Compact Graph Research Articles

Key Frame Selection for Temporal Graph Optimization of Skeleton-Based Action Recognition

Graph neural networks (GNNs) are extensively utilized to capture the spatial–temporal relationships among human body parts for skeleton-based action recognition. However, due to the inefficient information propagation caused by redundant sampling of video frames in the temporal domain, we focus on refining temporal graphs through key frame selection. To this end, we propose a multi-stage key frame selection (MSKFS) method, aiming to find the most representative frames as the graph nodes to learn compact temporal graph representations of human skeletons for action recognition. The MSKFS progressively selects key frames in two stages: (1) salient posture frame selection based on the global dynamics of body parts and (2) key frame refinement and alignment according to intra-frame correlations. The first stage captures the most salient information and aligns the corresponding information of skeleton sequences within the same category. The second stage enriches the subtle information for the integrity of the information derived by the salient frames. Moreover, variational inference is applied to differentiate the key frame refinement and alignment procedure, allowing the end-to-end optimization of arbitrary graph-based models to represent the obtained compact graph for skeleton-based action recognition. Our MSKFS method achieves state-of-the-art performances on two challenging action recognition datasets.

NEURD offers automated proofreading and feature extraction for connectomics.

We are now in the era of millimeter-scale electron microscopy (EM) volumes collected at nanometer resolution. Dense reconstruction of cellular compartments in these EM volumes has been enabled by recent advances in Machine Learning (ML). Automated segmentation methods produce exceptionally accurate reconstructions of cells, but post-hoc proofreading is still required to generate large connectomes free of merge and split errors. The elaborate 3-D meshes of neurons in these volumes contain detailed morphological information at multiple scales, from the diameter, shape, and branching patterns of axons and dendrites, down to the fine-scale structure of dendritic spines. However, extracting these features can require substantial effort to piece together existing tools into custom workflows. Building on existing open-source software for mesh manipulation, here we present "NEURD", a software package that decomposes meshed neurons into compact and extensively-annotated graph representations. With these feature-rich graphs, we automate a variety of tasks such as state of the art automated proofreading of merge errors, cell classification, spine detection, axon-dendritic proximities, and other annotations. These features enable many downstream analyses of neural morphology and connectivity, making these massive and complex datasets more accessible to neuroscience researchers focused on a variety of scientific questions.

A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to effectively integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research.

Prokrustean Graph: A substring index for rapid k-mer size analysis.

Despite the widespread adoption of -mer-based methods in bioinformatics, understanding the influence of -mer sizes remains a persistent challenge. Selecting an optimal -mer size or employing multiple -mer sizes is often arbitrary, application-specific, and fraught with computational complexities. Typically, the influence of -mer size is obscured by the outputs of complex bioinformatics tasks, such as genome analysis, comparison, assembly, alignment, and error correction. However, it is frequently overlooked that every method is built above a well-defined -mer-based object like Jaccard Similarity, de Bruijn graphs, -mer spectra, and Bray-Curtis Dissimilarity. Despite these objects offering a clearer perspective on the role of -mer sizes, the dynamics of -mer-based objects with respect to -mer sizes remain surprisingly elusive. This paper introduces a computational framework that generalizes the transition of -mer-based objects across -mer sizes, utilizing a novel substring index, the Prokrustean graph. The primary contribution of this framework is to compute quantities associated with -mer-based objects for all -mer sizes, where the computational complexity depends solely on the number of maximal repeats and is independent of the range of -mer sizes. For example, counting vertices of compacted de Bruijn graphs for can be accomplished in mere seconds with our substring index constructed on a gigabase-sized read set. Additionally, we derive a space-efficient algorithm to extract the Prokrustean graph from the Burrows-Wheeler Transform. It becomes evident that modern substring indices, mostly based on longest common prefixes of suffix arrays, inherently face difficulties at exploring varying -mer sizes due to their limitations at grouping co-occurring substrings. We have implemented four applications that utilize quantities critical in modern pangenomics and metagenomics. The code for these applications and the construction algorithm is available at https://github.com/KoslickiLab/prokrustean.

DoppelGanger++ in Action: A Database Replay System with Fast Dependency Graph Generation

A Database Replay System (DRS) captures workloads from a production system and subsequently replays them in a testing environment to verify correctness and performance. Prior to the replay process, DRS initially generates a dependency graph from the workload to ensure output determinism and to maximize replay concurrency in the testing system. However, the state-of-the-art inefficiently generates unnecessarily larger dependency graphs, creating a major bottleneck in the end-to-end pipeline. DoppelGanger++ is a new DRS supporting fast dependency graph generation. This demonstration illustrates how it captures and replays workloads, with a focus on efficiently generating compact dependency graphs. Specifically, we showcase the end-to-end database replay workflow using the complete database replay workload, accompanied by a web tool developed for our demo which can animate the dependency graph generation process and visualize important internal data structures.

