A generative-discriminative framework that integrates imaging, genetic, and diagnosis into coupled low dimensional space

We propose a novel optimization framework that integrates imaging and genetics data for simultaneous biomarker identification and disease classification. The generative component of our model uses a dictionary learning framework to project the imaging and genetic data into a shared low dimensional space. We have coupled both the data modalities by tying the linear projection coefficients to the same latent space. The discriminative component of our model uses logistic regression on the projection vectors for disease diagnosis. This prediction task implicitly guides our framework to find interpretable biomarkers that are substantially different between a healthy and disease population. We exploit the interconnectedness of different brain regions by incorporating a graph regularization penalty into the joint objective function. We also use a group sparsity penalty to find a representative set of genetic basis vectors that span a low dimensional space where subjects are easily separable between patients and controls. We have evaluated our model on a population study of schizophrenia that includes two task fMRI paradigms and single nucleotide polymorphism (SNP) data. Using ten-fold cross validation, we compare our generative-discriminative framework with canonical correlation analysis (CCA) of imaging and genetics data, parallel independent component analysis (pICA) of imaging and genetics data, random forest (RF) classification, and a linear support vector machine (SVM). We also quantify the reproducibility of the imaging and genetics biomarkers via subsampling. Our framework achieves higher class prediction accuracy and identifies robust biomarkers. Moreover, the implicated brain regions and genetic variants underlie the well documented deficits in schizophrenia.