Fast approximate quadratic programming for graph matching

Graph alignment exploiting the spatial organization improves the similarity of brain networks

Every brain is unique, having its structural and functional organization shaped by both genetic and environmental factors over the course of its development. Brain image studies tend to produce results by averaging across a group of subjects, under the common assumption that it is possible to subdivide the cortex into homogeneous areas while maintaining a correspondence across subjects. We investigate this assumption: can the structural properties of a specific region of an atlas be assumed to be the same across subjects? This question is addressed by looking at the network representation of the brain, with nodes corresponding to brain regions and edges to their structural relationships. Using an unsupervised graph matching strategy, we align the structural connectomes of a set of healthy subjects, considering parcellations of different granularity, to understand the connectivity misalignment between regions. First, we compare the obtained permutations with four different algorithm initializations: Spatial Adjacency, Identity, Barycenter, and Random. Our results suggest that applying an alignment strategy improves the similarity across subjects when the number of parcels is above 100 and when using Spatial Adjacency and Identity initialization (the most plausible priors). Second, we characterize the obtained permutations, revealing that the majority of permutations happens between neighbors parcels. Lastly, we study the spatial distribution of the permutations. By visualizing the results on the cortex, we observe no clear spatial patterns on the permutations and all the regions across the context are mostly permuted with first and second order neighbors.

Bisected graph matching improves automated pairing of bilaterally homologous neurons from connectomes

Graph matching algorithms attempt to find the best correspondence between the nodes of two networks. These techniques have been used to match individual neurons in nanoscale connectomes-in particular, to find pairings of neurons across hemispheres. However, since graph matching techniques deal with two isolated networks, they have only utilized the ipsilateral (same hemisphere) subgraphs when performing the matching. Here, we present a modification to a state-of-the-art graph matching algorithm that allows it to solve what we call the bisected graph matching problem. This modification allows us to leverage the connections between the brain hemispheres when predicting neuron pairs. Via simulations and experiments on real connectome datasets, we show that this approach improves matching accuracy when sufficient edge correlation is present between the contralateral (between hemisphere) subgraphs. We also show how matching accuracy can be further improved by combining our approach with previously proposed extensions to graph matching, which utilize edge types and previously known neuron pairings. We expect that our proposed method will improve future endeavors to accurately match neurons across hemispheres in connectomes, and be useful in other applications where the bisected graph matching problem arises.

Generative network modeling reveals quantitative definitions of bilateral symmetry exhibited by a whole insect brain connectome

Comparing connectomes can help explain how neural connectivity is related to genetics, disease, development, learning, and behavior. However, making statistical inferences about the significance and nature of differences between two networks is an open problem, and such analysis has not been extensively applied to nanoscale connectomes. Here, we investigate this problem via a case study on the bilateral symmetry of a larval Drosophila brain connectome. We translate notions of 'bilateral symmetry' to generative models of the network structure of the left and right hemispheres, allowing us to test and refine our understanding of symmetry. We find significant differences in connection probabilities both across the entire left and right networks and between specific cell types. By rescaling connection probabilities or removing certain edges based on weight, we also present adjusted definitions of bilateral symmetry exhibited by this connectome. This work shows how statistical inferences from networks can inform the study of connectomes, facilitating future comparisons of neural structures.

The connectome of an insect brain

Brains contain networks of interconnected neurons and so knowing the network architecture is essential for understanding brain function. We therefore mapped the synaptic-resolution connectome of an entire insect brain (Drosophila larva) with rich behavior, including learning, value computation, and action selection, comprising 3016 neurons and 548,000 synapses. We characterized neuron types, hubs, feedforward and feedback pathways, as well as cross-hemisphere and brain-nerve cord interactions. We found pervasive multisensory and interhemispheric integration, highly recurrent architecture, abundant feedback from descending neurons, and multiple novel circuit motifs. The brain's most recurrent circuits comprised the input and output neurons of the learning center. Some structural features, including multilayer shortcuts and nested recurrent loops, resembled state-of-the-art deep learning architectures. The identified brain architecture provides a basis for future experimental and theoretical studies of neural circuits.

