Spectral Graph Analysis Research Articles

A framework for collaborative multi-robot mapping using spectral graph wavelets

The exploration of large-scale unknown environments can benefit from the deployment of multiple robots for collaborative mapping. Each robot explores a section of the environment and communicates onboard pose estimates and maps to a central server to build an optimized global multi-robot map. Naturally, inconsistencies can arise between onboard and server estimates due to onboard odometry drift, failures, or degeneracies. The mapping server can correct and overcome such failure cases using computationally expensive operations such as inter-robot loop closure detection and multi-modal mapping. However, the individual robots do not benefit from the collaborative map if the mapping server provides no feedback. Although server updates from the multi-robot map can greatly alleviate the robotic mission strategically, most existing work lacks them, due to their associated computational and bandwidth-related costs. Motivated by this challenge, this paper proposes a novel collaborative mapping framework that enables global mapping consistency among robots and the mapping server. In particular, we propose graph spectral analysis, at different spatial scales, to detect structural differences between robot and server graphs, and to generate necessary constraints for the individual robot pose graphs. Our approach specifically finds the nodes that correspond to the drift’s origin rather than the nodes where the error becomes too large. We thoroughly analyze and validate our proposed framework using several real-world multi-robot field deployments where we show improvements of the onboard system up to 90% and can recover the onboard estimation from localization failures and even from the degeneracies within its estimation.

Graph spectral analysis of nonane isomers

Graph spectral analysis of nonane isomers

Sparse spectral graph analysis and its application to gastric cancer drug resistance-specific molecular interplays identification.

Uncovering acquired drug resistance mechanisms has garnered considerable attention as drug resistance leads to treatment failure and death in patients with cancer. Although several bioinformatics studies developed various computational methodologies to uncover the drug resistance mechanisms in cancer chemotherapy, most studies were based on individual or differential gene expression analysis. However the single gene-based analysis is not enough, because perturbations in complex molecular networks are involved in anti-cancer drug resistance mechanisms. The main goal of this study is to reveal crucial molecular interplay that plays key roles in mechanism underlying acquired gastric cancer drug resistance. To uncover the mechanism and molecular characteristics of drug resistance, we propose a novel computational strategy that identified the differentially regulated gene networks. Our method measures dissimilarity of networks based on the eigenvalues of the Laplacian matrix. Especially, our strategy determined the networks' eigenstructure based on sparse eigen loadings, thus, the only crucial features to describe the graph structure are involved in the eigenanalysis without noise disturbance. We incorporated the network biology knowledge into eigenanalysis based on the network-constrained regularization. Therefore, we can achieve a biologically reliable interpretation of the differentially regulated gene network identification. Monte Carlo simulations show the outstanding performances of the proposed methodology for differentially regulated gene network identification. We applied our strategy to gastric cancer drug-resistant-specific molecular interplays and related markers. The identified drug resistance markers are verified through the literature. Our results suggest that the suppression and/or induction of COL4A1, PXDN and TGFBI and their molecular interplays enriched in the Extracellular-related pathways may provide crucial clues to enhance the chemosensitivity of gastric cancer. The developed strategy will be a useful tool to identify phenotype-specific molecular characteristics that can provide essential clues to uncover the complex cancer mechanism.

TEE-Graph: efficient privacy and ownership protection for cloud-based graph spectral analysis.

Big graphs like social network user interactions and customer rating matrices require significant computing resources to maintain. Data owners are now using public cloud resources for storage and computing elasticity. However, existing solutions do not fully address the privacy and ownership protection needs of the key involved parties: data contributors and the data owner who collects data from contributors. We propose a Trusted Execution Environment (TEE) based solution: TEE-Graph for graph spectral analysis of outsourced graphs in the cloud. TEEs are new CPU features that can enable much more efficient confidential computing solutions than traditional software-based cryptographic ones. Our approach has several unique contributions compared to existing confidential graph analysis approaches. (1) It utilizes the unique TEE properties to ensure contributors' new privacy needs, e.g., the right of revocation for shared data. (2) It implements efficient access-pattern protection with a differentially private data encoding method. And (3) it implements TEE-based special analysis algorithms: the Lanczos method and the Nystrom method for efficiently handling big graphs and protecting confidentiality from compromised cloud providers. The TEE-Graph approach is much more efficient than software crypto approaches and also immune to access-pattern-based attacks. Compared with the best-known software crypto approach for graph spectral analysis, PrivateGraph, we have seen that TEE-Graph has 103-105 times lower computation, storage, and communication costs. Furthermore, the proposed access-pattern protection method incurs only about 10%-25% of the overall computation cost. Our experimentation showed that TEE-Graph performs significantly better and has lower costs than typical software approaches. It also addresses the unique ownership and access-pattern issues that other TEE-related graph analytics approaches have not sufficiently studied. The proposed approach can be extended to other graph analytics problems with strong ownership and access-pattern protection.

