Optimal Graph Research Articles

Self-adjusted graph based semi-supervised embedded feature selection

Graph-based semi-supervised feature selection has aroused continuous attention in processing high-dimensional data with most unlabeled and fewer data samples. Many graph-based models perform on a pre-defined graph, which is separated from the procedure of feature selection, making the model hard to select the discriminative features. To address this issue, we exploit a self-adjusted graph for semi-supervised embedded feature selection method (SAGFS), which learns an optimal sparse similarity graph to replace the pre-defined graph to alleviate the effect of data noise. SAGFS allows the learned graph itself to be adjusted according to the local geometric structure of the data and the procedure of selecting features to select the most representative features. Besides that, we introduce l2,p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_{2,p}$$\\end{document}-norm to constrain the projection matrix for efficient feature selection. An efficient alternating optimization algorithm is presented, together with analyses on its convergence. Systematical experiments on several publicly datasets are performed to analyze the proposed model from several aspects, and demonstrate that our approaches outperform other comparison methods.

Fractional Vertex Cover Reliability of Graphs

Let G be a graph and let 0 ≤ p , q and p + q ≤ 1 . Suppose that each vertex of G gets a weight of 1 with probability p , 1 2 with probability q , and 0 with probability 1 − p − q , and vertex weight probabilities are independent. The \textit{fractional vertex cover reliability} of G , denoted by FRel ( G ; p , q ) , is the probability that the sum of weights at the end-vertices of every edge in G is at least 1 . In this article, we first provide various computational formulas for FRel ( G ; p , q ) considering general graphs, basic graphs, and graph operations. Secondly, we determine the graphs which maximize FRel ( G ; p , q ) for all values of p and q in the classes of trees, connected unicyclic and bicyclic graphs with fixed order, and determine the graphs which minimize it in the classes of trees and connected unicyclic graphs with fixed order. Our results on optimal graphs extend some known results in the literature about independent sets, and the tools we developed in this paper have the potential to solve the optimality problem in other classes of graphs as well.

Learning the Graph Structure of Regular Vine-Copulas from Dependence Lists

Regular vine copulas (R-vines) provide a comprehensive framework for modeling high-dimensional dependencies using a hierarchy of trees and conditional pair-copulas. While the graphical structure of R-vines is traditionally derived from data, this work introduces a novel approach by utilizing a (conditional) pairwise dependence list. Our primary goal is to construct R-vine graphs that include the maximum possible number of dependence relationships specified in such lists. To tackle this optimization challenge, characterized by exponential growth in the search space and the structural constraints of R-vines, we propose two distinct methodologies: A 0-1 linear programming formulation and a Genetic Algorithm (GA). Additionally, the Randomized Constructive Technique (RCT) is employed to generate the initial population of the GA, serving as a baseline for our comparison. Experimental results reveal the superior performance of the GA over the RCT in terms of success rate, incorporating more relationships than RCT into the constructed R-vine graphs and achieving near-optimal or optimal graph structures.

Fast Multiview Clustering by Optimal Graph Mining.

Multiview clustering (MVC) aims to exploit heterogeneous information from different sources and was extensively investigated in the past decade. However, far less attention has been paid to handling large-scale multiview data. In this brief, we fill this gap and propose a fast multiview clustering by an optimal graph mining model to handle large-scale data. We mine a consistent clustering structure from landmark-based graphs of different views, from which the optimal graph based on the one-hot encoding of cluster labels is recovered. Our model is parameter-free, so intractable hyperparameter tuning is avoided. An efficient algorithm of linear complexity to the number of samples is developed to solve the optimization problems. Extensive experiments on real-world datasets of various scales demonstrate the superiority of our proposal.

