Group replicator dynamics: a novel group-wise evolutionary approach for sparse brain network detection

Shift of pairwise similarities for data clustering

Several clustering methods (e.g., Normalized Cut and Ratio Cut) divide the Min Cut cost function by a cluster dependent factor (e.g., the size or the degree of the clusters), in order to yield a more balanced partitioning. We, instead, investigate adding such regularizations to the original cost function. We first consider the case where the regularization term is the sum of the squared size of the clusters, and then generalize it to adaptive regularization of the pairwise similarities. This leads to shifting (adaptively) the pairwise similarities which might make some of them negative. We then study the connection of this method to Correlation Clustering and then propose an efficient local search optimization algorithm with fast theoretical convergence rate to solve the new clustering problem. In the following, we investigate the shift of pairwise similarities on some common clustering methods, and finally, we demonstrate the superior performance of the method by extensive experiments on different datasets.

Estimating Dynamic Connectivity States in fMRI Using Regime-Switching Factor Models

We consider the challenges in estimating the state-related changes in brain connectivity networks with a large number of nodes. Existing studies use the sliding-window analysis or time-varying coefficient models, which are unable to capture both smooth and abrupt changes simultaneously, and rely on ad-hoc approaches to the high-dimensional estimation. To overcome these limitations, we propose a Markov-switching dynamic factor model, which allows the dynamic connectivity states in functional magnetic resonance imaging (fMRI) data to be driven by lower-dimensional latent factors. We specify a regime-switching vector autoregressive (SVAR) factor process to quantity the time-varying directed connectivity. The model enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We develop a three-step estimation procedure: 1) extracting the factors using principal component analysis, 2) identifying connectivity regimes in a low-dimensional subspace based on the factor-based SVAR model, and 3) constructing high-dimensional state connectivity metrics based on the subspace estimates. Simulation results show that our estimator outperforms -means clustering of time-windowed coefficients, providing more accurate estimate of time-evolving connectivity. It achieves percentage of reduction in mean squared error by 60% when the network dimension is comparable to the sample size. When applied to the resting-state fMRI data, our method successfully identifies modular organization in the resting-statenetworksin consistencywith other studies. It further reveals changes in brain states with variations across subjects and distinct large-scale directed connectivity patterns across states.

Stable Overlapping Replicator Dynamics for Brain Community Detection

A fundamental means for understanding the brain's organizational structure is to group its spatially disparate regions into functional subnetworks based on their interactions. Most community detection techniques are designed for generating partitions, but certain brain regions are known to interact with multiple subnetworks. Thus, the brain's underlying subnetworks necessarily overlap. In this paper, we propose a technique for identifying overlapping subnetworks from weighted graphs with statistical control over false node inclusion. Our technique improves upon the replicator dynamics formulation by incorporating a graph augmentation strategy to enable subnetwork overlaps, and a graph incrementation scheme for merging subnetworks that might be falsely split by replicator dynamics due to its stringent mutual similarity criterion in defining subnetworks. To statistically control for inclusion of false nodes into the detected subnetworks, we further present a procedure for integrating stability selection into our subnetwork identification technique. We refer to the resulting technique as stable overlapping replicator dynamics (SORD). Our experiments on synthetic data show significantly higher accuracy in subnetwork identification with SORD than several state-of-the-art techniques. We also demonstrate higher test-retest reliability in multiple network measures on the Human Connectome Project data. Further, we illustrate that SORD enables identification of neuroanatomically-meaningful subnetworks and network hubs.

Deep neural network with weight sparsity control and pre-training extracts hierarchical features and enhances classification performance: Evidence from whole-brain resting-state functional connectivity patterns of schizophrenia

Functional connectivity (FC) patterns obtained from resting-state functional magnetic resonance imaging data are commonly employed to study neuropsychiatric conditions by using pattern classifiers such as the support vector machine (SVM). Meanwhile, a deep neural network (DNN) with multiple hidden layers has shown its ability to systematically extract lower-to-higher level information of image and speech data from lower-to-higher hidden layers, markedly enhancing classification accuracy. The objective of this study was to adopt the DNN for whole-brain resting-state FC pattern classification of schizophrenia (SZ) patients vs. healthy controls (HCs) and identification of aberrant FC patterns associated with SZ. We hypothesized that the lower-to-higher level features learned via the DNN would significantly enhance the classification accuracy, and proposed an adaptive learning algorithm to explicitly control the weight sparsity in each hidden layer via L1-norm regularization. Furthermore, the weights were initialized via stacked autoencoder based pre-training to further improve the classification performance. Classification accuracy was systematically evaluated as a function of (1) the number of hidden layers/nodes, (2) the use of L1-norm regularization, (3) the use of the pre-training, (4) the use of framewise displacement (FD) removal, and (5) the use of anatomical/functional parcellation. Using FC patterns from anatomically parcellated regions without FD removal, an error rate of 14.2% was achieved by employing three hidden layers and 50 hidden nodes with both L1-norm regularization and pre-training, which was substantially lower than the error rate from the SVM (22.3%). Moreover, the trained DNN weights (i.e., the learned features) were found to represent the hierarchical organization of aberrant FC patterns in SZ compared with HC. Specifically, pairs of nodes extracted from the lower hidden layer represented sparse FC patterns implicated in SZ, which was quantified by using kurtosis/modularity measures and features from the higher hidden layer showed holistic/global FC patterns differentiating SZ from HC. Our proposed schemes and reported findings attained by using the DNN classifier and whole-brain FC data suggest that such approaches show improved ability to learn hidden patterns in brain imaging data, which may be useful for developing diagnostic tools for SZ and other neuropsychiatric disorders and identifying associated aberrant FC patterns.