A Compact Vulnerability Knowledge Graph for Risk Assessment

Software vulnerabilities, also known as flaws, bugs or weaknesses, are common in modern information systems, putting critical data of organizations and individuals at cyber risk. Due to the scarcity of resources, initial risk assessment is becoming a necessary step to prioritize vulnerabilities and make better decisions on remediation, mitigation, and patching. Datasets containing historical vulnerability information are crucial digital assets to enable AI-based risk assessments. However, existing datasets focus on collecting information on individual vulnerabilities while simply storing them in relational databases, disregarding their structural connections. This article constructs a compact vulnerability knowledge graph, VulKG, containing over 276 K nodes and 1 M relationships to represent the connections between vulnerabilities, exploits, affected products, vendors, referred domain names, and more. We provide a detailed analysis of VulKG modeling and construction, demonstrating VulKG-based query and reasoning, and providing a use case of applying VulKG to a vulnerability risk assessment task, i.e., co-exploitation behavior discovery. Experimental results demonstrate the value of graph connections in vulnerability risk assessment tasks. VulKG offers exciting opportunities for more novel and significant research in areas related to vulnerability risk assessment. The data and codes of this article are available at https://github.com/happyResearcher/VulKG.git .

Edge Private Graph Neural Networks with Singular Value Perturbation

Graph neural networks (GNNs) play a key role in learning representations from graph-structured data and are demonstrated to be useful in many applications. However, the GNN training pipeline has been shown to be vulnerable to node feature leakage and edge extraction attacks. This paper investigates a scenario where an attacker aims to recover private edge information from a trained GNN model. Previous studies have employed differential privacy (DP) to add noise directly to the adjacency matrix or a compact graph representation. The added perturbations cause the graph structure to be substantially morphed, reducing the model utility. We propose a new privacy-preserving GNN training algorithm, Eclipse, that maintains good model utility while providing strong privacy protection on edges. Eclipse is based on two key observations. First, adjacency matrices in graph structures exhibit low-rank behavior. Thus, Eclipse trains GNNs with a low-rank format of the graph via singular values decomposition (SVD), rather than the original graph. Using the low-rank format, Eclipse preserves the primary graph topology and removes the remaining residual edges. Eclipse adds noise to the low-rank singular values instead of the entire graph, thereby preserving the graph privacy while still maintaining enough of the graph structure to maintain model utility. We theoretically show Eclipse provide formal DP guarantee on edges. Experiments on benchmark graph datasets show that Eclipse achieves significantly better privacy-utility tradeoff compared to existing privacy-preserving GNN training methods. In particular, under strong privacy constraints (𝜖 < 4), Eclipse shows significant gains in the model utility by up to 46%. We further demonstrate that Eclipse also has better resilience against common edge attacks (e.g., LPA), lowering the attack AUC by up to 5% compared to other state-of-the-art baselines.

Enhanced Compression of k-Mer Sets with Counters via de Bruijn Graphs.

An essential task in computational genomics involves transforming input sequences into their constituent k-mers. The quest for an efficient representation of k-mer sets is crucial for enhancing the scalability of bioinformatic analyses. One widely used method involves converting the k-mer set into a de Bruijn graph (dBG), followed by seeking a compact graph representation via the smallest path cover. This study introduces USTAR* (Unitig STitch Advanced constRuction), a tool designed to compress both a set of k-mers and their associated counts. USTAR leverages the connectivity and density of dBGs, enabling a more efficient path selection for constructing the path cover. The efficacy of USTAR is demonstrated through its application in compressing real read data sets. USTAR improves the compression achieved by UST (Unitig STitch), the best algorithm, by percentages ranging from 2.3% to 26.4%, depending on the k-mer size, and it is up to times faster.

