Cortical parcellation plays a pivotal role in elucidating the brain organization. Despite the growing efforts to develop parcellation algorithms using functional magnetic resonance imaging, achieving a balance between intra-individual specificity and inter-individual consistency proves challenging, making the generation of high-quality, subject-consistent cortical parcellations particularly elusive. To solve this problem, our paper proposes a fully automated individual cortical parcellation method based on consensus graph representation learning. The method integrates spectral embedding with low-rank tensor learning into a unified optimization model, which uses group-common connectivity patterns captured by low-rank tensor learning to optimize subjects\' functional networks. This not only ensures consistency in brain representations across different subjects but also enhances the quality of each subject\'s representation matrix by eliminating spurious connections. More importantly, it achieves an adaptive balance between intra-individual specificity and inter-individual consistency during this process. Experiments conducted on a test-retest dataset from the Human Connectome Project (HCP) demonstrate that our method outperforms existing methods in terms of reproducibility, functional homogeneity, and alignment with task activation. Extensive network-based comparisons on the HCP S900 dataset reveal that the functional network derived from our cortical parcellation method exhibits greater capabilities in gender identification and behavior prediction than other approaches.

The modular organization of the functional brain connectome implies its functional segregation. Correlation matrices extracted from fMRI data are used as adjacency matrices of the connectome, i.e., the functional connectivity network (FCN). The modular organization of FCN is widely solved using node-community detection methods, albeit with a requirement of edge filtering, mostly. However, network sparsification potentially leads to the loss of correlation information. With no ideal threshold values for edge filtering in literature, there is growing interest in finding communities in the complete weighted network. To address this requirement, we propose the use of exploratory factor analysis (EFA), thus, exploiting the semantics of the correlation matrix. In our recent work on using EFA for FCN analysis, we have proposed a novel consensus-based algorithm using a multiscale approach, where the number of factors nF is treated as the scale. The consensus procedure is employed for transforming the network before performing community detection. Here, we propose a novel extension to our multiscale EFA for finding relevant cliques. We use an ensemble of experiments and extensive quantitative analysis of its outcomes to identify the optimal set of scales for efficient node-partitioning. We perform case studies of datasets of FCN of the human brain at resting state, with different sizes and parcellation atlases (AAL, Schaefer). Our results of consensus communities and cliques correspond to relevant brain activity in its resting state, thus showing the effectiveness of consensus-based multiscale EFA.

Many recent developments surrounding the functional network organization of the human brain have focused on data that have been averaged across groups of individuals. While such group-level approaches have shed considerable light on the brain\'s large-scale distributed systems, they conceal individual differences in network organization, which recent work has demonstrated to be common and widespread. This individual variability produces noise in group analyses, which may average together regions that are part of different functional systems across participants, limiting interpretability. However, cost and feasibility constraints may limit the possibility for individual-level mapping within studies. Here our goal was to leverage information about individual-level brain organization to probabilistically map common functional systems and identify locations of high inter-subject consensus for use in group analyses. We probabilistically mapped 14 functional networks in multiple datasets with relatively high amounts of data. All networks show \"core\" (high-probability) regions, but differ from one another in the extent of their higher-variability components. These patterns replicate well across four datasets with different participants and scanning parameters. We produced a set of high-probability regions of interest (ROIs) from these probabilistic maps; these and the probabilistic maps are made publicly available, together with a tool for querying the network membership probabilities associated with any given cortical location. These quantitative estimates and public tools may allow researchers to apply information about inter-subject consensus to their own fMRI studies, improving inferences about systems and their functional specializations.

