Node data

Node_data.mat contains the arrays Node_Hessians,Node_gradients_at_0,Centralized_Hessian and Centralized_gradient_at_0. These arrays are used to define the quadratic optimization problem used in the article "Distributed Newton Method Over Graphs: Can Sharing of Second-order Information Eliminate the Condition Number Dependence?" See that article for details about the problem. At node i, the Hessian for the unregularized problem is Node_Hessians(:,:,i) and for a given variable vector w, the gradient is Node_Hessians(:,:,i)*w + Node_gradients_at_0. For the centralized, unregularized problem, the Hessian is Centralized_Hessian and for a given variable vector w, the gradient is Centralized_Hessian*w + Centralized_gradient_at_0. The original data, from which the gradient and Hessian arrays have been computed after centering and then distributing the data points among the 10 nodes, is part of the million song dataset, and can be found by using the provided link, titled "Original data source".