Structure learning with consensus label information for multi-view unsupervised feature selection

Structure learning based feature selection has attracted increasing attention for selecting these features which can preserve the learned structures. However, existing methods fail to effectively explore the heterogeneous and homogeneous information from multiple views, which leads to the suboptimal results. To solve this problem, we propose Structure Learning with Consensus Label Information for Multi-View Feature Selection (SCMvFS). Noting the heterogeneity of views, the graph of each view should be a perturbation of the intrinsic graph yet the clustering structure are shared across views. In light of this, we generate a unique clustering indicator through the spectral analysis of multiple Laplacian graphs for the structure learning based feature selection. Therefore, SCMvFS considers both the graph heterogeneity and indicator consistency to effectively explore the heterogeneous and homogeneous information for facilitating the feature selection task. Further, we carefully design an efficient algorithm to solve the resulting optimization problem. Extensive experimental results demonstrate that the proposed method outperforms the state-of-the-art methods on seven benchmark datasets with respect to two indicators. In particular, SCMvFS achieves an ACC of 61.87 (55.94) on the Outdoor Scene (Yale) dataset, which is an up to 43% (15%) performance improvement compared with the latest structure learning based method TLR. The code and datasets are available at https://github.com/HdTgon/2023-ESWA-SCMvFS.

Resting-state electroencephalographic characteristics related to mild cognitive impairments.

Alzheimer's disease (AD) causes a rapid deterioration in cognitive and physical functions, including problem-solving, memory, language, and daily activities. Mild cognitive impairment (MCI) is considered a risk factor for AD, and early diagnosis and treatment of MCI may help slow the progression of AD. Electroencephalography (EEG) analysis has become an increasingly popular tool for developing biomarkers for MCI and AD diagnosis. Compared with healthy elderly, patients with AD showed very clear differences in EEG patterns, but it is inconclusive for MCI. This study aimed to investigate the resting-state EEG features of individuals with MCI (n = 12) and cognitively healthy controls (HC) (n = 13) with their eyes closed. EEG data were analyzed using spectral power, complexity, functional connectivity, and graph analysis. The results revealed no significant difference in EEG spectral power between the HC and MCI groups. However, we observed significant changes in brain complexity and networks in individuals with MCI compared with HC. Patients with MCI exhibited lower complexity in the middle temporal lobe, lower global efficiency in theta and alpha bands, higher local efficiency in the beta band, lower nodal efficiency in the frontal theta band, and less small-world network topology compared to the HC group. These observed differences may be related to underlying neuropathological alterations associated with MCI progression. The findings highlight the potential of network analysis as a promising tool for the diagnosis of MCI.

Characterizing graphs with fully positive semidefinite Q-matrices

For q∈R, the Q-matrixQ=Qq of a connected simple graph G=(V,E) is Qq=(q∂(x,y))x,y∈V, where ∂ denotes the path-length distance. Describing the set π(G) consisting of those q∈R for which Qq is positive semidefinite is fundamental in asymptotic spectral analysis of graphs from the viewpoint of quantum probability theory. Assume that G has at least two vertices. Then π(G) is easily seen to be a nonempty closed subset of the interval [−1,1]. In this note, we show that π(G)=[−1,1] if and only if G is isometrically embeddable into a hypercube (infinite-dimensional if G is infinite) if and only if G is bipartite and does not possess certain five-vertex configurations, an example of which is an induced K2,3.

Multilayer graph spectral analysis for hyperspectral images

Hyperspectral imaging has broad applications and impacts in areas including environmental science, weather, and geo/space exploration. The intrinsic spectral–spatial structures and potential multi-level features in different frequency bands make multilayer graph an intuitive model for hyperspectral images (HSI). To study the underlying characteristics of HSI and to take the advantage of graph signal processing (GSP) tools, this work proposes a multilayer graph spectral analysis for hyperspectral images based on multilayer graph signal processing (M-GSP). More specifically, we present multilayer graph (MLG) models and tensor representations for HSI. By exploring multilayer graph spectral space, we develop MLG-based methods for HSI applications, including unsupervised segmentation and supervised classification. Our experimental results demonstrate the strength of M-GSP in HSI processing and spectral–spatial information extraction.

