Learning symmetry-aware atom mapping in chemical reactions through deep graph matching

Accurate atom mapping, which establishes correspondences between atoms in reactants and products, is a crucial step in analyzing chemical reactions. In this paper, we present a novel end-to-end approach that formulates the atom mapping problem as a deep graph matching task. Our proposed model, AMNet (Atom Matching Network), utilizes molecular graph representations and employs various atom and bond features using graph neural networks to capture the intricate structural characteristics of molecules, ensuring precise atom correspondence predictions. Notably, AMNet incorporates the consideration of molecule symmetry, enhancing accuracy while simultaneously reducing computational complexity. The integration of the Weisfeiler-Lehman isomorphism test for symmetry identification refines the model's predictions. Furthermore, our model maps the entire atom set in a chemical reaction, offering a comprehensive approach beyond focusing solely on the main molecules in reactions. We evaluated AMNet's performance on a subset of USPTO reaction datasets, addressing various tasks, including assessing the impact of molecular symmetry identification, understanding the influence of feature selection on AMNet performance, and comparing its performance with the state-of-the-art method. The result reveals an average accuracy of 97.3% on mapped atoms, with 99.7% of reactions correctly mapped when the correct mapped atom is within the top 10 predicted atoms.Scientific contributionThe paper introduces a novel end-to-end deep graph matching model for atom mapping, utilizing molecular graph representations to capture structural characteristics effectively. It enhances accuracy by integrating symmetry detection through the Weisfeiler-Lehman test, reducing the number of possible mappings and improving efficiency. Unlike previous methods, it maps the entire reaction, not just main components, providing a comprehensive view. Additionally, by integrating efficient graph matching techniques, it reduces computational complexity, making atom mapping more feasible.

EAGMN: Coronary artery semantic labeling using edge attention graph matching network

Coronary artery disease (CAD) is one of the primary causes leading deaths worldwide. The presence of atherosclerotic lesions in coronary arteries is the underlying pathophysiological basis of CAD, and accurate extraction of individual arterial branches using invasive coronary angiography (ICA) is crucial for stenosis detection and CAD diagnosis. However, deep-learning-based models face challenges in generating semantic segmentation for coronary arteries due to the morphological similarity among different types of arteries. To address this challenge, we propose an innovative approach called the Edge Attention Graph Matching Network (EAGMN) for coronary artery semantic labeling. Inspired by the learning process of interventional cardiologists in interpreting ICA images, our model compares arterial branches between two individual graphs generated from different ICAs. We begin with extracting individual graphs based on the vascular tree obtained from the ICA. Each node in the individual graph represents an arterial segment, and the EAGMN aims to learn the similarity between nodes from the two individual graphs. By converting the coronary artery semantic segmentation task into a graph node similarity comparison task, identifying the node-to-node correspondence would assign semantic labels for each arterial branch. More specifically, the EAGMN utilizes the association graph constructed from the two individual graphs as input. A graph attention module is employed for feature embedding and aggregation, while a decoder generates the linear assignment for node-to-node semantic mapping. Based on the learned node-to-node relationships, unlabeled coronary arterial segments are classified using the labeled coronary arterial segments, thereby achieving semantic labeling. A dataset with 263 labeled ICAs is used to train and validate the EAGMN. Experimental results indicate the EAGMN achieved a weighted accuracy of 0.8653, a weighted precision of 0.8656, a weighted recall of 0.8653 and a weighted F1-score of 0.8643. Furthermore, we employ ZORRO to provide interpretability and explainability of the graph matching for artery semantic labeling. These findings highlight the potential of the EAGMN for accurate and efficient coronary artery semantic labeling using ICAs. By leveraging the inherent characteristics of ICAs and incorporating graph matching techniques, our proposed model provides a promising solution for improving CAD diagnosis and treatment.

Building Multiple Classifier Systems Using Linear Combinations of Reduced Graphs

Despite great efforts done in research in the last decades, the classification of general graphs, i.e., graphs with unconstrained labeling and structure, remains a challenging task. Due to the inherent relational structure of graphs it is difficult, or even impossible, to apply standard pattern recognition methods to graphs to achieve high recognition accuracies. Common methods to solve the non-trivial problem of graph classification employ graph matching in conjunction with a distance-based classifier or a kernel machine. In the present paper, we address the specific task of graph classification by means of a novel framework that uses information acquired from a broad range of reduced graph subspaces. Our novel approach can be roughly divided into three successive steps. In the first step, differently reduced graphs are created out of the original graphs relying on node centrality measures. In the second step, we compute the graph edit distance between each reduced graph and all the other graphs of the corresponding graph subspace. Finally, we linearly combine the distances in the third step and feed them into a distance-based classifier to obtain the final classification result. On six graph data sets, we empirically confirm that the proposed multiple classifier system directly benefits from the combined distances computed in the various graph subspaces.

