While supervised and unsupervised learning on a single graph have been well explored in the literature, supervised learning frameworks on multiple graphs and the pertinent model construction have yet to be well established. In light of the trace regression which has been previously applied to compressed sensing, matrix completion, and multi-task regression, we propose a method to efficiently and accurately estimate a low rank coefficient matrix in the trace regression model where the explanatory variables are the adjacency matrices converted from the graphs. Given a collection of graphs, we utilize the so-called singular value thresholding algorithm that approximates the unknown coefficient matrix in the trace regression model with minimum nuclear norm among all candidates matrices satisfying the designated convex constraints. The algorithm iteratively produces a sequence of matrices ${mathbf{X}^k,ilde{Theta}^k}$ where soft-thresholding is operated on the singular values of the coefficient matrix $ilde{Theta}^k$. We show through simulation that the singular value thresholding algorithm yields decent prediction accuracy under various specification of the artificial error. Applying the singular value thresholding algorithm on the human brain graphs, we see that it can effectively produces a low-rank estimation of the coefficient matrix while the prediction accuracy is not unacceptable.
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