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.
A major challenge in cognitive neuroscience is to evaluate the ability of the human brain to categorize or group visual stimuli based on common features. This categorization process is very fast and occurs in few hundreds of millisecond time scale. However, an accurate tracking of the spatiotemporal dynamics of large-scale brain networks is still an unsolved issue. Here, we show the combination of recently developed method called dense-EEG source connectivity to identify functional brain networks with excellent temporal and spatial resolutions and an algorithm, called SimNet, to compute brain …
Quantifying the similarity between two networks is critical in many applications. A number of algorithms have been proposed to compute graph similarity, mainly based on the properties of nodes and edges. Interestingly, most of these algorithms ignore the physical location of the nodes, which is a key factor in the context of brain networks involving spatially defined functional areas. In this paper, we present a novel algorithm called "SimiNet" for measuring similarity between two graphs whose nodes are defined a priori within a 3D coordinate system. SimiNet provides a quantified index (rangin…
Cognition involves dynamic reconfiguration of functional brain networks at sub-second time scale. A precise tracking of these reconfigurations to categorize visual objects remains elusive. Here, we use dense electroencephalography (EEG) data recorded during naming meaningful (tools, animals) and scrambled objects from 20 healthy subjects. We combine technique for identifying functional brain networks and recently developed algorithm for estimating networks similarity to discriminate between the two categories. First, we showed that dynamic networks of both categories can be segmented into seve…
Perceptual similarity is a cognitive judgment that represents the end-stage of a complex cascade of hierarchical processing throughout visual cortex. Previous studies have shown a correspondence between the similarity of coarse-scale fMRI activation patterns and the perceived similarity of visual stimuli, suggesting that visual objects that appear similar also share similar underlying patterns of neural activation. Here we explore the temporal relationship between the human brain's time-varying representation of visual patterns and behavioral judgments of perceptual similarity. The visual stim…
The unique Hamiltonian description of neuro- and psycho-dynamics at the macroscopic, classical, inter-neuronal level of brain's neural networks, and microscopic, quantum, intra-neuronal level of brain's microtubules, is presented in the form of open Liouville equations. This implies the arrow of time in both neuro- and psycho-dynamic processes and shows the existence of the formal neuro-biological space-time self-similarity. Keywords: Neuro- and psycho-dynamics, Brain microtubules, Hamiltonian and Liouville dynamics, Neuro-biological self-similarity
Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain possesses a rich architecture organized over multiple scales linked to one another. We explored the multiscale organization of human connectomes using datasets of healthy subjects reconstructed at five different resolutions. We found that the structure of the human brain remains self-similar when the resolution of observation is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, a geometric network model, where dist…
I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.
Brain activity differs vastly between sleep, cognitive tasks, and action. Information theory is an appropriate concept to analytically quantify these brain states. Based on neurophysiological recordings, this concept can handle complex data sets, is free of any requirements about the data structure, and can infer the present underlying brain mechanisms. Specifically, by utilizing algorithmic information theory, it is possible to estimate the absolute information contained in brain responses. While current approaches that apply this theory to neurophysiological recordings can discriminate betwe…
Anatomical connectivity imposes strong constraints on brain function, but there is no general agreement about principles that govern its organization. Based on extensive quantitative data we tested the power of three models to predict connections of the primate cerebral cortex: architectonic similarity (structural model), spatial proximity (distance model) and thickness similarity (thickness model). Architectonic similarity showed the strongest and most consistent influence on connection features. This parameter was strongly associated with the presence or absence of inter-areal connections an…
Institute for Logic, Language and Computation（逻辑、语言与计算研究所）；University of Amsterdam（阿姆斯特丹大学）
In this paper, we define and apply representational stability analysis (ReStA), an intuitive way of analyzing neural language models. ReStA is a variant of the popular representational similarity analysis (RSA) in cognitive neuroscience. While RSA can be used to compare representations in models, model components, and human brains, ReStA compares instances of the same model, while systematically varying single model parameter. Using ReStA, we study four recent and successful neural language models, and evaluate how sensitive their internal representations are to the amount of prior context. Us…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Extended Kalman filter (EKF) does not guarantee consistent mean and covariance under linearization, even though it is the main framework for robotic localization. While Lie group improves the modeling of the state space in localization, the EKF on Lie group still relies on the arbitrary Gaussian assumption in face of nonlinear models. We instead use von Mises filter for orientation estimation together with the conventional Kalman filter for position estimation, and thus we are able to characterize the first two moments of the state estimates. Since the proposed algorithm holds a solid probabil…
