Deep collaborative learning with application to multimodal brain development study.

Multi-modal fMRI imaging has been used to study brain development such as the difference of functional connectivities (FCs) between different ages. Canonical correlation analysis (CCA) has been used to find correlations between multiple imaging modalities. However, it is unrelated to phenotypes. On the other hand, regression models can identify phenotype related imaging features but overlook the cross-modal data correlation. Collaborative regression (CR) is thus introduced to incorporate correlation as a penalization term into the regression model. Nevertheless, the complex relationship (e.g., nonlinear predictive relationship) between multiple data yet cannot be captured using linear CR models. To this end, we propose a novel method, deep collaborative learning (DCL), to address their limitations. DCL first uses a deep network to represent original data and then seeks their correlations, while also linking the data representation with phenotypical information. Therefore, DCL can better combine complex correlations between multiple data sets in addition to their fitting to phenotypes, with the potential to overcome the limitations of several current models. Based on DCL model, we study the difference of FCs between different age groups and also use FCs as a fingerprint to predict cognitive abilities. Our experiments demonstrated higher accuracy of using DCL over other conventional models when classifying populations of different ages and cognitive scores. Moreover, our experiments showed that different age or cognition groups may exhibit more significant differences of FCs in several networks than others. Furthermore, DCL revealed that brain connections became stronger at adolescence stage, demonstrating the importance of adolescence for brain development. In addition, DCL detected strong correlations between default mode network (DMN) and other networks which were overlooked by linear CCA, demonstrating DCL's ability of detecting nonlinear correlations.