Constrained Graph Research Articles

Incorporating hydrological constraints with deep learning for streamflow prediction

Streamflow prediction is a fundamental task serving for flood prevention and efficient water resource management. Deep learning-based methods have emerged as the dominant approach and have made remarkable progress in the task. However, these methods ignore the hydrological constraints on streamflow, such as water delay time and streamflow direction, resulting in inaccurate prediction. To address this problem, this study incorporates hydrological constraints with deep learning models to improve streamflow prediction, and develops a hydrological constrained graph convolutional network (HCGCN) model. Specifically, the model designs a time-delayed spatiotemporal directed graph to present the spatiotemporal relationships and hydrological constraints, and develops a hydrological feature aggregation module to adaptively learn the complex spatiotemporal dependencies. In addition, HCGCN proposes a streamflow prediction neural network to predict streamflow by stacking the feature aggregation modules. Experimental results show that HCGCN significantly improves the prediction accuracy in a real streamflow prediction task. This study provides an exploration of introducing hydrological constraints to improve streamflow prediction, and provides a new reference for various hydrological prediction tasks.

Ising-Machine-Based Solver for Constrained Graph Coloring Problems

Ising-Machine-Based Solver for Constrained Graph Coloring Problems

Graph partitioning algorithms with biological connectivity decisions for neuron reconstruction in electron microscope volumes

Neuron reconstruction algorithms used in electron microscope volumes have received increasing attention in recent years. Most current methods are highly reliant on neuron membrane boundary evidence without considering biological plausibility. In this investigation, we present a novel neuron reconstruction framework via the fusion of a global optimization goal and biologically inspired priors. We encode the 3D instances of synapses and mitochondria as two types of constraints to allow for the direct inclusion of non-local connectivity information in the neuron segmentation. Moreover, a flexible decision procedure is designed to retain high-confidence priors to deal with the possible influence of the upstream ultrastructure error. We construct the constrained graph partitioning model and adapt two greedy algorithms with the polynomial time complexity to solve the proposed model. We perform comparative studies on several public datasets and demonstrate that the decision of ultrastructural connectivity constraints contributes to significant improvements over existing hierarchical agglomeration algorithms. The ablation studies of ultrastructures from different recognition accuracy suggest the generality and applicability of the proposed method.

Egocentric video co-summarization using transfer learning and refined random walk on a constrained graph

In this paper, we address the problem of egocentric video co-summarization. We show how a shot level accurate summary can be obtained in a time-efficient manner using random walk on a constrained graph in transfer learned feature space with label refinement. While applying transfer learning, we propose a new loss function capturing egocentric characteristics in a pre-trained ResNet on the set of auxiliary egocentric videos. Transfer learning is used to generate i) an improved feature space and ii) a set of labels to be used as seeds for the test egocentric video. A complete weighted graph is created for a test video in the new transfer learned feature space with shots as the vertices. We derive two types of cluster label constraints in form of Must-Link (ML) and Cannot-link (CL) based on the similarity of the shots. ML constraints are used to prune the complete graph which is shown to result in substantial computational advantage, especially, for the long duration videos. We derive expressions for the number of vertices and edges for the ML-constrained graph and show that this graph remains connected. Random walk is applied to obtain labels of the unmarked shots in this new graph. CL constraints are applied to refine the cluster labels. Finally, shots closest to individual cluster centres are used to build the summary. Experiments on the short duration videos as in CoSum and TVSum datasets and long duration videos as in ADL and EPIC-Kitchens datasets clearly demonstrate the advantage of our solution over several state-of-the-art methods.

Semi-supervised constrained graph convolutional network for cross-modal retrieval

Exploiting relationship among samples in cross-modal data plays a key role in the task of cross-modal retrieval, but most of existing methods only extract the correlation from pairwise samples and ignore the relations of unpaired samples. Some graph regularization methods proposed a reasonable paradigm to exploit the correlation from multiple samples. However, limited by the traditional framework, the performance has much room to improve. Moreover, although some existing DNN-based methods achieve excellent performance, the requirement of massive labeled data is also a shortcoming. In this paper, we propose a novel semi-supervised method, named Semi-supervised Constrained Graph Convolutional Network (SCGCN), which adopts graph convolutional network to exploit correlation from batch samples of data with different modalities. For reducing the requirement of labeled data, we design a two stage training procedure: deep supervised learning stage and unsupervised learning stage. In deep supervised learning stage, we integrate two DNN-based semantic encoding networks and a shared classifier into Deep Cross-modal Semantic Encoding (DCSE) module which is trained by supervised learning with labeled data. From DCSE module, we learn a temporary modality-invariant space where the semantic embeddings of samples with different modalities are modality-invariant, and we also learn a classifier which can generate predicted label from the unlabeled data. In unsupervised learning stage, for fully exploiting the correlation from cross-modal data, we design a Constrained Graph Convolutional Network (CGCN) module which utilizes GCN to exploit the correlation and adopts both intra-modal discriminative loss and inter-modal pairwise similar loss to ensure the generated common representation modality-invariant and semantical discriminative. We perform extensive experiments on four conventional datasets and a large scale dataset to demonstrate the effectiveness of proposed approach.