Coupled Stable Overlapping Replicator Dynamics for Multimodal Brain Subnetwork Identification

Combining imaging modalities to synthesize their inherent strengths provides a promising means for improving brain subnetwork identification. We propose a multimodal integration technique based on a sex-differentiated formulation of replicator dynamics for identifying subnetworks of brain regions that exhibit high inter-connectivity both functionally and structurally. Our method has a number of desired properties, namely, it can operate on weighted graphs derived from functional magnetic resonance imaging (tMRI) and diffusion MRI (dMRI) data, allows for subnetwork overlaps, has an intrinsic criterion for setting the number of subnetworks, and provides statistical control on false node inclusion in the identified subnetworks via the incorporation of stability selection. We thus refer to our technique as coupled stable overlapping replicator dynamics (CSORD). On synthetic data, We demonstrate that CSORD achieves significantly higher subnetwork identification accuracy than state-of-the-art techniques. On real. data from the Human Connectome Project (HCP), we show that CSORD attains improved test-retest reliability on multiple network measures and superior task classification accuracy.

Identifying Sparse Connectivity Patterns in the brain using resting-state fMRI

The human brain processes information via multiple distributed networks. An accurate model of the brain's functional connectome is critical for understanding both normal brain function as well as the dysfunction present in neuropsychiatric illnesses. Current methodologies that attempt to discover the organization of the functional connectome typically assume spatial or temporal separation of the underlying networks. This assumption deviates from an intuitive understanding of brain function, which is that of multiple, inter-dependent spatially overlapping brain networks that efficiently integrate information pertinent to diverse brain functions. It is now increasingly evident that neural systems use parsimonious formations and functional representations to efficiently process information while minimizing redundancy. Hence we exploit recent advances in the mathematics of sparse modeling to develop a methodological framework aiming to understand complex resting-state fMRI connectivity data. By favoring networks that explain the data via a relatively small number of participating brain regions, we obtain a parsimonious representation of brain function in terms of multiple "Sparse Connectivity Patterns" (SCPs), such that differential presence of these SCPs explains inter-subject variability. In this manner the sparsity-based framework can effectively capture the heterogeneity of functional activity patterns across individuals while potentially highlighting multiple sub-populations within the data that display similar patterns. Our results from simulated as well as real resting state fMRI data show that SCPs are accurate and reproducible between sub-samples as well as across datasets. These findings substantiate existing knowledge of intrinsic functional connectivity and provide novel insights into the functional organization of the human brain.

A functional network estimation method of resting-state fMRI using a hierarchical Markov random field

We propose a hierarchical Markov random field model for estimating both group and subject functional networks simultaneously. The model takes into account the within-subject spatial coherence as well as the between-subject consistency of the network label maps. The statistical dependency between group and subject networks acts as a regularization, which helps the network estimation on both layers. We use Gibbs sampling to approximate the posterior density of the network labels and Monte Carlo expectation maximization to estimate the model parameters. We compare our method with two alternative segmentation methods based on K-Means and normalized cuts, using synthetic and real fMRI data. The experimental results show that our proposed model is able to identify both group and subject functional networks with higher accuracy on synthetic data, more robustness, and inter-session consistency on the real data.

Group analysis of resting-state fMRI by hierarchical Markov random fields

Identifying functional networks from resting-state functional MRI is a challenging task, especially for multiple subjects. Most current studies estimate the networks in a sequential approach, i.e., they identify each individual subject's network independently to other subjects, and then estimate the group network from the subjects networks. This one-way flow of information prevents one subject's network estimation benefiting from other subjects. We propose a hierarchical Markov random field model, which takes into account both the within-subject spatial coherence and between-subject consistency of the network label map. Both population and subject network maps are estimated simultaneously using a Gibbs sampling approach in a Monte Carlo expectation maximization framework. We compare our approach to two alternative groupwise fMRI clustering methods, based on K-means and normalized Cuts, using both synthetic and real fMRI data. We show that our method is able to estimate more consistent subject label maps, as well as a stable group label map.

Overlapping replicator dynamics for functional subnetwork identification

Functional magnetic resonance imaging (fMRI) has been widely used for inferring brain regions that tend to work in tandem and grouping them into subnetworks. Despite that certain brain regions are known to interact with multiple subnetworks, few existing techniques support identification of subnetworks with overlaps. To address this limitation, we propose a novel approach based on replicator dynamics that facilitates detection of sparse overlapping subnetworks. We refer to our approach as overlapping replicator dynamics (RDOL). On synthetic data, we show that RDOL achieves higher accuracy in subnetwork identification than state-of-the-art methods. On real data, we demonstrate that RDOL is able to identify major functional hubs that are known to serve as communication channels between brain regions, in addition to detecting commonly observed functional subnetworks. Moreover, we illustrate that knowing the subnetwork overlaps enables inference of functional pathways, e.g. from primary sensory areas to the integration hubs.