Facebook AI Research（Facebook AI研究院）；Université de Paris（巴黎大学）；CoML, ENS/CNRS/EHESS/INRIA/PSL University（计算语言学实验室，巴黎高等师范学院/法国国家科学研究中心/法国社会科学高等研究院/法国国家信息与自动化研究所/巴黎文理研究大学）；CRI, Département Frontières du Vivant et de l’Apprendre, IIFR, Université de Paris（认知研究所，生命与学习前沿系，法国医学研究院，巴黎大学）；École normale supérieure, PSL University, CNRS（巴黎高等师范学院，巴黎文理研究大学，法国国家科学研究中心）
Our ability to comprehend speech remains, to date, unrivaled by deep learning models. This feat could result from the brain's ability to fine-tune generic sound representations for speech-specific processes. To test this hypothesis, we compare i) five types of deep neural networks to ii) human brain responses elicited by spoken sentences and recorded in 102 Dutch subjects using functional Magnetic Resonance Imaging (fMRI). Each network was either trained on an acoustics scene classification, a speech-to-text task (based on Bengali, English, or Dutch), or not trained. The similarity between eac…
Brain networks can be defined and explored through their connectivity. Here, we analyzed the relationship between structural connectivity (SC) across 2,514 regions that cover the entire brain and brainstem, and their dynamic functional connectivity (DFC). To do so, we focused on a combination of two metrics: the first assesses the degree of SC-DFC similarity and the second is the intrinsic variability of the DFC networks over time. Overall, we found that cerebellar networks have a smaller DFC variability than other networks in the brain. Moreover, the internal structure of the cerebellum could…
Istituto Italiano di Tecnologia（意大利技术研究院）；Università degli Studi di Genova（热那亚大学）；Scientific Institute IRCCS “E. Medea”（IRCCS“E. Medea”科学研究所）；Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico（IRCCS Ca’ Granda马焦雷医院基金会）；Università di Milano（米兰大学）；Università di Verona（维罗纳大学）；Wayne State University（韦恩州立大学）；Fondazione Bruno Kessler（布鲁诺·凯斯勒基金会）
fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs to propose a novel approach for assessing similarity in functional networks. In particular, we compared network similarity between pairs of twins in task-relevant and task-orthogonal networks. The proposed method measures the similarity between functional networks using a geodesic…
Intrinsic brain activity is characterized by highly structured co-activations between different regions, whose origin is still under debate. In this paper, we address the question whether it is possible to unveil how the underlying anatomical connectivity shape the brain's spontaneous correlation structure. We start from the assumption that in order for two nodes to exhibit large covariation, they must be exposed to similar input patterns from the entire network. We then acknowledge that information rarely spreads only along an unique route, but rather travels along all possible paths. In real…
Electroencephalogram (EEG) has been one of the common neuromonitoring modalities for real-world brain-computer interfaces (BCIs) because of its non-invasiveness, low cost, and high temporal resolution. Recently, light-weight and portable EEG wearable devices based on low-density montages have increased the convenience and usability of BCI applications. However, loss of EEG decoding performance is often inevitable due to reduced number of electrodes and coverage of scalp regions of a low-density EEG montage. To address this issue, we introduce knowledge distillation (KD), a learning mechanism d…
Objective: Endophenotypes such as brain age and fluid intelligence are important biomarkers of disease status. However, brain imaging studies to identify these biomarkers often encounter limited numbers of subjects and high dimensional imaging features, hindering reproducibility. Therefore, we develop an interpretable, multivariate classification/regression algorithm, called Latent Similarity (LatSim), suitable for small sample size, high feature dimension datasets. Methods: LatSim combines metric learning with a kernel similarity function and softmax aggregation to identify task-related simil…
Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and global organization of a brain network can shed light on mechanisms of complex cognitive functions, while disruptions within the network can be linked to neurodevelopmental disorders. In this effort, the construction of a representative brain network for each individual is critical for further analysis. Additionally, graph comparison is an essential step for…
Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relation…
National Digital Switching System Engineering and Technological Research Center（国家数字交换系统工程技术研究中心）；People's Hospital of Henan Province（河南省人民医院）；Shanghai Mental Health Center, Shanghai Jiao Tong University School of Medicine（上海交通大学医学院附属精神卫生中心）；Institute of Psychology and Behavioral Science, Shanghai Jiao Tong University（上海交通大学心理与行为科学研究院）
Despite the remarkable similarities between convolutional neural networks (CNN) and the human brain, CNNs still fall behind humans in many visual tasks, indicating that there still exist considerable differences between the two systems. Here, we leverage adversarial noise (AN) and adversarial interference (AI) images to quantify the consistency between neural representations and perceptual outcomes in the two systems. Humans can successfully recognize AI images as corresponding categories but perceive AN images as meaningless noise. In contrast, CNNs can correctly recognize AN images but mista…
