Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framewo...

ecause scientists don't have proper tensor-display techB niques, they now visualize many physical problems incompletely in terms of vector or scalar data. Scientists could undoubtedly get new insights into these problems if they had a methodology for visualizing 3D second-order tensor fields. We present hyperstreamlines as a way of visualizing these data. Second-order tensor fields are fundamen...

Abstract. We propose a novel and constructive algorithm that decomposes an arbitrary tensor into a finite sum of orthonormal rank-1 outer factors. The algorithm, named TTr1SVD, works by converting the tensor into a rank-1 tensor train (TT) series via singular value decomposition (SVD). TTr1SVD naturally generalizes the SVD to the tensor regime and delivers elegant notions of tensor rank and err...

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a...

a new and significant source of information on earthquake studies has been provided by space geodesy. the data which are gathered by various techniques of space geodesy, can quantify potential of seismic activity in the region of interest. to achieve this goal, the main advantage of extra-terrestrial geodetic data in comparison with the conventional data from geology and seismology is the abili...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

This paper briefly describes a framework for storage of geometric tensor array data, useful for storage of regularly sampled tensor fields and regularly sampled tensor-valued functions on charts of manifolds in differential geometry. The framework, called Similar Tensor Array Core Headers, abbreviated STACH and pronounced like the english word ”stash”, capture the essence of tensor field proces...

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem is capturing some delay/shift-invariant structure. In this study, we consider a low-rank model in an embedded space of a tensor. For this purpose, we extend a...

With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, ho...

We present " GEMM-like Tensor-Tensor multiplication " (GETT), a novel approach to tensor contractions that mirrors the design of a high-performance general matrix-matrix multiplication (GEMM). The critical insight behind GETT is the identification of three index sets, involved in the tensor contraction, which enable us to systematically reduce an arbitrary tensor contraction to loops around a h...