O19 CAUSAL INFERENCE FOR HYPERTENSION DETECTION WITH WEARABLE DEVICES

Background and Objective: Hypertension is a leading cause of cardiovascular disease and premature death worldwide and it puts a heavy burden on the healthcare system. It is, therefore, very important to detect and evaluate hypertension and related cardiovascular events so as for early prevention, detection and management. Hypertension can be evaluated in real time with wearable noninvasive cardiac signals, such as electro-cardiogram (ECG) and photoplethysmography (PPG). Most previous studies predicted hypertension from ECG and PPG signals with extracted features that are correlated with hypertension. However, correlation is sometimes unreliable and may be affected by confounding factors. In this study, we explored the feasibility of predicting the risk of hypertension using causal inference methods. Additionally, we paid special attention to and verified the reliability and effectiveness of causality compared to correlation. Methods: Firstly, we constructed causal graphs by the Greedy Equivalence Search algorithm, and then applied causal strategies to obtain the optimal causal graph. Finally, we used machine learning classification algorithms to achieve hypertension prediction. Results: The machine learning classification models achieve great classification performance, with accuracy being 0.89, precision being 0.92, recall being 0.82, and F1-score being 0.87, which outperformed the correlation-based hypertension detection. Conclusions: The results indicate that the causal inference-based approach can potentially clarify the mechanism of hypertension detection with noninvasive signal and effectively detect hypertension. In addition, the results also re-veal that causality is more reliable and effective compared to correlation.

Co-regularized optimal high-order graph embedding for multi-view clustering

Real-world applications frequently involve multiple data modalities in the same samples, which are regarded as multi-view data. Multi-view clustering has been studied extensively in recent years to demonstrate embedded heterogeneity. However, most existing methods emphasize low-order correlation in multiple views, whereas approaches that incorporate high-order correlation are limited by the equal view-specific significance problem or a trade-off between global and local consistency. In this paper, we propose a co-regularized optimal graph-based clustering method known as Co-MSE, which integrates the correlation of different orders. By integrating the first-order and second-order similarities, the local structure is preserved, while an optimized embedding representation for multi-view data is obtained simultaneously through co-regularization. We demonstrate that Co-MSE can aid in providing a more suitable embedding representation and further enable satisfactory clustering performance. Extensive experiments on real-world datasets confirm the effectiveness and advantages of the proposed method.

Generation and Analysis of a Dataset of Optimal Double-Loop Circulant Networks

Optimal circulant networks are of practical interest as graph models of reliable communication networks for supercomputer systems and networks on a chip. A large dataset of parameters of optimal double-loop circulant networks with a number of nodes of up to 50,000 and 451,000 points has been constructed. The dataset contains, for each number of vertices, all generators corresponding to optimal or suboptimal (in the absence of optimal) descriptions of the graph. This made it possible to find analytical dependencies of the parameters that define families of optimal graphs. Based on the analysis of the constructed dataset, the solution to the problem of determining optimal two-dimensional circulant networks is studied. A process is automated for determining analytical, parametric descriptions of the families of optimal double-loop networks, described polynomials of diameter. Having applied the methods of integrating differential evolution and reduced local search to the analysis of the generated dataset, we rediscovered a number of previously known families and found more than 200 new, different from all those known in literature, families of optimal double-loop networks with generators of linear and quadratic types of polynomials. Our new ap­proach can be applied to studing datasets of other promising classes of graphs and networks.

Kemeny Constant-Based Optimization of Network Clustering Using Graph Neural Networks.

The recent trend in using network and graph structures to represent a variety of different data types has renewed interest in the graph partitioning (GP) problem. This interest stems from the need for general methods that can both efficiently identify network communities and reduce the dimensionality of large graphs while satisfying various application-specific criteria. Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalize to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning representations of graph data provides new approaches to solving the problem. Previous work has shown GNNs to be capable of proposing partitionings using a variety of criteria. However, these approaches have not yet been extended to Markov chains or kinetic networks. These arise frequently in the study of molecular systems and are of particular interest to the biomolecular modeling community. In this work, we propose several GNN-based architectures to tackle the GP problem for Markov Chains described as kinetic networks. This approach aims to maximize the Kemeny constant, which is a variational quantity and it represents the sum of time scales of the system. We propose using an encoder-decoder architecture and show how simple GraphSAGE-based GNNs with linear layers can outperform much larger and more expressive attention-based models in this context. As a proof of concept, we first demonstrate the method's ability to cluster randomly connected graphs. We also use a linear chain architecture corresponding to a 1D free energy profile as our kinetic network. Subsequently, we demonstrate the effectiveness of our method through experiments on a data set derived from molecular dynamics. We compare the performance of our method to other partitioning techniques, such as PCCA+. We explore the importance of feature and hyperparameter selection and propose a general strategy for large-scale parallel training of GNNs for discovering optimal graph partitionings.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

Unsupervised Graph Structure Learning Based on Optimal Graph Topology Modeling and Adaptive Data Augmentation

Unsupervised Graph Structure Learning Based on Optimal Graph Topology Modeling and Adaptive Data Augmentation

Hybrid deep learning and optimal graph search method for optical coherence tomography layer segmentation in diseases affecting the optic nerve.

