2013/07/17 by Bernardino Romera-Paredes, Bernardino Romera‐Paredes, Romera-Paredes, Bernardino +2 · 108 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Computer science #Convex analysis #Convex optimization #FOS: Computer and information sciences #FOS: Mathematics #Generalization #Geometry #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical analysis #Mathematical optimization #Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Proximal gradient methods for learning #Pure mathematics #Regular polygon #Regularization (linguistics) #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1307.4653
published in arXiv (Cornell University) 26, 2967-2975 (Cornell University)
arxiv created 2013/07/17 · openalex publication_date 2013/07/17 · arxiv updated 2013/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the problem of learning a tensor from a set of linear measurements. A prominent methodology for this problem is based on a generalization of trace norm regularization, which has been used extensively for learning low rank matrices, to the tensor setting. In this paper, we highlight some limitations of this approach and propose an alternative convex relaxation on the Euclidean ball. We then describe a technique to solve the associated regularization problem, which builds upon the alternating direction method of multipliers. Experiments on one synthetic dataset and two real datasets indicate that the proposed method improves significantly over tensor trace norm regularization in terms of estimation error, while remaining computationally tractable.