Functional connectome reorganization relates to post-stroke motor recovery and structural and functional disconnection

Motor recovery following ischemic stroke is contingent on the ability of surviving brain networks to compensate for damaged tissue. In rodent models, sensory and motor cortical representations have been shown to remap onto intact tissue around the lesion site, but remapping to more distal sites (e.g. in the contralesional hemisphere) has also been observed. Resting state functional connectivity (FC) analysis has been employed to study compensatory network adaptations in humans, but mechanisms and time course of motor recovery are not well understood. Here, we examine longitudinal FC in 23 first-episode ischemic pontine stroke patients and utilize a graph matching approach to identify patterns of functional connectivity reorganization during recovery. We quantified functional reorganization between several intervals ranging from 1 week to 6 months following stroke, and demonstrated that the areas that undergo functional reorganization most frequently are in cerebellar/subcortical networks. Brain regions with more structural and functional connectome disruption due to the stroke also had more remapping over time. Finally, we show that functional reorganization is correlated with the extent of motor recovery in the early to late subacute phases, and furthermore, individuals with greater baseline motor impairment demonstrate more extensive early subacute functional reorganization (from one to two weeks post-stroke) and this reorganization correlates with better motor recovery at 6 months. Taken together, these results suggest that our graph matching approach can quantify recovery-relevant, whole-brain functional connectivity network reorganization after stroke.

Automated Iterative Label Transfer Improves Segmentation of Noisy Cells in Adaptive Optics Retinal Images

High quality data labeling is essential for improving the accuracy of deep learning applications in medical imaging. However, noisy images are not only under-represented in training datasets, but also, labeling of noisy data is low quality. Unfortunately, noisy images with poor quality labels are exacerbated by traditional data augmentation strategies. Real world images contain noise and can lead to unexpected drops in algorithm performance. In this paper, we present a non-traditional, purposeful data augmentation method to specifically transfer high quality automated labels into noisy image regions for incorporation into the training dataset. The overall approach is based on the use of paired images of the same cells in which variable image noise results in cell segmentation failures. Iteratively updating the cell segmentation model with accurate labels of noisy image areas resulted in an improvement in Dice coefficient from 77% to 86%. This was achieved by adding only 3.4% more cells to the training dataset, showing that local label transfer through graph matching is an effective augmentation strategy to improve segmentation.

Graph matching survey for medical imaging: On the way to deep learning

The interest on graph matching has not stopped growing since the late seventies. The basic idea of graph matching consists of generating graph representations of different data or structures and compare those representations by searching correspondences between them. There are manifold techniques that have been developed to find those correspondences and the choice of one or another depends on the characteristics of the application of interest. These applications range from pattern recognition (e.g. biometric identification) to signal processing or artificial intelligence. One of the aspects that make graph matching so attractive is its ability to facilitate data analysis, and medical imaging is one of the fields that can benefit from this in a greater extent. The potential of graph matching to find similarities and differences between data acquired at different points in time shows its potential to improve diagnosis, follow-up of human diseases or any other of the clinical scenarios that require comparison between different datasets. In spite of the large amount of papers that were published in this field to the date there is no survey paper of graph matching for clinical applications. This survey aims to fill this gap.

Iterative closest graph matching for non-rigid 3D/2D coronary arteries registration

Background and objective Fusion of the preoperative computed tomography angiography and intraoperative X-ray angiography images can considerably enhance the visual perception of physicians during percutaneous coronary interventions. This technique can provide 3D information of the arteries and reduce the uncertainty of 2D guidance images. For this purpose, 3D/2D vascular registration with high accuracy and robustness is crucial for performing accurate surgery. Methods In this study, we propose an iterative closest graph matching (ICGM) method that utilizes an alternative iteration framework including correspondence and transformation phases. A coarse-to-fine matching approach based on redundant graph matching is proposed for the correspondence phase. The transformation phase involves rigid and non-rigid transformations, in which rigid transformation is calculated using a closed-form solution, and non-rigid transformation is achieved using a statistical shape model established from a synthetic deformation dataset. Results The proposed method is evaluated and compared with nine state-of-the-art methods on simulated data and clinical datasets. Experiments demonstrate that our method is insensitive to the pose of data and robust to noise and deformation. Moreover, it outperforms other methods in terms of registering real data. Conclusions Given its high capture range, the proposed method can register 3D vessels without prior initialization in clinical practice.