Graph Summarization: Compactness Meets Efficiency

As the volume and ubiquity of graphs increase, a compact graph representation becomes essential for enabling efficient storage, transfer, and processing of graphs. Given a graph, the graph summarization problem asks for a compact representation that consists of a summary graph and the corrections, such that we can recreate the original graph from the representation exactly. Although this problem has been studied extensively, the existing works either trade summary compactness for efficiency, or vice versa. In particular, a well-known greedy method provides the most compact summary but incurs prohibitive time cost, while the state-of-the-art algorithms with practical overheads are more than 20% behind in summary compactness in our comparison with the greedy method. This paper presents Mags and Mags-DM, two algorithms that aim to bridge the compactness and efficiency in graph summarization. Mags adopts the existing greedy paradigm that provides state-of-the-art compactness, but significantly improves its efficiency with a novel algorithm design. Meanwhile, Mags-DM follows a different paradigm with practical efficiency and overcomes its limitations in compactness. Moreover, both algorithms can support parallel computing environments. We evaluate Mags and Mags-DM on graphs up to billion-scale and demonstrate that they achieve state-of-the-art in both compactness and efficiency, rather than in one of them. Compared with the method that offers state-of-the-art compactness, Mags and Mags-DM have a small difference (< 0.1% and < 2.1%) in compactness. For efficiency, Mags is on average 11.1x and 4.2x faster than the two state-of-the-art algorithms with practical overheads, while Mags-DM can further reduce the running time by 13.4x compared with Mags. This shows that graph summarization algorithms can be made practical while still offering a compact summary.

Unitig-centered pan-genome machine learning approach for predicting antibiotic resistance and discovering novel resistance genes in bacterial strains

In current genomic research, the widely used methods for predicting antimicrobial resistance (AMR) often rely on prior knowledge of known AMR genes or reference genomes. However, these methods have limitations, potentially resulting in imprecise predictions owing to incomplete coverage of AMR mechanisms and genetic variations. To overcome these limitations, we propose a pan-genome-based machine learning approach to advance our understanding of AMR gene repertoires and uncover possible feature sets for precise AMR classification. By building compacted de Brujin graphs (cDBGs) from thousands of genomes and collecting the presence/absence patterns of unique sequences (unitigs) for Pseudomonas aeruginosa, we determined that using machine learning models on unitig-centered pan-genomes showed significant promise for accurately predicting the antibiotic resistance or susceptibility of microbial strains. Applying a feature-selection-based machine learning algorithm led to satisfactory predictive performance for the training dataset (with an area under the receiver operating characteristic curve (AUC) of > 0.929) and an independent validation dataset (AUC, approximately 0.77). Furthermore, the selected unitigs revealed previously unidentified resistance genes, allowing for the expansion of the resistance gene repertoire to those that have not previously been described in the literature on antibiotic resistance. These results demonstrate that our proposed unitig-based pan-genome feature set was effective in constructing machine learning predictors that could accurately identify AMR pathogens. Gene sets extracted using this approach may offer valuable insights into expanding known AMR genes and forming new hypotheses to uncover the underlying mechanisms of bacterial AMR.

Abstract 6246: De novo mutation discovery in a mouse model and a human patient sample of non-Hodgkin's lymphoma

Abstract Cancer encompasses many different diseases, all typically involving an accumulation of genetic alterations. However, despite the genomic complexity of this group of diseases, cancer genomic studies typically rely on sequence alignment to a "reference genome" prior to analysis. Such approaches can provide gene expression quantification of known, annotated genes. However, they miss the detection of fusion genes, novel transcripts, virus insertions, and other genetic insults that may be present in cancer beyond an altered gene expression profile. Here, we develop a workflow for de novo identification and quantification of "outside of reference genome" genetic aberrations. This workflow leverages klue, a method we developed that is based on the compact de Bruijn graph, which can extract sequences uniquely found in a "tumor" sample but not in a "normal" control sample from genomic sequencing data. We first applied this method to an RNA-seq experiment from the EμSRα-tTA/TetO-MYC mouse model, which is a MYC-driven autochthonous transgenic mouse model of T-cell acute lymphoblastic lymphoma (T-ALL). We extracted k-mer contigs present in the mouse tumor samples but are present neither in the spleens of wild-type mice of the same genetic background nor in the standard mouse reference genome assembly. We then mapped RNA-seq reads from the T-ALL mouse tumor samples to these contigs. The contigs with the highest number of mapped reads (i.e. the highest counts) were run through BLAST to determine their identities. The mapped contigs with the highest counts were the tTA transgenic element sequence and the human MYC transgene. This result showcases this workflow's success in isolating and quantifying "reference-absent” tumor-unique sequences. Next, we applied klue to whole genome sequencing (WGS), whole exome sequencing (WES), and RNA-seq data from a patient with B-cell follicular lymphoma (with matched normal specimen) from the Texas Cancer Research Biobank, as this data is unrestricted open access. Tumor-unique contigs in sequencing reads were extracted and analyzed with BLAST and BLAT. In one case, a nonsynonymous point mutation in the SPI1 (also known as PU.1) oncogene was found. The sequencing reads from the tumor sample showed both the "normal variant" of SPI1 as well as the mutant SPI1:H268P, suggesting a heterozygous mutation. Altogether, these results suggest that the idea of first identifying tumor-unique sequences then doing post hoc analysis of those sequences is a viable approach for de novo mutation discovery in cancer genomics. Citation Format: Delaney K. Sullivan, Eissa Albinali, Mayuko Boffelli, Lior Pachter. De novo mutation discovery in a mouse model and a human patient sample of non-Hodgkin's lymphoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 6246.