What is the relationship between brain and behavior? The answer to this question necessitates characterizing the mapping between structure and function. The aim of this paper is to discuss broad issues surrounding the link between structure and function in the brain that will motivate a network perspective to understanding this question. As others in the past, I argue that a network perspective should supplant the common strategy of understanding the brain in terms of individual regions. Whereas this perspective is needed for a fuller characterization of the mind-brain, it should not be viewed…
Istanbul Technical University（伊斯坦布尔理工大学）；University of Dundee（邓迪大学）
One of the greatest scientific challenges in network neuroscience is to create a representative map of a population of heterogeneous brain networks, which acts as a connectional fingerprint. The connectional brain template (CBT), also named network atlas, presents a powerful tool for capturing the most representative and discriminative traits of a given population while preserving its topological patterns. The idea of a CBT is to integrate a population of heterogeneous brain connectivity networks, derived from different neuroimaging modalities or brain views (e.g., structural and functional), …
University of Rome, Tor Vergata（罗马第二大学）；Istituto di Bioimmagini e Fisiologia Molecolare, CNR（意大利国家研究委员会生物成像与分子生理学研究所）；Martinos Center for Biomedical Imaging（马丁诺斯生物医学成像中心）；MGH（麻省总医院）；Harvard Medical School（哈佛医学院）
Brain decoding is a field of computational neuroscience that uses measurable brain activity to infer mental states or internal representations of perceptual inputs. Therefore, we propose a novel approach to brain decoding that also relies on semantic and contextual similarity. We employ an fMRI dataset of natural image vision and create a deep learning decoding pipeline inspired by the existence of both bottom-up and top-down processes in human vision. We train a linear brain-to-feature model to map fMRI activity features to visual stimuli features, assuming that the brain projects visual info…
The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essent…
Exploring the human brain networks during rest is a topic of great interest. Several structural and functional studies have previously been conducted to study the intrinsic brain networks. In this paper, we focus on investigating the human brain network topology using dense Electroencephalography (EEG) source connectivity approach. We applied graph theoretical methods on functional networks reconstructed from resting state data acquired using EEG in 14 healthy subjects. Our findings confirmed the existence of sets of brain regions considered as functional hubs. In particular, the isthmus cingu…
Existing brain network distances are often based on matrix norms. The element-wise differences in the existing matrix norms may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A major disadvantage to element-wise distance calculations is that it could be severely affected even by a small number of extreme edge weights. Thus it is necessary to develop network distances that recognize topology. In this paper, we provide a survey of bottleneck, Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances that are adapted for brain networks, and …
Higher brain function relies upon the ability to flexibly integrate information across specialized communities of brain regions, however it is unclear how this mechanism manifests over time. In this study, we use time-resolved network analysis of functional magnetic resonance imaging data to demonstrate that the human brain traverses between two functional states that maximize either segregation into tight-knit communities or integration across otherwise disparate neural regions. The integrated state enables faster and more accurate performance on a cognitive task, and is associated with dilat…
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com…
It is widely believed that the formation of brain network structure is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the question of whether this trade-off exists in empirical human brain networks and, if so, how it takes effect is still not well understood. Here, we employed a multiobjective evolutionary algorithm to directly and quantitatively explore the cost-efficiency trade-off in human brain networks. Using this algorithm, we generated a population of synthetic networks with optimal but diverse cost-efficiency trade-…
Many recent efforts in computational modeling of macro-scale brain dynamics have begun to take a data-driven approach by incorporating structural and/or functional information derived from subject data. Here, we discuss recent work using personalized brain network models to study structure-function relationships in human brains. We describe the steps necessary to build such models and show how this computational approach can provide previously unobtainable information through the ability to perform virtual experiments. Finally, we present examples of how personalized brain network models can b…
In Indian history of arts, Rasas are the aesthetics associated with any auditory, visual, literary or musical piece of art that evokes highly orchestrated emotional states. In this work, we study the functional response of the brain to movie clippings meant to evoke the Rasas through network analysis. We extract functional brain networks using coherence measures on EEG recordings of film clips from popular Indian Bollywood movies representing nine Rasas in the Indian Natyasastra. Structural and functional network measures were computed for these brain networks, averaging over a range of signif…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Representational Similarity Analysis (RSA) aims to explore similarities between neural activities of different stimuli. Classical RSA techniques employ the inverse of the covariance matrix to explore a linear model between the neural activities and task events. However, calculating the inverse of a large-scale covariance matrix is time-consuming and can reduce the stability and robustness of the final analysis. Notably, it becomes severe when the number of samples is too large. For facing this shortcoming, this paper proposes a novel RSA method called gradient-based RSA (GRSA). Moreover, the p…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Macquarie University（麦考瑞大学）；Suzhou University（宿州学院）