Scalable Quickest Line Outage Detection and Localization Via Graph Spectral Analysis

This paper proposes a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalable</i> framework for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real-time</i> detection and localization of power line outages in transmission networks. While localizing outages is pivotal for ensuring grid reliability, forming such decisions faces an inherent combinatorial complexity that grows with the grid size and becomes prohibitive even for moderate grid sizes. Hence, designing outage detection and localization algorithms that are amenable to real-time implementation critically hinges on circumventing the computational complexity. This paper proposes a graph-guided quickest change detection (GG-QCD) approach that leverages the grid topology and performs quickest change detection in the spectral domain of the graph underlying grid's topology. The GG-QCD algorithm's key features are that (i) it uses a one-dimensional metric that tests the data's conformity to the grid topology, and (ii) it decouples the detection and localization processes to avoid testing all the lines at all times. Specifically, a lack of such conformity of the data to the system model will be alarming the potential existence of an outage. Once an outage is deemed to exist, an active graph clustering approach will be used to localize the line in outage. The clustering approach will also be relying on the same one-dimensional conformity metric. Overall, this approach will be performing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only one</i> test over time when the system is outage-free. Once an outage is detected, it will require <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\log (L))$</tex-math></inline-formula> additional tests to identify the line in outage. This paper presents the theory for GG-QCD and algorithms for outage detection and localization. To evaluate these algorithms’ efficiency and complexity, they are examined in the standard IEEE 30- and 118-bus systems.

Graph Signal Processing for Heterogeneous Change Detection

This paper provides a new strategy for the heterogeneous change detection (HCD) problem: solving HCD from the perspective of graph signal processing (GSP). We construct a graph to represent the structure of each image, and treat each image as a graph signal defined on the graph. In this way, we convert the HCD into a GSP problem: a comparison of the responses of signals on systems defined on the graphs, which attempts to find structural differences and signal differences due to the changes between heterogeneous images. Firstly, we analyze the GSP for HCD from the vertex domain. We show that once a region has changed, the local structure of image changes, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> . the connectivity of the vertex containing this region changes. Therefore, we can compare the output signals of the same input graph signal passing through filters defined on the two graphs to detect changes. We analyze the negative effects of changing regions on the change detection results from the viewpoint of signal propagation, and we also design different filters from the vertex domain to explore the high-order neighborhood information hidden in original graphs. Secondly, we analyze the GSP for HCD from the spectral domain. We explore the spectral properties of different images on the same graph, and show that their spectra exhibit commonalities and dissimilarities. Specifically, it is the change that leads to the dissimilarities of their spectra. With the help of graph spectral analysis, we propose a regression model for the HCD, which decomposes the source signal into the regressed signal and changed signal, and constrains the spectral property of the regressed signal. Experiments conducted on seven real data sets show the effectiveness of the vertex domain filtering based and spectral domain analysis based HCD methods. Source code will be made available at https://github.com/yulisun/HCD-GSP.

Unsupervised, Supervised and Semi‐supervised Dimensionality Reduction by Low‐Rank Regression Analysis

Techniques for dimensionality reduction have attracted much attention in computer vision and pattern recognition. However, for the supervised or unsupervised case, the methods combining regression analysis and spectral graph analysis do not consider the global structure of the subspace; For semi-supervised case, how to use the unlabeled samples more effectively is still an open problem. In this paper, we propose the methods by Low-rank regression analysis (LRRA) to deal with these problems. For supervised or unsupervised dimensionality reduction, combining spectral graph analysis and LRRA can make a global constraint on the subspace. For semi-supervised dimensionality reduction, the proposed method incorporating LRRA can exploit the unlabeled samples more effectively. The experimental results show the effectiveness of our methods.

Gradients of connectivity as graph Fourier bases of brain activity.

The application of graph theory to model the complex structure and function of the brain has shed new light on its organization, prompting the emergence of network neuroscience. Despite the tremendous progress that has been achieved in this field, still relatively few methods exploit the topology of brain networks to analyze brain activity. Recent attempts in this direction have leveraged on the one hand graph spectral analysis (to decompose brain connectivity into eigenmodes or gradients) and the other graph signal processing (to decompose brain activity “coupled to” an underlying network in graph Fourier modes). These studies have used a variety of imaging techniques (e.g., fMRI, electroencephalography, diffusion-weighted and myelin-sensitive imaging) and connectivity estimators to model brain networks. Results are promising in terms of interpretability and functional relevance, but methodologies and terminology are variable. The goals of this paper are twofold. First, we summarize recent contributions related to connectivity gradients and graph signal processing, and attempt a clarification of the terminology and methods used in the field, while pointing out current methodological limitations. Second, we discuss the perspective that the functional relevance of connectivity gradients could be fruitfully exploited by considering them as graph Fourier bases of brain activity.