Here we show a method of directing the edges of the connectomes, prepared from HARDI datasets from the human brain. Before the present work, no high-definition directed braingraphs were published, because the tractography methods in use are not capable of assigning directions to the neural tracts discovered. Previous work on the functional connectomes applied low-resolution functional MRI-detected statistical causality for the assignment of directions of connectomes of typically several dozens of vertices. Our method is based on the phenomenon of the \"Consensus Connectome Dynamics\", described earlier by our research group. In this contribution, we apply the method to the 423 braingraphs, each with 1015 vertices, computed from the public release of the Human Connectome Project, and we also made the directed connectomes publicly available at the site http://braingraph.org. We also show the robustness of our edge directing method in four independently chosen connectome datasets: we have found that 86% of the edges, which were present in all four datasets, get the same directions in all datasets; therefore the direction method is robust. While our new edge-directing method still needs more empirical validation, we think that our present contribution opens up new possibilities in the analysis of the high-definition human connectome.

Large-scale structural brain networks encode white matter connectivity patterns among distributed brain areas. These connection patterns are believed to support cognitive processes and, when compromised, can lead to neurocognitive deficits and maladaptive behavior. A powerful approach for studying the organizing principles of brain networks is to construct group-representative networks from multisubject cohorts. Doing so amplifies signal to noise ratios and provides a clearer picture of brain network organization. Here, we show that current approaches for generating sparse group-representative networks overestimate the proportion of short-range connections present in a network and, as a result, fail to match subject-level networks along a wide range of network statistics. We present an alternative approach that preserves the connection-length distribution of individual subjects. We have used this method in previous papers to generate group-representative networks, though to date its performance has not been appropriately benchmarked and compared against other methods. As a result of this simple modification, the networks generated using this approach successfully recapitulate subject-level properties, outperforming similar approaches by better preserving features that promote integrative brain function rather than segregative. The method developed here holds promise for future studies investigating basic organizational principles and features of large-scale structural brain networks.

In the applications of the graph theory, it is unusual that one considers numerous, pairwise different graphs on the very same set of vertices. In the case of human braingraphs or connectomes, however, this is the standard situation: the nodes correspond to anatomically identified cerebral regions, and two vertices are connected by an edge if a diffusion MRI-based workflow identifies a fiber of axons, running between the two regions, corresponding to the two vertices. Therefore, if we examine the braingraphs of n subjects, then we have n graphs on the very same, anatomically identified vertex set. It is a natural idea to describe the k-frequently appearing edges in these graphs: the edges that are present between the same two vertices in at least k out of the n graphs. Based on the NIH-funded large Human Connectome Project\'s public data release, we have reported the construction of the Budapest Reference Connectome Server http://www.connectome.pitgroup.org that generates and visualizes these k-frequently appearing edges. We call the graphs of the k-frequently appearing edges \"k-consensus connectomes\" since an edge could be included only if it is present in at least k graphs out of n. Considering the whole human brain, we have reported a surprising property of these consensus connectomes earlier. In the present work we are focusing on the frontal lobe of the brain, and we report here a similarly surprising dynamical property of the consensus connectomes when k is gradually changed from k = n to k = 1: the connections between the nodes of the frontal lobe are seemingly emanating from those nodes that were connected to sub-cortical structures of the dorsal striatum: the caudate nucleus, and the putamen. We hypothesize that this dynamic behavior copies the axonal fiber development of the frontal lobe. An animation of the phenomenon is presented at https://youtu.be/wBciB2eW6_8.

Consensus Connectome Dynamics (CCD) is a remarkable phenomenon of the human connectomes (braingraphs) that was discovered by continuously decreasing the minimum confidence-parameter at the graphical interface of the Budapest Reference Connectome Server, which depicts the cerebral connections of n = 418 subjects with a frequency-parameter k: For any k = 1, 2, …, n one can view the graph of the edges that are present in at least k connectomes. If parameter k is decreased one-by-one from k = n through k = 1 then more and more edges appear in the graph, since the inclusion condition is relaxed. The surprising observation is that the appearance of the edges is far from random: it resembles a growing, complex structure. We hypothesize that this growing structure copies the axonal development of the human brain. Here we show the robustness of the CCD phenomenon: it is almost independent of the particular choice of the set of underlying connectomes. This result shows that the CCD phenomenon is most likely a biological property of the human brain and not just a property of the data sets examined. We also present a simulation that well-describes the growth of the CCD structure: in our random graph model a doubly-preferential attachment distribution is found to mimic the CCD.

