We apply the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors. In order to learn an accurate classifier from limited amounts of labeled data, we borrow statistical strength, via an intrinsic network structure, across the dataset. The resulting logistic network Lasso amounts to a regularized empirical risk minimization problem using the total variation of a classifier as a regularizer. This minimization problem is a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.

We apply network Lasso to solve binary classification (clustering) problems on network structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data defined over a complex network structure. The resulting logistic network Lasso classifier amounts to solving a non-smooth convex optimization problem. A scalable classification algorithm is obtained by applying the alternating direction methods of multipliers to solve this optimization problem.