2016/12/05 by Alexander Jung, Alfred O. Hero III, Jung, Alexander +6
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Graph Neural Networks #Complex Network Analysis Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1612.01414
openalex publication_date 2016/12/05 · arxiv created 2017/05/15 · arxiv updated 2017/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph signal, defined over some graph (network) structure intrinsic to the dataset. Following the key principle of supervised learning, i.e., similar inputs yield similar outputs, we require the graph signals induced by labels to have small total variation. Accordingly, we formulate the problem of learning the labels of data points as a non-smooth convex optimization problem which amounts to balancing between the empirical loss, i.e., the discrepancy with some partially available label information, and the smoothness quantified by the total variation of the learned graph signal. We solve this optimization problem by appealing to a recently proposed preconditioned variant of the popular primal-dual method by Pock and Chambolle, which results in a sparse label propagation algorithm. This learning algorithm allows for a highly scalable implementation as message passing over the underlying data graph. By applying concepts of compressed sensing to the learning problem, we are also able to provide a transparent sufficient condition on the underlying network structure such that accurate learning of the labels is possible. We also present an implementation of the message passing formulation allows for a highly scalable implementation in big data frameworks.