NDLI: Learning with tensors: a framework based on convex optimization and spectral regularization

Content Provider	Springer Nature Link
Author	Sigretto, Marco Tran Dinh, Quoc Lathauwer, Lieven Suykens, Johan A. K.
Copyright Year	2013
Abstract	We present a framework based on convex optimization and spectral regularization to perform learning when feature observations are multidimensional arrays (tensors). We give a mathematical characterization of spectral penalties for tensors and analyze a unifying class of convex optimization problems for which we present a provably convergent and scalable template algorithm. We then specialize this class of problems to perform learning both in a transductive as well as in an inductive setting. In the transductive case one has an input data tensor with missing features and, possibly, a partially observed matrix of labels. The goal is to both infer the missing input features as well as predict the missing labels. For induction, the goal is to determine a model for each learning task to be used for out of sample prediction. Each training pair consists of a multidimensional array and a set of labels each of which corresponding to related but distinct tasks. In either case the proposed technique exploits precise low multilinear rank assumptions over unknown multidimensional arrays; regularization is based on composite spectral penalties and connects to the concept of Multilinear Singular Value Decomposition. As a by-product of using a tensor-based formalism, our approach allows one to tackle the multi-task case in a natural way. Empirical studies demonstrate the merits of the proposed methods.
Starting Page	303
Ending Page	351
Page Count	49
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	94
Issue Number	3
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2013-05-17
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Spectral regularization Matrix and tensor completion Tucker decomposition Multilinear rank Transductive and inductive learning Multi-task learning Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics Computing Methodologies Simulation and Modeling Language Translation and Linguistics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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