Construction of embedded fMRI resting-state functional connectivity networks using manifold learning

Abstract

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.

ISOMAP and machine learning algorithms for the construction of embedded functional connectivity networks of anatomically separated brain regions from resting state fMRI data of patients with Schizophrenia

“…The selection of the embedding dimension p was based on the spectrum of the eigenvalues resulting from the last step of the algorithm (the MDS decomposition on the geodesic distance matrix D G ) (see also in [27] ). A gap between some of the first larger eigenvalues and the rest of the spectrum suggests that these few larger eigenmodes extract most of the information related to the distance differences among data points.…”

“…Besides the use of linear correlation for the construction of FCN, nonlinear manifold learning algorithms such as Isometric Mapping (ISOMAP) and Diffusion Maps, have been also applied for the construction of FCN [16] , [27] . Other approaches such as cross-recurrence analysis and multilayer modelling [28] have been also proposed.…”

“…The analysis revealed differences in small-world properties among groups and 13 global-graph theoretic features led to a reported 65% accuracy rate (evaluating the model using a 10-fold cross validation scheme). Gallos et al [27] used both linear (multidimensional scaling) and nonlinear manifold approaches (ISOMAP, Locally Linear Embedding, kernel PCA and Diffusion Maps) to construct embedded FCN based on the COBRE dataset. The classification performance of the global network properties was tested using key global graph-theoretic properties and several machine learning techniques including radial SVM and neural networks.…”

“…Thus, here, building on recent methodological advances [16] , [27] , [30] , we used ISOMAP to construct embedded FCN towards the classification of 71 schizophrenia patients and 74 healthy controls from the COBRE dataset, targeting at the local graph theoretical properties of the embedded FCN. Thus, we matched the different anatomical regions of each individual in accordance with the Desikan-Killiany Atlas [31] .…”

“…We constructed FCN by (a) the standard approach, i.e. by-cross-correlating the rsfMRI time series [15] , [18] , [19] and, (b) using ISOMAP [16] , [27] , [33] to produce low dimensional embeddings of the correlation matrices. Based on the constructed FCN, we calculated five local graph theoretic measures, namely the participation coefficient, the strength of node, the betweenness centrality, the nodal efficiency and the local clustering coefficient.…”