RV-ESA: A novel computer-aided elastic shape analysis system for retinal vessels in diabetic retinopathy

Diabetic retinopathy (DR), one of the most common and serious complications of diabetes, has become one of the main blindness diseases. The retinal vasculature is the only part of the human circulatory system that allows direct noninvasive visualization of the body's microvasculature, which provides the opportunity to detect the structural and functional changes before DR becomes unable to intervene. For decades, as the fundamental step in computer-assisted analysis of retinopathy, retinal vascular extraction methods have been largely developed. However, further research focusing on retinal vascular analysis is still in its infancy. Meanwhile, due to the complexity of retinal vascular structure, the relationship between vascular geometry and DR has never been concluded. This paper aims to provide a novel computer-aided shape analysis system for retinal vessels. To perform retinal vascular shape analysis, a mathematical geometric representation is firstly generated by utilizing the proposed shape modeling method. Then, several useful statistical tools (e.g. Graph Mean, Graph PCA) are adopted to quantitatively analyze the vascular shape. Besides, in order to visualize the changes in vascular shape in the progression of DR, a geodesic tool is used to display the deformation process for ophthalmologists to observe. The efficacy of this analysis system is demonstrated in the EyePACS dataset and the subsequent visit records of 98 patients from the proprietary dataset. The experimental results show that there is a certain correlation between the variation of retinal vascular shape and DR progression, and the Graph PCA scores of retinal vessels are negatively correlated with DR grades. The code of our RV-ESA system can be publicly available at github.com/XiaolingLuo/RV-ESA.

Ability-Based Methods for Personalized Keyboard Generation

This study introduces an ability-based method for personalized keyboard generation, wherein an individual's own movement and human-computer interaction data are used to automatically compute a personalized virtual keyboard layout. Our approach integrates a multidirectional point-select task to characterize cursor control over time, distance, and direction. The characterization is automatically employed to develop a computationally efficient keyboard layout that prioritizes each user's movement abilities through capturing directional constraints and preferences. We evaluated our approach in a study involving 16 participants using inertial sensing and facial electromyography as an access method, resulting in significantly increased communication rates using the personalized keyboard (52.0 bits/min) when compared to a generically optimized keyboard (47.9 bits/min). Our results demonstrate the ability to effectively characterize an individual's movement abilities to design a personalized keyboard for improved communication. This work underscores the importance of integrating a user's motor abilities when designing virtual interfaces.

Ability-based Keyboards for Augmentative and Alternative Communication: Understanding How Individuals' Movement Patterns Translate to More Efficient Keyboards: Methods to Generate Keyboards Tailored to User-specific Motor Abilities

This study presents the evaluation of ability-based methods extended to keyboard generation for alternative communication in people with dexterity impairments due to motor disabilities. Our approach characterizes user-specific cursor control abilities from a multidirectional point-select task to configure letters on a virtual keyboard based on estimated time, distance, and direction of movement. These methods were evaluated in three individuals with motor disabilities against a generically optimized keyboard and the ubiquitous QWERTY keyboard. We highlight key observations relating to the heterogeneity of the manifestation of motor disabilities, perceived importance of communication technology, and quantitative improvements in communication performance when characterizing an individual's movement abilities to design personalized AAC interfaces.

Network alignment and similarity reveal atlas-based topological differences in structural connectomes

The interactions between different brain regions can be modeled as a graph, called connectome, whose nodes correspond to parcels from a predefined brain atlas. The edges of the graph encode the strength of the axonal connectivity between regions of the atlas that can be estimated via diffusion magnetic resonance imaging (MRI) tractography. Herein, we aim to provide a novel perspective on the problem of choosing a suitable atlas for structural connectivity studies by assessing how robustly an atlas captures the network topology across different subjects in a homogeneous cohort. We measure this robustness by assessing the alignability of the connectomes, namely the possibility to retrieve graph matchings that provide highly similar graphs. We introduce two novel concepts. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Leman (WL) graph-isomorphism test. We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available.

