A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskalfactor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model is adapted for online learning, which allows dictionary learning on large data...

Tensor decompositions and tensor networks are emerging and promising tools for data analysis and data mining. In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of tensorization (i.e., creating very high-order tensors...

• BCI pipeline with tensor feature reduction and analytical regularization. Comparison three state-of-the-art methods during different perturbations. Achieves high accuracy in short trials small sample sizes. Offers performance both low number of electrodes. Suitable for noisy data, channel setups limited training data. Periodic signals called Steady-State Visual Evoked Potentials (SSVEP) are e...

This paper investigates the trifocal tensor for an affine trinocular rig and defines an affine trifocal tensor. The question of the degrees of freedom of the tensor entries will be addressed, and a novel algorithm to compute the tensor by a linear technique is presented. It will be shown that 4 point or 8 line correspondences along the three images are enough for a reliable computation of the t...

Low-rank tensor completion is a well-studied problem and has applications in various fields. However, in many real-world applications the data is dynamic, i.e., the tensor grows as new data arrives. Besides the tensor, in many real-world scenarios, side information is also available in the form of matrices which also grow. Existing work on dynamic tensor completion do not incorporate side infor...

Registration or spatial normalization of diffusion tensor images plays an important role in many areas of human brain white matter research, such as analysis of Fraction Anisotropy (FA) or whiter matter tracts. More difficult than registration of scalar images, spatial normalization of tensor images requires two important parts: one is tensor interpolation, and the other is tensor reorientation...

We consider a two-form antisymmetric tensor field φ minimally coupled to a nonabelian vector field with a field strength F . Canonical analysis suggests that a pseudoscalar mass term μ 2 2 Tr(φ∧φ) for the tensor field eliminates degrees of freedom associated with this field. Explicit one loop calculations show that an additional coupling mTr(φ ∧ F ) (which can be eliminated classically by a ten...

We present a visual approach for the exploration of stress tensor fields. Therefore, we introduce the idea of multiple linked views to tensor visualization. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress te...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix m n × ∈ X  , the time...