Mean Distance on Metric Graphs

We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectral gap of the graph Laplacian with standard vertex conditions: it is maximised among all graphs of fixed length by the path graph (interval), or by the loop in the restricted class of doubly connected graphs, and it is minimised among all graphs of fixed length and number of edges by the equilateral flower graph. We also establish bounds for the correctly scaled product of the spectral gap and the square of the mean distance which depend only on combinatorial, and not metric, features of the graph. This raises the open question whether this product admits absolute upper and lower bounds valid on all compact metric graphs.

Metric Approximation of Set-Valued Functions of Bounded Variation by Integral Operators

AbstractWe introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval [a, b] into the space of compact non-empty subsets of $${\mathbb {R}}^d$$ R d . All operators are adapted by replacing the Riemann integral for real-valued functions by the weighted metric integral for SVFs of bounded variation with compact graphs. For such a SVF F, we obtain pointwise error estimates for sequences of integral operators at points of continuity, leading to convergence at such points to F. At points of discontinuity of F, we derive estimates, which yield the convergence to a certain set described in terms of the metric selections of F. To obtain these estimates we refine and extend known results on approximation of real-valued functions by integral operators. Our analysis uses recently defined one-sided local quasi-moduli at points of discontinuity and several notions of local Lipschitz property at points of continuity. We also provide a global approach for error bounds. A multifunction F is represented by the set of all its metric selections, while its approximation (its image under the operator) is represented by the set of images of these metric selections under the operator. A bound on the Hausdorff distance between these two sets of single-valued functions in $$L^1$$ L 1 provides our global estimates. The theory is applied to concrete operators: the Bernstein–Durrmeyer operator and the Kantorovich operator.

Fulgor: a fast and compact k-mer index for large-scale matching and color queries.

The problem of sequence identification or matching-determining the subset of reference sequences from a given collection that are likely to contain a short, queried nucleotide sequence-is relevant for many important tasks in Computational Biology, such as metagenomics and pangenome analysis. Due to the complex nature of such analyses and the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance. This poses the threefold challenge of representing the reference collection with a data structure that is efficient to query, has light memory usage, and scales well to large collections. To solve this problem, we describe an efficient colored de Bruijn graph index, arising as the combination of a k-mer dictionary with a compressed inverted index. The proposed index takes full advantage of the fact that unitigs in the colored compacted de Bruijn graph are monochromatic (i.e., all k-mers in a unitig have the same set of references of origin, or color). Specifically, the unitigs are kept in the dictionary in color order, thereby allowing for the encoding of the map from k-mers to their colors in as little as 1 + o(1) bits per unitig. Hence, one color per unitig is stored in the index with almost no space/time overhead. By combining this property with simple but effective compression methods for integer lists, the index achieves very small space. We implement these methods in a tool called Fulgor, and conduct an extensive experimental analysis to demonstrate the improvement of our tool over previous solutions. For example, compared to Themisto-the strongest competitor in terms of index space vs. query time trade-off-Fulgor requires significantly less space (up to 43% less space for a collection of 150,000 Salmonella enterica genomes), is at least twice as fast for color queries, and is 2-6[Formula: see text] faster to construct.

