We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations.

We construct Functional Connectivity Networks (FCN) from resting state fMRI (rsfMRI) recordings towards the classification of brain activity between healthy and schizophrenic subjects using a publicly available dataset (the COBRE dataset) of 145 subjects (74 healthy controls and 71 schizophrenic subjects). First, we match the anatomy of the brain of each individual to the Desikan-Killiany brain atlas. Then, we use the conventional approach of correlating the parcellated time series to construct FCN and ISOMAP, a nonlinear manifold learning algorithm to produce low-dimensional embeddings of the correlation matrices. For the classification analysis, we computed five key local graph-theoretic measures of the FCN and used the LASSO and Random Forest (RF) algorithms for feature selection. For the classification we used standard linear Support Vector Machines. The classification performance is tested by a double cross-validation scheme (consisting of an outer and an inner loop of “Leave one out” cross-validation (LOOCV)). The standard cross-correlation methodology produced a classification rate of 73.1%, while ISOMAP resulted in 79.3%, thus providing a simpler model with a smaller number of features as chosen from LASSO and RF, namely the participation coefficient of the right thalamus and the strength of the right lingual gyrus.

We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parameter space. In the second step, based on the selected features, we learn the right-hand-side of the effective PDEs using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks (RPNNs), which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to perform numerical bifurcation analysis of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was $$\sim $$ ∼ 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for the data-driven numerical solution of the inverse problem for high-dimensional PDEs.

We localize the sources of brain activity of children with epilepsy based on electroencephalograph (EEG) recordings acquired during a visual discrimination working memory task. For the numerical solution of the inverse problem, with the aid of age-specific MRI scans processed from a publicly available database, we use and compare three regularization numerical methods, namely the standardized low resolution brain electromagnetic tomography (sLORETA), the weighted minimum norm estimation (wMNE) and the dynamic statistical parametric mapping (dSPM). We show that all three methods provide the same spatio-temporal patterns of differences between the groups of epileptic and control children. In particular, our analysis reveals statistically significant differences between the two groups in regions of the parietal cortex indicating that these may serve as "biomarkers" for diagnostic purposes and ultimately localized treatment.

No abstract