Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties
This provides a theoretical framework for tensor learning problems with applications in multimodal data analysis, but appears to be an incremental extension of existing kernel methods.
The authors developed a framework for learning functions in tensor product reproducing kernel Hilbert spaces using novel spectral penalties, which generalizes existing tensor completion problems and enables nonlinear extensions of multilinear multitask learning. Their experiments demonstrated the usefulness of these extensions.
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.