Saliency-aware regularized graph neural network

The crux of graph classification lies in the effective representation learning for the entire graph. Typical graph neural networks focus on modeling the local dependencies when aggregating features of neighboring nodes, and obtain the representation for the entire graph by aggregating node features. Such methods have two potential limitations: 1) the global node saliency w.r.t. graph classification is not explicitly modeled, which is crucial since different nodes may have different semantic relevance to graph classification; 2) the graph representation directly aggregated from node features may have limited effectiveness to reflect graph-level information. In this work, we propose the Saliency-Aware Regularized Graph Neural Network (SAR-GNN) for graph classification, which consists of two core modules: 1) a traditional graph neural network serving as the backbone for learning node features and 2) the Graph Neural Memory designed to distill a compact graph representation from node features of the backbone. We first estimate the global node saliency by measuring the semantic similarity between the compact graph representation and node features. Then the learned saliency distribution is leveraged to regularize the neighborhood aggregation of the backbone, which facilitates the message passing of features for salient nodes and suppresses the less relevant nodes. Thus, our model can learn more effective graph representation. We demonstrate the merits of SAR-GNN by extensive experiments on seven datasets across various types of graph data.

Mathematical models and exact algorithms for the Colored Bin Packing Problem

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the same color can appear consecutively in the same bin. To simplify modeling, we present a characterization of any feasible packing of this problem in a way that does not depend on its ordering. This allows us to describe the problem with a simple mathematical model. Furthermore, we present four exact algorithms for the CBPP. First, we propose a generalization of Valério de Carvalho’s arc flow formulation for the CBPP using a graph with multiple layers, each representing a color. Second, we present an improved arc flow formulation that uses a more compact graph and has the same linear relaxation bound as the first formulation. And finally, we design two exponential set-partition models based on reductions to a generalized vehicle routing problem, which are solved by a branch-cut-and-price algorithm through VRPSolver. To compare the proposed algorithms, a varied benchmark set with 574 instances of the CBPP is presented. Experimental results show that our best model, the improved arc flow formulation, was able to solve instances of up to 500 items and 37 colors. The set-partition models are also shown to exceed their arc flow counterparts in instances with a very small number of colors.

Structure Representation With Adaptive and Compact Facial Graph for Micro-Expression Recognition

Structure Representation With Adaptive and Compact Facial Graph for Micro-Expression Recognition

A Compact Graph Convolutional Network With Adaptive Functional Connectivity for Seizure Prediction.

Seizure prediction using EEG has significant implications for the daily monitoring and treatment of epilepsy patients. However, the task is challenging due to the underlying spatiotemporal correlations and patient heterogeneity. Traditional methods often use large-scale models with independent components to capture the spatial and temporal features of EEG separately or explore shared patterns among patients with the help of pre-defined functional connectivity. In this paper, we propose a compact model, called the graph convolutional network based on adaptive functional connectivity (AFC-GCN), for seizure prediction. The model can adaptively infer evolution of functional connectivity in epilepsy patients during seizures through data-driven methods and synchronously analyze spatiotemporal response of functional connectivity in multiple topologies. On CHB-MIT datasets, the experimental results demonstrate that AFC-GCN achieves accurate and robust performance with low complexity. (AUC: 0.9820, accuracy: 0.9815, sensitivity: 0.9802, FPR: 0.0172). The proposed method has the potential to predict seizure during daily monitoring.

Regularity and numerical approximation of fractional elliptic differential equations on compact metric graphs

The fractional differential equation L β u = f L^\beta u = f posed on a compact metric graph is considered, where β > 0 \beta >0 and L = κ 2 − ∇ ( a ∇ ) L = \kappa ^2 - \nabla (a\nabla ) is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients κ , a \kappa ,a . We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L − β L^{-\beta } . For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L 2 ( Γ × Γ ) L_2(\Gamma \times \Gamma ) -error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for L = κ 2 − Δ , κ > 0 {L = \kappa ^2 - \Delta , \kappa >0} are performed to illustrate the results.

Prediction of cancer recurrence based on compact graphs of whole slide images

Cancer recurrence is one of the primary causes of patient mortality following treatment, indicating increased aggressiveness of cancer cells and difficulties in achieving a cure. A critical step to improve patients’ survival is accurately predicting recurrence status and giving appropriate treatment. Whole Slide Images (WSIs) are a common type of image data in the field of digital pathology, containing high-resolution tissue information. Furthermore, WSIs of primary tumors contain microenvironmental information directly associated with the growth of tumor cells. To effectively utilize this microenvironmental information. Firstly, we represented microenvironmental features of histopathological images as compact graphs. Secondly, this work aims to develop an enhanced lightweight graph neural network called the Adaptive Graph Clustering Network (AGCNet) for predicting cancer recurrence. Experiments are conducted on three cancer datasets from The Cancer Genome Atlas (TCGA), and AGCNet achieved an accuracy of 81.81% in BLCA, 69.66% in PAAD, and 81.96% in STAD. These results indicated that AGCNet is an effective model for predicting cancer recurrence and is expected to be applied in clinical applications.