2013/10/18 by Marco Signoretto, Signoretto, Marco, Lieven De Lathauwer +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Speech Recognition and Synthesis #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1310.4977
openalex publication_date 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors. When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems. Other special cases include transfer learning with multimodal side information and multilinear multitask learning. For the latter case, our kernel-based view is instrumental to derive nonlinear extensions of existing model classes. We give a novel algorithm and show in experiments the usefulness of the proposed extensions.