Accurate segmentation of retinal layers in optical coherence tomography (OCT) images is critical for assessing diseases that affect the optic nerve, but existing automated algorithms often fail when pathology causes irregular layer topology, such as extreme thinning of the ganglion cell-inner plexiform layer (GCIPL). Deep LOGISMOS, a hybrid approach that combines the strengths of deep learning and 3D graph search to overcome their limitations, was developed to improve the accuracy, robustness and generalizability of retinal layer segmentation. The method was trained on 124 OCT volumes from both eyes of 31 non-arteritic anterior ischemic optic neuropathy (NAION) patients and tested on three cross-sectional datasets with available reference tracings: Test-NAION (40 volumes from both eyes of 20 NAION subjects), Test-G (29 volumes from 29 glaucoma subjects/eyes), and Test-JHU (35 volumes from 21 multiple sclerosis and 14 control subjects/eyes) and one longitudinal dataset without reference tracings: Test-G-L (155 volumes from 15 glaucoma patients/eyes). In the three test datasets with reference tracings (Test-NAION, Test-G, and Test-JHU), Deep LOGISMOS achieved very high Dice similarity coefficients (%) on GCIPL: 89.97±3.59, 90.63±2.56, and 94.06±1.76, respectively. In the same context, Deep LOGISMOS outperformed the Iowa reference algorithms by improving the Dice score by 17.5, 5.4, and 7.5, and also surpassed the deep learning framework nnU-Net with improvements of 4.4, 3.7, and 1.0. For the 15 severe glaucoma eyes with marked GCIPL thinning (Test-G-L), it demonstrated reliable regional GCIPL thickness measurement over five years. The proposed Deep LOGISMOS approach has potential to enhance precise quantification of retinal structures, aiding diagnosis and treatment management of optic nerve diseases.

Semi-supervised bipartite graph construction with active EEG sample selection for emotion recognition.

Electroencephalogram (EEG) signals are derived from the central nervous system and inherently difficult to camouflage, leading to the recent popularity of EEG-based emotion recognition. However, due to the non-stationary nature of EEG, inter-subject variabilities become obstacles for recognition models to well adapt to different subjects. In this paper, we propose a novel approach called semi-supervised bipartite graph construction with active EEG sample selection (SBGASS) for cross-subject emotion recognition, which offers two significant advantages. Firstly, SBGASS adaptively learns a bipartite graph to characterize the underlying relationships between labeled and unlabeled EEG samples, effectively implementing the semantic connection for samples from different subjects. Secondly, we employ active sample selection technique in this paper to reduce the impact of negative samples (outliers or noise in the data) on bipartite graph construction. Drawing from the experimental results with the SEED-IV data set, we have gained the following three insights. (1) SBGASS actively rejects negative labeled samples, which helps mitigate the impact of negative samples when constructing the optimal bipartite graph and improves the model performance. (2) Through the learned optimal bipartite graph in SBGASS, the transferability of labeled EEG samples is quantitatively analyzed, which exhibits a decreasing tendency as the distance between each labeled sample and the corresponding class centroid increases. (3) Besides the improved recognition accuracy, the spatial-frequency patterns in emotion recognition are investigated by the acquired projection matrix.

Optimal bipartite graph matching-based goal selection for policy-based hindsight learning

The sparse reward problem stands as a significant challenge in the field of reinforcement learning. Hindsight Experience Replay (HER) addresses this by goal relabeling, allowing the agent to learn from unsuccessful experiences. Some studies combine policy gradient methods with HER, resulting in policy-based hindsight learning algorithms. However, Policy-based hindsight learning involves the use of importance sampling, where the distribution of hindsight goals and the distribution of desired goals contribute to the computation of importance weights. When there is a significant difference between the two distributions, importance weights may become skewed, thereby impacting the evaluation of the policy and leading to suboptimal policies. To address this, we propose modeling the goal selection as an optimization problem for distribution matching. After we augment the original desired goals using Kernel Density Estimation (KDE), we further convert the optimization problem for distribution matching into a bipartite graph matching problem that minimizes the sum of weights. Our optimal bipartite graph matching-based hindsight goal selection method can select hindsight goals that are the most closely aligned with the original goals. Experimental results show that algorithms combined with the optimal bipartite graph matching-based hindsight goal selection outperform the original algorithms. Visualizations also demonstrate the superiority of our method in selecting hindsight goals.

