In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensorW∗ and an entrywise sparse corruption tensor V∗. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We...

BACKGROUND Histological behavior of glioblastoma multiforme suggests it would benefit more from a global rather than regional evaluation. A global (whole-brain) calculation of diffusion tensor imaging (DTI) derived tensor metrics offers a valid method to detect the integrity of white matter structures without missing infiltrated brain areas not seen in conventional sequences. In this study we c...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

Second-order tensors may be described in terms of shape and orientation. Shape is quantified by tensor invariants, which are fixed with respect to coordinate system changes. This chapter describes an anatomically-motivated method of detecting edges in diffusion tensor fields based on the gradients of invariants. Three particular invariants (the mean, variance, and skewness of the tensor eigenva...

Moment tensors derived from seismic measurements during earthquakes are related to stress tensors and keep important information about surface displacement in the earth’s mantle. We present methods facilitating an interactive visualization of scattered moment data to support earthquake and displacement analysis. For this goal, we combine and link visualizations of spatial location and orientati...

Tensor decompositions are a valuable tool in data analysis, but the computational cost of standard tensor algorithms quickly becomes prohibitive, especially when considering large and time-evolving data sets such as those found in signal processing applications. In this work multilinear PCA, a common tensor analysis technique, will be modified to enable the processing of large scale tensorial t...

In this chapter we define the topology of 2D asymmetric tensor fields in terms of two graphs corresponding to the eigenvalue and eigenvector analysis for the tensor fields, respectively. Asymmetric tensor field topology can not only yield a concise representation of the field, but also provide a framework for spatial-temporal tracking of field features. Furthermore, inherent topological constra...

Human action can be naturally represented as multidimensional arrays known as tensors. In this paper, a simple and efficient algorithm based on tensor subspace learning is proposed for human action recognition. An action is represented as a 3th-order tensor first, then tensor principal component analysis is used to reduce dimensionality and extract the most useful features for action recognitio...

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require matrixinversion; and (ii) they cannot (or at least is very difficult to) handle structured regularizations. We propose a new tensor factorization algorithm that circumven...