Brain Electroencephalography (EEG) classification is widely applied to analyze cerebral diseases in recent years. Unfortunately, invalid/noisy EEGs degrade the diagnosis performance and most previously developed methods ignore the necessity of EEG selection for classification. To this end, this paper proposes a novel maximum weight clique-based EEG selection approach, named mwcEEGs, to map EEG selection to searching maximum similarity-weighted cliques from an improved Fréchet distance-weighted undirected EEG graph simultaneously considering edge weights and vertex weights. Our mwcEEGs improves…
University of Tübingen（蒂宾根大学）；Baylor College of Medicine（贝勒医学院）；Rice University（莱斯大学）
Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We propose to regularize CNNs using large-scale neuroscience data to learn more robust neural features in terms of representational similarity. We presented natural images to mice and measured the responses of thousands of neurons from cortical visual areas. Next, we denoised the notoriously variable neural activity using strong predictive models trained on thi…
We investigated the degree distribution of brain networks extracted from functional magnetic resonance imaging of the human brain. In particular, the distributions are compared between macroscopic brain networks using region-based nodes and mesoscopic brain networks using voxel-based nodes. We found that the distribution from these networks follow the same family of distributions and represent a continuum of exponentially truncated power law distributions.
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two most often observed characteristics of complex networks are scale-free and small-world properties. In this paper, we will explore whether brain networks follow scale-free and small-worldness among other graph theory properties.
Traditional approaches to understanding the brain's resilience to neuropathology have identified neurophysiological variables, often described as brain or cognitive 'reserve,' associated with better outcomes. However, mechanisms of function and resilience in large-scale brain networks remain poorly understood. Dynamic network theory may provide a basis for substantive advances in understanding functional resilience in the human brain. In this perspective, we describe recent theoretical approaches from network control theory as a framework for investigating network level mechanisms underlying c…
Neuropsychiatric disorders impact functional connectivity of the brain at the network level. The identification and statistical testing of disorder-related networks remains challenging. We propose novel methods to streamline the detection and testing of the hidden, disorder-related connectivity patterns as network-objects. We define an abnormal connectome subnetwork as a network-object that includes three classes: nodes of brain areas, edges representing brain connectomic features, and an organized graph topology formed by these nodes and edges. Comparing to the conventional statistical method…
In this research, a number of popular network measurement algorithms have been applied to several brain networks (based on applicability of algorithms) for finding out statistical correlation among these popular network measurements which will help scientists to understand these popular network measurement algorithms and their applicability to brain networks. By analysing the results of correlations among these network measurement algorithms, statistical comparison among selected brain networks has also been summarized. Besides that, to understand each brain network, the visualization of each …
We explore the main characteristics of big brain network data that offer unique statistical challenges. The brain networks are biologically expected to be both sparse and hierarchical. Such unique characterizations put specific topological constraints onto statistical approaches and models we can use effectively. We explore the limitations of the current models used in the field and offer alternative approaches and explain new challenges.
Small-world structures are often used to describe structural connections in the brain. In this work, we compare the structural connection of cortical areas of a healthy brain and a brain affected by Alzheimer's disease with artificial small-world networks. Based on statistics analysis, we demonstrate that similar small-world networks can be constructed using Newman-Watts procedure. The network quantifiers of both structural matrices are identified inside the probabilistic valley. Despite of similarities between structural connection matrices and sampled small-world networks, increased assortat…
This report discusses the application of neural networks (NNs) as small segments of the brain. The networks representing the biological connectome are altered both spatially and temporally. The degradation techniques applied here are "weight degradation", "weight scrambling", and variable activation function. These methods aim to shine light on the study of neurodegenerative diseases such as Alzheimer's, Huntington's and Parkinson's disease as well as strokes and brain tumors disrupting the flow of information in the brain's network. Fundamental insights to memory loss and generalized learning…
