. Based on a very large population (with more than 104 individuals) and modern graphical processing units, the algorithm performs many local searches in parallel to ensure an intensive exploitation of the search space. The algorithm employs a dedicated crossover with a specific parent matching strategy to create a large number of diversified and information-preserving offspring at each generation. Extensive experiments on 1800 benchmark instances show a high competitiveness of the algorithm compared to the current best performing methods. Competitive results are also reported on the related Latin square completion problem. Analyses are performed to shed lights on the roles of the main algorithmic components.

Analysing ill-conditioned Markov chains.

Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Branch-and-refine for solving time-expanded MILP formulations

One of the standard approaches for solving discrete optimization problems which include the aspect of time, such as the traveling salesman problem with time windows or the shortest path problem with time windows is to derive a so-called time-indexed formulation. If the problem has an underlying structure that can be described by a graph, the time-indexed formulation is usually based on a different, extended graph, commonly referred to as the time-expanded graph. The time-expanded graph can often be derived in such a way that all time constraints are incorporated in its topology, and therefore algorithms for the corresponding time-independent variant become applicable. The downside of this approach is, that the sets of vertices and arcs of the time-expanded graph are much larger than the ones of the original graph. In recent works, however, it has been shown that for many practical applications a partial graph expansion, that might contain time infeasible paths, often suffices to find a proven optimal solution. These approaches, instead, iteratively refine the original graph and solve a relaxation of the time-expanded formulation in each iteration. When the solution of the current relaxation is time feasible an optimal solution can be derived from it and the algorithm terminates. In this work we present new ideas, that allow for the propagation of information about the optimal solution of a coarser graph to a more refined graph and show how these can be used in algorithms, which are based on graph refinement. More precisely we present a new algorithm for solving Mixed Integer Linear Program (MILP) formulations that allows for the graph refinement to be carried out during the exploration of the branch-and-bound tree instead of restarting whenever the optimal solution was found to be infeasible. For demonstrating the practical relevance of this algorithm we present numerical results on its application to the shortest path problem with time windows and the traveling salesman problem with time windows.

Influence of Teaching and Course Evaluation of Performing Arts Students Based on Improved Ant Colony Algorithm and Data Fusion

Teaching quality evaluation plays a very important role in the evaluation of teaching and learning in universities, especially in performing arts courses. Therefore, in this study, the application and detailed analysis process of clustering analysis on student performance data is used to finally obtain the guidance of clustering results on teaching and management. A mathematical model of teachers was established using graph theory to transform the evaluation process into a bipartite graph model and to fully utilize the memory capacity, mastery of prior knowledge, adaptability, and collaboration of the ant colony algorithm. Moving back and forth between the two sets of partial graphs completed the evaluation of the teacher teaching process. In addition, the maximum and minimum pheromone strategies were applied in the original ant colony algorithm; the robustness of the algorithm itself was enhanced by making full use of the memory ability and the necessary prior knowledge mastery in solving the teacher teaching evaluation problem. For the unqualified teachers, according to the principle of PDCA (quality environment), regular training, mutual lectures, and further training can be adopted to improve teachers’ teaching levels. Through comparison, it is found that the general and practical courses of art performance majors do not have professional characteristics, and the professional courses are mostly dance and performance courses, while physical education, sports training, and other related courses are insufficient. Through the method of this study, all students are concentrated in the group of teachers with higher satisfaction, and “teaching” can achieve the expected effect and provide theoretical and practical basis for the development of performing arts courses.

Four Way Human Quantum Turiyam Cognition Analysis

Recently, the Turiyam set was introduced for characterization of data sets beyond true, false and uncertain regions. This set is able to represent unknown, undefined, or conduit metaphor of human quantum cognition. One of the examples is USA-Russia conflicts or Cold war is beyond the characterization of win, draw or loss. It is totally based on the conduit metaphor of USA and Russia. In this case, a set of countries may support Russia (Sr) can be characterized as true regions. A set of countries does not support Russia (i.e. supporting the USA) can be characterized as false regions (Su). A set of countries supports both Russia-USA based on the given situation. These types of countries and their vote is uncertain. The fourth case is some countries like India, China, UAE choose nothing to fulfill their conduit metaphor. It is called Turiyam or four dimension cognition. The characterization of this four dimension data and its graphical visualization is one of the crucial tasks for the current researchers. To tackle this issue, the current paper will try to introduce a method for characterization of this undefined, unknown or Turiyam cognition via a defined interval-set. The objective is to provide a way to explore them in known graph (t), not known graph (f), partial graph (i) or unknown graph (l) with an example.

Atriodic tree-like continua as inverse limits on [0,1] with interval-valued functions

For an inverse sequence on [0,1] with interval-valued functions, it is shown that chainability of the graphs of the bonding functions, and chainability of the partial graphs associated with the inverse sequence are necessary conditions for an atriodic tree-like inverse limit. An analogous result is proved for inverse sequences with functions fi where each fi−1 is interval-valued. It follows that non-chainable, atriodic tree-like continua cannot be realized as inverse limits on [0,1] with functions from either of these subclasses of set-valued functions.

Adaptive partial graph learning and fusion for incomplete multi‐view clustering

Adaptive partial graph learning and fusion for incomplete multi‐view clustering

River Stage Forecasting using Enhanced Partial Correlation Graph

River Stage Forecasting using Enhanced Partial Correlation Graph

Addressing indirect frequency coupling via partial generalized coherence

Distinguishing between direct and indirect frequency coupling is an important aspect of functional connectivity analyses because this distinction can determine if two brain regions are directly connected. Although partial coherence quantifies partial frequency coupling in the linear Gaussian case, we introduce a general framework that can address even the nonlinear and non-Gaussian case. Our technique, partial generalized coherence (PGC), expands prior work by allowing pairwise frequency coupling analyses to be conditioned on other processes, enabling model-free partial frequency coupling results. By taking advantage of recent advances in conditional mutual information estimation, we are able to implement our technique in a way that scales well with dimensionality, making it possible to condition on many processes and produce a partial frequency coupling graph. We analyzed both linear Gaussian and nonlinear simulated networks. We then performed PGC analysis of calcium recordings from mouse olfactory bulb glomeruli under anesthesia and quantified the dominant influence of breathing-related activity on the pairwise relationships between glomeruli for breathing-related frequencies. Overall, we introduce a technique capable of eliminating indirect frequency coupling in a model-free way, empowering future research to correct for potentially misleading frequency interactions in functional connectivity analyses.

The partial duplication random graph with edge deletion

The partial duplication random graph with edge deletion