Structural textile pattern recognition and processing based on hypergraphs

The humanities, like many other areas of society, are currently undergoing major changes in the wake of digital transformation. However, in order to make collection of digitised material in this area easily accessible, we often still lack adequate search functionality. For instance, digital archives for textiles offer keyword search, which is fairly well understood, and arrange their content following a certain taxonomy, but search functionality at the level of thread structure is still missing. To facilitate the clustering and search, we introduce an approach for recognising similar weaving patterns based on their structures for textile archives. We first represent textile structures using hypergraphs and extract multisets of k-neighbourhoods describing weaving patterns from these graphs. Then, the resulting multisets are clustered using various distance measures and various clustering algorithms (K-Means for simplicity and hierarchical agglomerative algorithms for precision). We evaluate the different variants of our approach experimentally, showing that this can be implemented efficiently (meaning it has linear complexity), and demonstrate its quality to query and cluster datasets containing large textile samples. As, to the best of our knowledge, this is the first practical approach for explicitly modelling complex and irregular weaving patterns usable for retrieval, we aim at establishing a solid baseline.

Alignment of biological networks by integer linear programming: virus-host protein-protein interaction networks

BACKGROUND

The alignment of protein-protein interaction networks was recently formulated as an integer quadratic programming problem, along with a linearization that can be solved by integer linear programming software tools. However, the resulting integer linear program has a huge number of variables and constraints, rendering it of no practical use.

RESULTS

We present a compact integer linear programming reformulation of the protein-protein interaction network alignment problem, which can be solved using state-of-the-art mathematical modeling and integer linear programming software tools, along with empirical results showing that small biological networks, such as virus-host protein-protein interaction networks, can be aligned in a reasonable amount of time on a personal computer and the resulting alignments are structurally coherent and biologically meaningful.

CONCLUSIONS

The implementation of the integer linear programming reformulation using current mathematical modeling and integer linear programming software tools provided biologically meaningful alignments of virus-host protein-protein interaction networks.

Graph Matching Based Connectomic Biomarker with Learning for Brain Disorders

Advances in neuroimaging techniques such as diffusion MRI and functional MRI enabled evaluation of the brain as an information processing network that is called connectome. Connectomic analysis has led to numerous findings on the organization of the brain its pathological changes with diseases, providing imaging-based biomarkers that help in diagnosis and prognosis. A large majority of connectomic biomarkers benefit either from graph-theoretical measures that evaluate brain's network structure, or use standard metrics such as Euclidean distance or Pearson's correlation to show between-connectomes relations. However, such methods are limited in diagnostic evaluation of diseases, because they do not simultaneously measure the difference between individual connectomes, incorporate disease-specific patterns, and utilize network structure information. To address these limitations, we propose a graph matching based method to quantify connectomic similarity, which can be trained for diseases at functional systems level to provide a subject-specific biomarker assessing the disease. We validate our measure on a dataset of patients with traumatic brain injury and demonstrate that our measure achieves better separation between patients and controls compared to commonly used connectomic similarity measures. We further evaluate the vulnerability of the functional systems to the disease by utilizing the parameter tuning aspect of our method. We finally show that our similarity score correlates with clinical scores, highlighting its potential as a subject-specific biomarker for the disease.

Brain network similarity: methods and applications

Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience applications. Here, we discuss the current state of the art, challenges, and a collection of analysis tools that have been developed in recent years to compare brain networks. We first introduce the graph similarity problem in brain network application. We then describe the methodological background of the available metrics and algorithms of comparing graphs, their strengths, and limitations. We also report results obtained in concrete applications from normal brain networks. More precisely, we show the potential use of brain network similarity to build a “network of networks” that may give new insights into the object categorization in the human brain. Additionally, we discuss future directions in terms of network similarity methods and applications.

Discovering large conserved functional components in global network alignment by graph matching

BACKGROUND

Aligning protein-protein interaction (PPI) networks is very important to discover the functionally conserved sub-structures between different species. In recent years, the global PPI network alignment problem has been extensively studied aiming at finding the one-to-one alignment with the maximum matching score. However, finding large conserved components remains challenging due to its NP-hardness.