An Optimal Edge-weighted Graph Semantic Correlation Framework for Multi-view Feature Representation Learning

In this article, we present an optimal edge-weighted graph semantic correlation (EWGSC) framework for multi-view feature representation learning. Different from most existing multi-view representation methods, local structural information and global correlation in multi-view feature spaces are exploited jointly in the EWGSC framework, leading to a new and high-quality multi-view feature representation. Specifically, a novel edge-weighted graph model is first conceptualized and developed to preserve local structural information in each of the multi-view feature spaces. Then, the explored structural information is integrated with a semantic correlation algorithm, labeled multiple canonical correlation analysis (LMCCA), to form a powerful platform for effectively exploiting local and global relations across multi-view feature spaces jointly. We then theoretically verified the relation between the upper limit on the number of projected dimensions and the optimal solution to the multi-view feature representation problem. To validate the effectiveness and generality of the proposed framework, we conducted experiments on five datasets of different scales, including visual-based (University of California Irvine (UCI) iris database, Olivetti Research Lab (ORL) face database, and Caltech 256 database), text-image-based (Wiki database), and video-based (Ryerson Multimedia Lab (RML) audio-visual emotion database) examples. The experimental results show the superiority of the proposed framework on multi-view feature representation over state-of-the-art algorithms.

A dynamic graph structure identification method of spatio-temporal correlation in an aluminum electrolysis cell

The dynamic correlation analysis of cell-spatial information (distributed anode current signal, DACS) is of great significance in the regional-refined control of industrial aluminum electrolysis cell. Due to the strong-dynamic spatio-temporal correlation of DACS and the complex dynamic cell noise, the existing methods are difficult to effectively obtain the spatio-temporal correlation analysis results of aluminum electrolysis cell. To solve these problems, a dynamic graph structure identification method of spatio-temporal correlation (DGSI-StC) in an aluminum electrolysis cell is proposed. The identified dynamic graph structure is used to describe the dynamic correlation analysis results of cell-spatial information. Specifically, a novel strongly robust distance function Edit Distance on Real sequences with Adaptive threshold (At-EDR) is proposed to weaken the impact of complex dynamic cell noise on the dynamic correlation analysis of cell-spatial information. Under the guidance of aluminum electrolysis process mechanism knowledge, the matrix-representation of dynamic cell noise information obtained from production data is used as the adaptive threshold of At-EDR to construct the dynamic graph structure. Then, based on the single-layer classical graph convolutional network, a framework for optimizing the dynamic graph structure is designed to capture the strong-dynamic spatio-temporal correlation of DACS. The framework obtains the optimal dynamic graph structure by optimizing the hyper-parameters. Finally, the experimental results on the public datasets show that the robustness of At-EDR is superior to existing methods. Meanwhile the experimental results on multiple sets of industrial aluminum electrolysis production datasets show that DGSI-StC improves the classification accuracy by 2.82% compared with existing classification methods.

Multimodal Graph Neural Architecture Search under Distribution Shifts

Multimodal graph neural architecture search (MGNAS) has shown great success for automatically designing the optimal multimodal graph neural network (MGNN) architecture by leveraging multimodal representation, crossmodal information and graph structure in one unified framework. However, existing MGNAS fails to handle distribution shifts that naturally exist in multimodal graph data, since the searched architectures inevitably capture spurious statistical correlations under distribution shifts. To solve this problem, we propose a novel Out-of-distribution Generalized Multimodal Graph Neural Architecture Search (OMG-NAS) method which optimizes the MGNN architecture with respect to its performance on decorrelated OOD data. Specifically, we propose a multimodal graph representation decorrelation strategy, which encourages the searched MGNN model to output representations that eliminate spurious correlations through iteratively optimizing the feature weights and controller. In addition, we propose a global sample weight estimator that facilitates the sharing of optimal sample weights learned from existing architectures. This design promotes the effective estimation of the sample weights for candidate MGNN architectures to generate decorrelated multimodal graph representations, concentrating more on the truly predictive relations between invariant features and ground-truth labels. Extensive experiments on real-world multimodal graph datasets demonstrate the superiority of our proposed method over SOTA baselines.