NMFLRR: Clustering scRNA-Seq Data by Integrating Nonnegative Matrix Factorization With Low Rank Representation.

Fast-developing single-cell technologies create unprecedented opportunities to reveal cell heterogeneity and diversity. Accurate classification of single cells is a critical prerequisite for recovering the mechanisms of heterogeneity. However, the scRNA-seq profiles we obtained at present have high dimensionality, sparsity, and noise, which pose challenges for existing clustering methods in grouping cells that belong to the same subpopulation based on transcriptomic profiles. Although many computational methods have been proposed developing novel and effective computational methods to accurately identify cell types remains a considerable challenge. We present a new computational framework to identify cell types by integrating low-rank representation (LRR) and nonnegative matrix factorization (NMF); this framework is named NMFLRR. The LRR captures the global properties of original data by using nuclear norms, and a locality constrained graph regularization term is introduced to characterize the data's local geometric information. The similarity matrix and low-dimensional features of data can be simultaneously obtained by applying the alternating direction method of multipliers (ADMM) algorithm to handle each variable alternatively in an iterative way. We finally obtained the predicted cell types by using a spectral algorithm based on the optimized similarity matrix. Nine real scRNA-seq datasets were used to test the performance of NMFLRR and fifteen other competitive methods, and the accuracy and robustness of the simulation results suggest the NMFLRR is a promising algorithm for the classification of single cells. The simulation code is freely available at: https://github.com/wzhangwhu/NMFLRR_code.

Multi-view unsupervised feature selection with tensor low-rank minimization

To describe objects more comprehensively and accurately, multi-view learning has attracted considerable attention. Recently, graph embedding based multi-view feature selection methods have been proposed and shown efficient in many real applications. The existing methods generally construct one common graph matrix to exploit the local structure of multi-view data via the linear weight fusion or learning one common graph matrix across all views. However, since all views share the identical graph structure, this emphasizes the consistency too much, resulting in restricting the diversity among different views. In this paper, a tensor low-rank constrained graph embedding method is proposed for multi-view unsupervised feature selection. To embody the view-specific information of each view, our model constructs the graph structure for each corresponding view, respectively. To capture the consistency across views, a tensor low-rank regularization constraint is imposed on the tensor data formed by these graph matrices. An efficient optimization algorithm with theoretical convergence guarantee is designed to solve the proposed method. Extensive experimental results validate that the proposed method outperforms some state-of-the-art methods. The code of our model can be found athttps://www.researchgate.net/publication/353902948_demoTLR.

Total Variation Constrained Graph Manifold Learning Strategy for Cerenkov Luminescence Tomography.

Harnessing the power and flexibility of radiolabeled molecules, Cerenkov luminescence tomography (CLT) provides a novel technique for non-invasive visualisation and quantification of viable tumour cells in a living organism. However, owing to the photon scattering effect and the ill-posed inverse problem, CLT still suffers from insufficient spatial resolution and shape recovery in various preclinical applications. In this study, we proposed a total variation constrained graph manifold learning (TV-GML) strategy for achieving accurate spatial location, dual-source resolution, and tumour morphology. TV-GML integrates the isotropic total variation term and dynamic graph Laplacian constraint to make a trade-off between edge preservation and piecewise smooth region reconstruction. Meanwhile, the tetrahedral mesh-Cartesian grid pair method based on the k-nearest neighbour, and the adaptive and composite Barzilai-Borwein method, were proposed to ensure global super linear convergence of the solution of TV-GML. The comparison results of both simulation experiments and in vivo experiments further indicated that TV-GML achieved superior reconstruction performance in terms of location accuracy, dual-source resolution, shape recovery capability, robustness, and in vivo practicability. Significance: We believe that this novel method will be beneficial to the application of CLT for quantitative analysis and morphological observation of various preclinical applications and facilitate the development of the theory of solving inverse problem.

Unsupervised RGB-T saliency detection by node classification distance and sparse constrained graph learning

Unsupervised RGB-T saliency detection by node classification distance and sparse constrained graph learning

Local search for constrained graph clustering in biological networks

Semi-supervised or constrained graph clustering incorporates prior information in order to improve clustering results. Pairwise constraints are often utilized to guide the clustering process. This work addresses a constrained graph clustering problem in biological networks where (1) subgraph connectivity constraints are strictly required to be satisfied and (2) clustering quality is assessed with respect to pairwise constraint violations. Existing constrained graph clustering methods often fail to fully satisfy connectivity constraints. This paper presents an iterated local search algorithm which aims to find the clustering with the highest quality in a short computing time. Experiments demonstrate how the proposed solutions are of good quality, often being optimal. Additionally, the proposed method significantly outperforms an existing branch-and-cut algorithm in terms of computational runtime and produces competitive results with regard to other local search techniques and graph clustering algorithms. Furthermore, a multilevel algorithm for clustering is designed to handle large-scale graphs. The performance of the overall scheme for a variety of coarsening methods from the literature is studied on a large number of biological networks exceeding 10,000 genes.