RESULTS

We propose a new graph matching method GMAlign for global PPI network alignment. It first selects some pairs of important proteins as seeds, followed by a gradual expansion to obtain an initial matching, and then it refines the current result to obtain an optimal alignment result iteratively based on the vertex cover. We compare GMAlign with the state-of-the-art methods on the PPI network pairs obtained from the largest BioGRID dataset and validate its performance. The results show that our algorithm can produce larger size of alignment, and can find bigger and denser common connected subgraphs as well for the first time. Meanwhile, GMAlign can achieve high quality biological results, as measured by functional consistency and semantic similarity of the Gene Ontology terms. Moreover, we also show that GMAlign can achieve better results which are structurally and biologically meaningful in the detection of large conserved biological pathways between species.

CONCLUSIONS

GMAlign is a novel global network alignment tool to discover large conserved functional components between PPI networks. It also has many potential biological applications such as conserved pathway and protein complex discovery across species. The GMAlign software and datasets are avaialbile at https://github.com/yzlwhu/GMAlign .

Accurate Correspondence of Cone Photoreceptor Neurons in the Human Eye Using Graph Matching Applied to Longitudinal Adaptive Optics Images

Loss of cone photoreceptor neurons is a leading cause of many blinding retinal diseases. Direct visualization of these cells in the living human eye is now feasible using adaptive optics scanning light ophthalmoscopy (AOSLO). However, it remains challenging to monitor the state of specific cells across multiple visits, due to inherent eye-motion-based distortions that arise during data acquisition, artifacts when overlapping images are montaged, as well as substantial variability in the data itself. This paper presents an accurate graph matching framework that integrates (1) robust local intensity order patterns (LIOP) to describe neuron regions with illumination variation from different visits; (2) a sparse-coding based voting process to measure visual similarities of neuron pairs using LIOP descriptors; and (3) a graph matching model that combines both visual similarity and geometrical cone packing information to determine the correspondence of repeated imaging of cone photoreceptor neurons across longitudinal AOSLO datasets. The matching framework was evaluated on imaging data from ten subjects using a validation dataset created by removing 15% of the neurons from 713 neuron correspondences across image pairs. An overall matching accuracy of 98% was achieved. The framework was robust to differences in the amount of overlap between image pairs. Evaluation on a test dataset showed that the matching accuracy remained at 98% on approximately 3400 neuron correspondences, despite image quality degradation, illumination variation, large image deformation, and edge artifacts. These experimental results show that our graph matching approach can accurately identify cone photoreceptor neuron correspondences on longitudinal AOSLO images.

INDEX: Incremental depth extension approach for protein-protein interaction networks alignment

High-throughput methods have provided us with a large amount of data pertaining to protein-protein interaction networks. The alignment of these networks enables us to better understand biological systems. Given the fact that the alignment of networks is computationally intractable, it is important to introduce a more efficient and accurate algorithm which finds as large as possible similar areas among networks. This paper proposes a new algorithm named INDEX for the global alignment of protein-protein interaction networks. INDEX has multiple phases. First, it computes topological and biological scores of proteins and creates the initial alignment based on the proposed matching score strategy. Using networks topologies and aligned proteins, it then selects a set of high scoring proteins in each phase and extends new alignments around them until final alignment is obtained. Proposing a new alignment strategy, detailed consideration of matching scores, and growth of the alignment core has led INDEX to obtain a larger common connected subgraph with a much greater number of edges compared with previous methods. Regarding other measures such as edge correctness, symmetric substructure score, and runtime, the proposed algorithm performed considerably better than existing popular methods. Our results show that INDEX can be a promising method for identifying functionally conserved interactions.

AVAILABILITY

The INDEX executable file is available at https://github.com/a-mir/index/.

Sequential Monte Carlo for Maximum Weight Subgraphs with Application to Solving Image Jigsaw Puzzles

We consider a problem of finding maximum weight subgraphs (MWS) that satisfy hard constraints in a weighted graph. The constraints specify the graph nodes that must belong to the solution as well as mutual exclusions of graph nodes, i.e., pairs of nodes that cannot belong to the same solution. Our main contribution is a novel inference approach for solving this problem in a sequential monte carlo (SMC) sampling framework. Usually in an SMC framework there is a natural ordering of the states of the samples. The order typically depends on observations about the states or on the annealing setup used. In many applications (e.g., image jigsaw puzzle problems), all observations (e.g., puzzle pieces) are given at once and it is hard to define a natural ordering. Therefore, we relax the assumption of having ordered observations about states and propose a novel SMC algorithm for obtaining maximum a posteriori estimate of a high-dimensional posterior distribution. This is achieved by exploring different orders of states and selecting the most informative permutations in each step of the sampling. Our experimental results demonstrate that the proposed inference framework significantly outperforms loopy belief propagation in solving the image jigsaw puzzle problem. In particular, our inference quadruples the accuracy of the puzzle assembly compared to that of loopy belief propagation.