Progressive Multiple Alignment of Graphs

The comparison of multiple (labeled) graphs with unrelated vertex sets is an important task in diverse areas of applications. Conceptually, it is often closely related to multiple sequence alignments since one aims to determine a correspondence, or more precisely, a multipartite matching between the vertex sets. There, the goal is to match vertices that are similar in terms of labels and local neighborhoods. Alignments of sequences and ordered forests, however, have a second aspect that does not seem to be considered for graph comparison, namely the idea that an alignment is a superobject from which the constituent input objects can be recovered faithfully as well-defined projections. Progressive alignment algorithms are based on the idea of computing multiple alignments as a pairwise alignment of the alignments of two disjoint subsets of the input objects. Our formal framework guarantees that alignments have compositional properties that make alignments of alignments well-defined. The various similarity-based graph matching constructions do not share this property and solve substantially different optimization problems. We demonstrate that optimal multiple graph alignments can be approximated well by means of progressive alignment schemes. The solution of the pairwise alignment problem is reduced formally to computing maximal common induced subgraphs. Similar to the ambiguities arising from consecutive indels, pairwise alignments of graph alignments require the consideration of ambiguous edges that may appear between alignment columns with complementary gap patterns. We report a simple reference implementation in Python/NetworkX intended to serve as starting point for further developments. The computational feasibility of our approach is demonstrated on test sets of small graphs that mimimc in particular applications to molecular graphs.

First Fit Algorithm: A Graph Coloring Approach to Conflict-Free University Course Timetabling

Aims: Tackling scheduling issues with the most optimal graph coloring algorithm has consistently posed significant difficulties. The university scheduling problem can be expressed as a graph coloring problem, where courses are depicted as vertices and the connections between courses that have common students or teachers are represented as edges. Subsequently, the task at hand is to assign the vertices with the minimum number of colors. In order to accomplish this task, this paper present a graph coloring technique to conflict free university course timetabling using first fit algorithms.
 Methodology: The conflict graph is partitioned into a set of independent color classes to be assigned time slots and transformed into a conflict-free timetable. The Ladoke Akintola University of Technology (LAUTECH) University Course Timetabling Data was adopted. The allocation of venue based on the allotted time slots is done using first fit packing algorithm. The proposed model is implemented using Python programming language. The developed model had courses being represented as vertices and edges. The course conflict graph was created based on the acquired dataset using vertices-edges relationship diagram. The implemented model is evaluated in terms of Halstead complexity metrics: Program Volume (PV), Program Length (PL), Program Effort (PE), Program Difficulty (PD) and Execution Time (ET). The PV, PL, PE, PD and ET values obtained for the implemented model are 18.45kbits, 0.51, 1037684, 1.97 and 20.45 secs, respectively.
 Conclusion: The proposed model shows a significant improvement over the existing models by producing conflict-free course timetabling problem with better evaluation results. This work will be highly useful in solving various scheduling, optimization and NP-hard related computational problems.

Multi-armed bandits, Thomson sampling and unsupervised machine learning in phylogenetic graph search.

A phylogenetic graph search relies on a large number of highly parameterized search procedures (e.g. branch-swapping, perturbation, simulated annealing, genetic algorithm). These procedures vary in effectiveness over datasets and at alternative points in analytical pipelines. The multi-armed bandit problem is applied to phylogenetic graph searching to more effectively utilize these procedures. Thompson sampling is applied to a collection of search and optimization "bandits" to favour productive search strategies over those that are less successful. This adaptive random sampling strategy is shown to be more effective in producing heuristically optimal phylogenetic graphs and more time efficient than existing uniform probability randomized search strategies. The strategy acts as a form of unsupervised machine learning that can be applied to a diversity of phylogenetic datasets without prior knowledge of their properties.

Near optimal colourability on hereditary graph families

In this paper, we initiate a systematic study on a new notion called near optimal colourability which is closely related to perfect graphs and the Lovász theta function. A graph family G is near optimal colourable if there is a constant number c such that every graph G∈G satisfies χ(G)≤max⁡{c,ω(G)}, where χ(G) and ω(G) are the chromatic number and clique number of G, respectively. The near optimal colourable graph families together with the Lovász theta function are useful for the study of the colouring problems for hereditary graph families. We investigate the near optimal colourability for (H1,H2)-free graphs. Our main result is an almost complete characterisation for the near optimal colourability for (H1,H2)-free graphs with two exceptional cases, one of which is the celebrated Gyárfás conjecture. As an application of our results, we show that the colouring problem for (2K2,P4∨Kn)-free graphs is polynomial time solvable, which solves an open problem in Dabrowski and Paulusma (2018) [6].