On quantum adjacency algebras of Doob graphs and their irreducible modules

For fixed integers $$n \ge 1$$ and $$m \ge 0$$ , we consider the Doob graph $$D=D(n,m)$$ formed by taking direct product of n copies of Shrikhande graph and m copies of complete graph $$K_4$$ . Fix a vertex x of D, and let $$T=T(x)$$ denote the Terwilliger algebra of D with respect to x. Let A denote the adjacency matrix of D. There exists a decomposition of A into a sum $$A = L + F + R$$ of elements in T where L, F, and R are the lowering, flat, and raising matrices, respectively. We call $$A = L + F + R$$ the quantum decomposition of A. Hora and Obata (Quantum Probability and Spectral Analysis of Graphs. Theoretical and Mathematical Physics, Springer, Berlin, 2007) introduced a semi-simple matrix algebra based on the quantum decomposition of the adjacency matrix. This algebra is generated by the quantum components of the decomposition and is called the quantum adjacency algebra of the graph. Let $$Q=Q(x)$$ denote the quantum adjacency algebra of D with respect to x. In this paper, we display an action of the special orthogonal Lie algebra $$\mathfrak {so}_4$$ on the standard module for D. We also prove Q is generated by the center and the homomorphic image of the universal enveloping algebra $$U(\mathfrak {so}_4)$$ . To do these, we exploit the work of Tanabe (JAC 6: 173–195, 1997) on irreducible T-modules of D.

Partial Discharge Detection Framework Employing Spectral Analysis of Horizontal Visibility Graph

In this article, we propose a novel method for identification of partial discharge (PD) signals employing horizontal visibility graph spectral analysis (HVGSA). Horizontal visibility graph (HVG) converts a time series into an undirected graphical network while preserving its temporal characteristics. In the present contribution, PD signals of single and multiple void discharges were measured using a high frequency current transformer (HFCT) sensor and subsequently transformed to undirected graphical networks using HVG. From the HVG of the PD signals, several spectral graph features were extracted for recognition of PD signals. The extracted features were further subjected to analysis of variance (ANOVA) test to examine their statistical significance and followed by FDR correction to select the most discriminative features. The PD signals were classified using three machine learning classifiers. We also investigated the performance of our method by varying penetrable distance- an important parameter of HVG for robust detection of PD signals in presence of noise. Investigations revealed that very high recognition accuracy has been obtained in discriminating different PD signals using HVGSA. Interestingly, we also observed that in the presence of noise, detection accuracy can be improved significantly by increasing the penetrable distance within a permissible range. Finally, an optimum value of penetrable distance parameter has been determined for accurate recognition of PD signals at different noise levels. The proposed technique can be applied for real-life PD signal detection for insulation condition monitoring.

A Manifold-Based Dimension Reduction Algorithm Framework for Noisy Data Using Graph Sampling and Spectral Graph

This paper proposes a new manifold-based dimension reduction algorithm framework. It can deal with the dimension reduction problem of data with noise and give the dimension reduction results with the deviation values caused by noise interference. Commonly used manifold learning methods are sensitive to noise in the data. Mean computation, a denoising method, is an important step in data preprocessing but leads to a loss of local structural information. In addition, it is difficult to measure the accuracy of the dimension reduction of noisy data. Thus, manifold learning methods often transform the data into an approximately smooth manifold structure; however, practical data from the physical world may not meet the requirements. The proposed framework follows the idea of the localization of manifolds and uses graph sampling to determine some local anchor points from the given data. Subsequently, the specific range of localities is determined using graph spectral analysis, and the density within each local range is estimated to obtain the distribution parameters. Then, manifold-based dimension reduction with distribution parameters is established, and the deviation values in each local range are measured and further extended to all data. Thus, our proposed framework gives a measurement method for deviation caused by noise.

