A Manifold Regularized Multi-Task Learning Model for IQ Prediction From Two fMRI Paradigms

Abstract

Objective: Multi-modal brain functional connectivity (FC) data have shown great potential for providing insights into individual variations in behavioral and cognitive traits. The joint learning of multi-modal data can utilize intrinsic association, and thus can boost learning performance. Although several multi-task based learning models have already been proposed by viewing feature learning on each modality as one task, most of them ignore the structural information inherent across the modalities, which may play an important role in extracting discriminative features.

Methods: In this paper, we propose a new manifold regularized multi-task learning model by simultaneously considering between-subject and between-modality relationships. Specifically, the l_2,1-norm (i.e., group-sparsity) regularizer is enforced to jointly select a few common features across different modalities. A novelly designed manifold regularizer is further imposed as a crucial underpinning to preserve the structural information both within and between modalities. Such designed regularizers will make our model more adaptive to realistic neuroimaging data, which are usually of small sample size but high dimensional features.

Results: Our model is validated on the Philadelphia Neurodevelopmental Cohort dataset, where our modalities are regarded as two types of functional MRI (fMRI) data collected under two paradigms. We conduct experimental studies on fMRI-based FC network data in two task conditions for intelligence quotient (IQ) prediction. The results show that our proposed model can not only achieve improved prediction performance, but also yield a set of IQ-relevant biomarkers.

Conclusion and significance: This paper develops a new multi-task learning model, enabling the discovery of significant biomarkers that may account for a proportion of the variance in human intelligence.

Fig. 1.

The illustration of the relation of data among modalities when M = 2 and N = 3. Circles and rectangles respectively represent the subjects in two modalities. Blue connections denote the relation of subjects within each single modality, and orange connections denote the relation of subjects between modalities. (a) and (b) characterize the manifold regularizers in the M2TL model and our proposed NM2TL model, respectively. The M2TL model overlooks the inter-modal connections.

Fig. 2.

The flowchart of the proposed framework in this study.

Fig. 3.

The IQ score distribution among the 355 subjects.

Fig. 4.

The regression performance of the proposed NM2TL model on different parameters’ settings, i.e., β, γ, λ ∈ {10⁻³, 3 × 10⁻³, 10⁻², 3 × 10⁻², 10⁻¹, 0.3, 1, 3, 10, 30}. (a) nback fMRI (CCs). (b) nback fMRI (RMSEs). (c) emotion fMRI (CCs). (d) emotion fMRI (RMSEs).

Fig. 5.

The regression performance with respect to the values of β, i.e., β ∈ {10⁻³, 3 × 10⁻³, 10⁻², 3 × 10⁻², 10⁻¹, 0.3, 1, 3, 10, 30}, and the selection of γ and λ. (a) The performance of nback fMRI and emotion fMRI in terms of the CC. (b) The performance of nback fMRI and emotion fMRI in terms of the RMSE.

Fig. 6.

The regression results of combining nback fMRI and emotion fMRI as in (26) with respect to different values of α.

Fig. 7.

The visualization of the overlapping FCs between the top 150 FCs selected separately by the 5-fold CV and 10-fold CV techniques, for (a) nback and (b) emotion modalities, respectively. The left are brain plots of functional graph in the anatomical space, where the selected FCs are represented as the edges. The thicknesses of the edges consensus the corresponding FCs with their weights. The ROIs are color-coded according to the cortical lobes: frontal (FRO), parietal (PAR), temporal (TEM), occipital (OCC), limbic (LIM), cerebellum (CER), and sub-lobar (SUB). The right are matrix plots that represent the total number of the overlapping edges connecting the ROIs across the cortical lobes.

Fig. 8.

The visualization of the overlapping ROIs between the top 100 ROIs selected separately by the 5-fold CV and 10-fold CV techniques, for (a) nback and (b) emotion modalities, respectively. The left are brain plots of functional graph in the anatomical space, where the selected ROIs are represented as the nodes. The sizes of the nodes consensus the corresponding ROIs with their weights. The ROIs are color-coded according to the cortical lobes. The right are bar plots that represent the total number of the overlapping ROIs in each cortical lobe.