In the context of supervised tensor learning, preserving the structural information and exploiting the discriminative nonlinear relationships of tensor data are crucial for improving the performance of learning tasks. Based on tensor factorization theory and kernel methods, we propose a novel Kernelized Support Tensor Machine (KSTM) which integrates kernelized tensor factorization with maximum-...

[A] matrix with constants describing the anisotropy of the material [B] strain matrix [BL] linear strain matrix [BNL] nonlinear strain matrix c speed of sound d rate of deformation tensor dp plastic rate of deformation D elastic constitutive tensor [D] matrix of the elastic constitutive tensor [DT] matrix form of the constitutive tensor ds lengths of the vector dx dS lengths of the vector dX dv...

The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the 27 and tensor fields in the 27 representation of E6(6). This novel tensor-vector system is subject to an intricate set of gauge transformations, describing 3(27 − t) massless helicity degrees of freedom for the vector fields and 3t massive spin degrees of freedom for the tenso...

Introduction: Population and longitudinal analyses using Diffusion Tensor Imaging (DTI) data have become feasible over the past decade with advanced sequences and sophisticated mathematical tools. These studies make use of some form of elastic tensor field registration framework to derive a population average brain and the deviation modes. These registration algorithms need to employ a speciali...

We introduce an algorithm to compute tensor Interpolative Decomposition (tensor ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ǫ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. Tensor ID can be used as an alternative to or in combinati...

We propose a nonlinear partial differential equation (PDE) for regularizing a tensor which contains the first derivative information of an image such as strength of edges and a direction of the gradient of the image. Unlike a typical diffusivity matrix which consists of derivatives of a tensor data, we propose a diffusivity matrix which consists of the tensor data itself, i.e., derivatives of a...

The problem of testing whether an incomplete tensor lies in a given tensor subspace is significant when it is impossible to observe all entries of a tensor. We focus on this problem under tubal-sampling and elementwise-sampling. Different from the matrix case, our problem is much more challenging due to the curse of dimensionality and different definitions for tensor operators. In this paper, t...

Diffusion Tensor MRI (DT-MRI) can provide important in vivo information for the detection of brain abnormalities in diseases characterized by compromised neural connectivity. To quantify diffusion tensor abnormalities based on voxel-based statistical analysis, spatial normalization is required to minimize the anatomical variability between studied brain structures. In this article, we used a mu...

Moment tensors are indefinite tensors derived from seismic measurements and encode important information about earthquakes and surface displacement in the earth’s mantle. Appropriate analysis of scattered moment tensor fields requires multi-scale visualization to identify related seismic events. For this matter we provide a visualization of the tensor field at different scales based on multivar...