A Constrained Graph-Based Semi-Supervised Algorithm Combined with Particle Cooperation and Competition for Hyperspectral Image Classification

Semi-supervised learning (SSL) focuses on the way to improve learning efficiency through the use of labeled and unlabeled samples concurrently. However, recent research indicates that the classification performance might be deteriorated by the unlabeled samples. Here, we proposed a novel graph-based semi-supervised algorithm combined with particle cooperation and competition, which can improve the model performance effectively by using unlabeled samples. First, for the purpose of reducing the generation of label noise, we used an efficient constrained graph construction approach to calculate the affinity matrix, which is capable of constructing a highly correlated similarity relationship between the graph and the samples. Then, we introduced a particle competition and cooperation mechanism into label propagation, which could detect and re-label misclassified samples dynamically, thus stopping the propagation of wrong labels and allowing the overall model to obtain better classification performance by using predicted labeled samples. Finally, we applied the proposed model into hyperspectral image classification. The experiments used three real hyperspectral datasets to verify and evaluate the performance of our proposal. From the obtained results on three public datasets, our proposal shows great hyperspectral image classification performance when compared to traditional graph-based SSL algorithms.

Constrained Dual Graph Regularized Orthogonal Nonnegative Matrix Tri-Factorization for Co-Clustering

Coclustering approaches for grouping data points and features have recently been receiving extensive attention. In this paper, we propose a constrained dual graph regularized orthogonal nonnegative matrix trifactorization (CDONMTF) algorithm to solve the coclustering problems. The new method improves the clustering performance obviously by employing hard constraints to retain the priori label information of samples, establishing two nearest neighbor graphs to encode the geometric structure of data manifold and feature manifold, and combining with biorthogonal constraints as well. In addition, we have also derived the iterative optimization scheme of CDONMTF and proved its convergence. Clustering experiments on 5 UCI machine-learning data sets and 7 image benchmark data sets show that the achievement of the proposed algorithm is superior to that of some existing clustering algorithms.

Constraints for generating graphs with imposed and forbidden patterns: an application to molecular graphs

Although graphs are widely used to encode and solve various computational problems, little research exists on constrained graph construction. The current research was carried out to shed light on the problem of generating graphs, where the construction process is guided by various structural restrictions, like vertex degrees, proximity among vertices, and imposed and forbidden patterns. The main contribution of this paper is an encoding of the constrained graph generation problem in terms of a constraint satisfaction problem (CSP). This approach is motivated by the flurry of efficient solution algorithms available within the constraint programming (CP) framework. The obtained encoding has given rise to the CP-MolGen program, a new open source program dedicated to the generation of molecular graphs with imposed and forbidden fragments. Experimental results on several real-world molecular graph generation instances have shown the effectiveness and efficiency of the proposed program, especially the benefits of forbidding cyclic patterns as induced subgraphs.

An Efficient Approach for Graph-Based Fault Diagnosis in UAVs

In this work, we tackle the problem of systematic population of a bank of residual generators for model-based fault diagnosis in Unmanned Aerial Vehicles (UAVs). Intended for detailed, large and non-linear system models, Structural Analysis (SA) is applied to produce a graph-based abstraction of the problem in the form of a bipartite graph. The Branch and Bound Integer Linear Programming (BBILP) algorithm is employed, properly adapted to seek a solution for the constrained graph matching problem. Appropriate causality constraints are formulated, which link the structure of the system graph with the analytical form of the residual generators and certify that all resulting residual generators can be implemented automatically using numerical processes. An extensive performance investigation of the proposed approach is carried out, which is shown to be more efficient than other similar algorithms. Benchmarks of UAV models taken from the literature are presented and a simulated response of the diagnostic system against a fault in the roll-rate sensor is showcased.

