  We apply the network Lasso to solve binary classification and clustering
problems for network-structured data. To this end, we generalize ordinary
logistic regression to non-Euclidean data with an intrinsic network structure.
The resulting "logistic network Lasso" amounts to solving a non-smooth convex
regularized empirical risk minimization. The risk is measured using the
logistic loss incurred over a small set of labeled nodes. For the
regularization, we propose to use the total variation of the classifier
requiring it to conform to the underlying network structure. A scalable
implementation of the learning method is obtained using an inexact variant of
the alternating direction methods of multipliers which results in a scalable
learning algorithm