PRIGSA2: Improved version of protein repeat identification by graph spectral analysis

Tandemly repeated structural motifs in proteins form highly stable structural folds and provide multiple binding sites associated with diverse functional roles. The tertiary structure and function of these proteins are determined by the type and copy number of the repeating units. Each repeat type exhibits a unique pattern of intra- and inter-repeat unit interactions that is well-captured by the topological features in the network representation of protein structures. Here we present an improved version of our graph based algorithm, PRIGSA, with structure-based validation and filtering steps incorporated for accurate detection of tandem structural repeats. The algorithm integrates available knowledge on repeat families with de novo prediction to detect repeats in single monomer chains as well as in multimeric protein complexes. Three levels of performance evaluation are presented: comparison with state-of-the-art algorithms on benchmark dataset of repeat and nonrepeat proteins, accuracy in the detection of members of 13 known repeat families reported in UniProt and execution on the complete Protein Data Bank to show its ability to identify previously uncharacterized proteins. A ~3-fold increase in the coverage of the members of 13 known families and 3408 novel uncharacterized structural repeat proteins are identified on executing it on PDB. PRIGSA2 is available at http:// bioinf.iiit.ac.in/PRIGSA2/.

Forecasting Trajectory and Behavior of Road-Agents Using Spectral Clustering in Graph-LSTMs

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%.

Efficient Vector Partitioning Algorithms for Graph Clustering

This paper addressed the problem of finding clusters included in graph-structured data such as Web graphs, social networks, and others. Graph clustering is one of the fundamental techniques for understanding structures present in the complex graphs such as Web pages, social networks, and others. In the Web and data mining communities, the modularity-based graph clustering algorithm is successfully used in many applications. However, it is difficult for the modularity-based methods to find fine-grained clusters hidden in large-scale graphs; the methods fail to reproduce the ground truth. In this paper, we present a novel modularity-based algorithm, \textit{CAV}, that shows better clustering results than the traditional algorithm. The proposed algorithm employs a cohesiveness-aware vector partitioning into the graph spectral analysis to improve the clustering accuracy. Additionally, this paper also presents a novel efficient algorithm \textit{P-CAV} for further improving the clustering speed of CAV; P-CAV is an extension of CAV that utilizes the thread-based parallelization on a many-core CPU. Our extensive experiments on synthetic and public datasets demonstrate the performance superiority of our approaches over the state-of-the-art approaches.

Graph-Based Blind Hyperspectral Unmixing via Nonnegative Matrix Factorization

Hyperspectral unmixing (HU) is a crucial step in the hyperspectral image (HSI) analysis. It aims at decomposing the observed spectrum at each pixel into a collection of constituent endmembers, weighted by their abundances. In a close spatial neighborhood, due to spatial autocorrelation, the abundances of an endmember tend to be similar to each other. Therefore, the spectra at the neighboring pixels are also very much alike. Recently, many studies have focused on graph-regularized nonnegative matrix factorization (NMF) approaches to address the blind HU problem. This is mainly because graph structures allow spatial–spectral relations to be effectively embedded in the NMF framework. This article takes one step further by defining each abundance map as a signal on a suitable graph, which enables the HU problem to be analyzed for the first time from a graph signal processing perspective. This article introduces a novel Laplacian regularizer based on the $l_{1}$ -norm, where graph spectral analysis is utilized to show that the regularizer has natural piecewise smooth (PWS) signal promotion and noise rejection capabilities. A graph-based blind HU algorithm is developed by incorporating this regularizer and an $l_{1/2}$ -abundance sparsity constraint into the NMF problem. Since the featured regularizer exploits the PWS property of abundance maps, the proposed method is effective in HU. The experiments conducted on synthetic and real HSIs demonstrate that it has superior performance compared with several popular HU algorithms.

Autoencoder based sample selection for self-taught learning

Self-taught learning is a technique that uses a large number of unlabeled data as source samples to improve the task performance on target samples. Compared with other transfer learning techniques, self-taught learning can be applied to a broader set of scenarios due to the loose restrictions on the source data. However, knowledge transferred from source samples that are not sufficiently related to the target domain may negatively influence the target learner, which is referred to as negative transfer. In this paper, we propose a metric for the relevance between a source sample and the target samples. To be more specific, both source and target samples are reconstructed through a single-layer autoencoder with a linear relationship between source samples and reconstructed target samples being simultaneously enforced. An ℓ2,1-norm sparsity constraint is imposed on the transformation matrix to identify source samples relevant to the target domain. Source domain samples that are deemed relevant are assigned pseudo-labels reflecting their relevance to target domain samples, and are combined with target samples in order to provide an expanded training set for classifier training. Local data structures are also preserved during source sample selection through spectral graph analysis. Promising results in extensive experiments show the advantages of the proposed approach.