Non-Negative Matrix Factorization With Locality Constrained Adaptive Graph

Non-negative matrix factorization (NMF) has recently attracted much attention due to its good interpretation in perception science and widely applications in various fields. In this paper, a novel graph regularized NMF algorithm called NMF with locality constrained adaptive graph (NMF-LCAG) is proposed. Compared with other NMF based algorithms, the proposed NMF-LCAG algorithm has the following advantages: 1) Unlike the traditional NMF method which neglects the geometric information of original data, the proposed algorithm introduces a locality constrained graph to discover the latent manifold structure of the data and 2) Different from most graph regularized NMF algorithms in which the graphs are predefined and kept unchanged during the NMF procedure, two locality constraint terms are employed in our NMF-LCAG to adaptively optimize the graph. Thus, the weight matrix of graph and low dimensional features of data can be simultaneously learned by our algorithm, which makes NMF-LCAG more flexible than other approaches. Moreover, an iterative updating strategy is developed to optimize the objective function of our algorithm and the convergence analysis is also given. Extensive experiments are conducted on four face image databases and three UCI datasets to demonstrate the effectiveness of the proposed NMF-LCAG algorithm. Compared with some other related algorithms, the proposed NMF-LCAG algorithm can achieve at least 1% ~ 3% accuracy improvement in most cases.

Constrained Graph Partitioning via Matrix Differential Equations

A novel algorithmic approach is presented for the problem of partitioning a connected undirected weighted graph under constraints such as cardinality or membership requirements or must-link and can...

A unified agent-based framework for constrained graph partitioning

Social networks offer various services such as recommendations of social events, or delivery of targeted advertising material to certain users. In this work, we focus on a specific type of services modeled as constrained graph partitioning (CGP). CGP assigns users of a social network to a set of classes with bounded capacities so that the similarity and the social costs are minimized. The similarity cost is proportional to the dissimilarity between a user and his class, whereas the social cost is measured in terms of friends that are assigned to different classes. In this work, we investigate two solutions for CGP. The first utilizes a game-theoretic framework, where each user constitutes a player that wishes to minimize his own social and similarity cost. The second employs local search, and aims at minimizing the global cost. We show that the two approaches can be unified under a common agent-based framework that allows for two types of deviations. In a unilateral deviation, an agent switches to a new class, whereas in a bilateral deviation a pair of agents exchange their classes. We develop a number of optimization techniques to improve result quality and facilitate efficiency. Our experimental evaluation on real datasets demonstrates that the proposed methods always outperform the state of the art in terms of solution quality, while they are up to an order of magnitude faster.

Nonnegative Constrained Graph Based Canonical Correlation Analysis for Multi-view Feature Learning

Understanding and analyzing multi-view data is a fundamental research topic of feature learning for a wide range of practical applications such as image classification. Canonical correlation analysis (CCA) is a popular unsupervised method of analyzing multi-view data, which captures common subspace of two groups of variable sets by maximizing the correlations between them. However, traditional CCA ignores the underlying geometric structure within dataset, which shows great power in describing data distribution, and thus fails in some tasks such as classification. To handle this limitation, this paper proposes an improved CCA variant of Nonnegative Constrained Graph regularized CCA (NCGCCA). Specifically, we improve CCA to NCGCCA with the following two contributions. Firstly, we develop a nonnegative constrained graph based self-representation to explore the underlying group-wise structure within dataset. Secondly, based on the proposed informative representation, we offer a graph embedding schema to incorporate the underlying structure into CCA. Experiments of image classification on four face datasets including Yale, ORL, UMIST, and YaleB demonstrate the efficacy of NCGCCA compared with existing baseline CCA methods.

Automatic Segmentation of Retinal Layer in OCT Images With Choroidal Neovascularization

Age-related macular degeneration is one of the main causes of blindness. However, the internal structures of retinas are complex and difficult to be recognized due to the occurrence of neovascularization. Traditional surface detection methods may fail in the layer segmentation. In this paper, a supervised method is reported for simultaneously segmenting layers and neovascularization. Three spatial features, seven gray-level-based features, and 14 layer-like features are extracted for the neural network classifier. The coarse surfaces of different optical coherence tomography (OCT) images can thus be found. To describe and enhance retinal layers with different thicknesses and abnormalities, multi-scale bright and dark layer detection filters are introduced. A constrained graph search algorithm is also proposed to accurately detect retinal surfaces. The weights of nodes in the graph are computed based on these layer-like responses. The proposed method was evaluated on 42 spectral-domain OCT images with age-related macular degeneration. The experimental results show that the proposed method outperforms state-of-the-art methods.

Revisiting Stress Majorization as a Unified Framework for Interactive Constrained Graph Visualization.

We present an improved stress majorization method that incorporates various constraints, including directional constraints without the necessity of solving a constraint optimization problem. This is achieved by reformulating the stress function to impose constraints on both the edge vectors and lengths instead of just on the edge lengths (node distances). This is a unified framework for both constrained and unconstrained graph visualizations, where we can model most existing layout constraints, as well as develop new ones such as the star shapes and cluster separation constraints within stress majorization. This improvement also allows us to parallelize computation with an efficient GPU conjugant gradient solver, which yields fast and stable solutions, even for large graphs. As a result, we allow the constraint-based exploration of large graphs with 10K nodes - an approach which previous methods cannot support.