An important part of our current understanding of the structure of the human brain relies on the concept of brain network, which is obtained by looking at how different brain regions are connected with each other. In this paper we present a strategy for choosing a suitable parcellation of the brain for structural connectivity studies by making use of the concepts of network alignment and similarity. To do so, we design a novel similarity measure between weighted networks called graph Jaccard index, and a new network alignment technique called WL-align. By assessing the possibility to retrieve graph matchings that provide highly similar graphs, we show that morphology- and structure-based atlases define brain networks that are more topologically robust across a wide range of resolutions.

Graph Matching between Bipartite and Unipartite Networks: to Collapse, or not to Collapse, that is the Question

Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. We theoretically demonstrate that our methodology is consistent, and provide non-asymptotic conditions that ensure exact recovery of the matching solution. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair, and brain structural and functional data.

Cellular connectomes as arbiters of local circuit models in the cerebral cortex

With the availability of cellular-resolution connectivity maps, connectomes, from the mammalian nervous system, it is in question how informative such massive connectomic data can be for the distinction of local circuit models in the mammalian cerebral cortex. Here, we investigated whether cellular-resolution connectomic data can in principle allow model discrimination for local circuit modules in layer 4 of mouse primary somatosensory cortex. We used approximate Bayesian model selection based on a set of simple connectome statistics to compute the posterior probability over proposed models given a to-be-measured connectome. We find that the distinction of the investigated local cortical models is faithfully possible based on purely structural connectomic data with an accuracy of more than 90%, and that such distinction is stable against substantial errors in the connectome measurement. Furthermore, mapping a fraction of only 10% of the local connectome is sufficient for connectome-based model distinction under realistic experimental constraints. Together, these results show for a concrete local circuit example that connectomic data allows model selection in the cerebral cortex and define the experimental strategy for obtaining such connectomic data.

Matchability of heterogeneous networks pairs

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks directly. We further demonstrate that under mild model assumptions, matchability is almost perfectly recovered by centering the networks using universal singular value thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.

Matched Filters for Noisy Induced Subgraph Detection

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to Drosophila and human connectomes that this approach can achieve good performance.

A statistical model for brain networks inferred from large-scale electrophysiological signals

Network science has been extensively developed to characterize the structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally obtained biological data represent one instance of a larger number of realizations with similar intrinsic topology. A modelling approach is therefore needed to support statistical inference on the bottom-up local connectivity mechanisms influencing the formation of the estimated brain networks. Here, we adopted a statistical model based on exponential random graph models (ERGMs) to reproduce brain networks, or connectomes, estimated by spectral coherence between high-density electroencephalographic (EEG) signals. ERGMs are made up by different local graph metrics, whereas the parameters weight the respective contribution in explaining the observed network. We validated this approach in a dataset of N = 108 healthy subjects during eyes-open (EO) and eyes-closed (EC) resting-state conditions. Results showed that the tendency to form triangles and stars, reflecting clustering and node centrality, better explained the global properties of the EEG connectomes than other combinations of graph metrics. In particular, the synthetic networks generated by this model configuration replicated the characteristic differences found in real brain networks, with EO eliciting significantly higher segregation in the alpha frequency band (8-13 Hz) than EC. Furthermore, the fitted ERGM parameter values provided complementary information showing that clustering connections are significantly more represented from EC to EO in the alpha range, but also in the beta band (14-29 Hz), which is known to play a crucial role in cortical processing of visual input and externally oriented attention. Taken together, these findings support the current view of the functional segregation and integration of the brain in terms of modules and hubs, and provide a statistical approach to extract new information on the (re)organizational mechanisms in healthy and diseased brains.

The Development and Analysis of Integrated Neuroscience Data

There is a strong emphasis on developing novel neuroscience technologies, in particular on recording from more neurons. There has thus been increasing discussion about how to analyze the resulting big datasets. What has received less attention is that over the last 30 years, papers in neuroscience have progressively integrated more approaches, such as electrophysiology, anatomy, and genetics. As such, there has been little discussion on how to combine and analyze this multimodal data. Here, we describe the growth of multimodal approaches, and discuss the needed analysis advancements to make sense of this data.

Graph Matching: Relax at Your Own Risk

Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.