Connections of the living human brain, on a macroscopic scale, can be mapped by a diffusion MR imaging based workflow. Since the same anatomic regions can be corresponded between distinct brains, one can compare the presence or the absence of the edges, connecting the very same two anatomic regions, among multiple cortices. Previously, we have constructed the consensus braingraphs on 1015 vertices first in five, then in 96 subjects in the Budapest Reference Connectome Server v1.0 and v2.0, respectively. Here we report the construction of the version 3.0 of the server, generating the common edges of the connectomes of variously parameterizable subsets of the 1015-vertex connectomes of 477 subjects of the Human Connectome Project\'s 500-subject release. The consensus connectomes are downloadable in CSV and GraphML formats, and they are also visualized on the server\'s page. The consensus connectomes of the server can be considered as the \"average, healthy\" human connectome since all of their connections are present in at least k subjects, where the default value of [Formula: see text], but it can also be modified freely at the web server. The webserver is available at http://connectome.pitgroup.org.

The number of resting state functional connectivity MRI studies continues to expand at a rapid rate along with the options for data processing. Of the processing options, few have generated as much controversy as global signal regression and the subsequent observation of negative correlations (anti-correlations). This debate has motivated new processing strategies and advancement in the field, but has also generated significant confusion and contradictory guidelines. In this article, we work towards a consensus regarding global signal regression. We highlight several points of agreement including the fact that there is not a single \"right\" way to process resting state data that reveals the \"true\" nature of the brain. Although further work is needed, different processing approaches likely reveal complementary insights about the brain\'s functional organisation.

The human braingraph or the connectome is the object of an intensive research today. The advantage of the graph-approach to brain science is that the rich structures, algorithms and definitions of graph theory can be applied to the anatomical networks of the connections of the human brain. In these graphs, the vertices correspond to the small (1-1.5 cm2) areas of the gray matter, and two vertices are connected by an edge, if a diffusion-MRI based workflow finds fibers of axons, running between those small gray matter areas in the white matter of the brain. One main question of the field today is discovering the directions of the connections between the small gray matter areas. In a previous work we have reported the construction of the Budapest Reference Connectome Server http://connectome.pitgroup.org from the data recorded in the Human Connectome Project of the NIH. The server generates the consensus braingraph of 96 subjects in Version 2, and of 418 subjects in Version 3, according to selectable parameters. After the Budapest Reference Connectome Server had been published, we recognized a surprising and unforeseen property of the server. The server can generate the braingraph of connections that are present in at least k graphs out of the 418, for any value of k = 1, 2, …, 418. When the value of k is changed from k = 418 through 1 by moving a slider at the webserver from right to left, certainly more and more edges appear in the consensus graph. The astonishing observation is that the appearance of the new edges is not random: it is similar to a growing shrub. We refer to this phenomenon as the Consensus Connectome Dynamics. We hypothesize that this movement of the slider in the webserver may copy the development of the connections in the human brain in the following sense: the connections that are present in all subjects are the oldest ones, and those that are present only in a decreasing fraction of the subjects are gradually the newer connections in the individual brain development. An animation on the phenomenon is available at https://youtu.be/yxlyudPaVUE. Based on this observation and the related hypothesis, we can assign directions to some of the edges of the connectome as follows: Let Gk + 1 denote the consensus connectome where each edge is present in at least k+1 graphs, and let Gk denote the consensus connectome where each edge is present in at least k graphs. Suppose that vertex v is not connected to any other vertices in Gk+1, and becomes connected to a vertex u in Gk, where u was connected to other vertices already in Gk+1. Then we direct this (v, u) edge from v to u.