We apply multilinear principal component analysis to dimension reduction and classification of human volumetric organ data, which are expressed as multiway array data. For the decomposition of multiway array data, tensor-based principal component analysis extracts multilinear structure of the data. We numerically clarify that low-pass filtering after the multidimensional discrete cosine transfo...

The ability to approximate a multivariate function/tensor as a sum of separable functions/tensors is quite useful, but algorithms to do so exhibit unpleasantly interesting behavior known as swamps. Such swamps have been the bane of users for decades and need to be understood so they can be alleviated. In previous work, we developed and applied dynamical systems concepts to analyze the simplest ...

In this paper we introduce a statistic snake that learns and tracks image features by means of statistic learning techniques. Using probabilistic principal component analysis a feature description is obtained from a training set of object profiles. In our approach a sound statistical model is introduced to define a likelihood estimate of the grey-level local image profiles together with their l...

In this paper, we explore a novel observational signature of gravitational corrections during slow-roll inflation. We study the coupling of the inflaton field to highercurvature tensors in models with a minimal breaking of conformal symmetry. In that case, the most general correction to the tensor two-point function is captured by a coupling to the square of the Weyl tensor. We show that these ...

We point out that hard exclusive production of tensor mesons f 2 (1270) with helicity λ = ±2 is dominated by the gluon component in the meson wave function and can be used to determine gluon admixture in tensor mesons in a theoretically clean manner. We present a detailed analysis of the tensor meson distribution amplitudes and calculate the transition form factor γ + γ * → f 2 (1270) for one r...

Tensor representation is helpful to reduce the small sample size problem in discriminative subspace selection. As pointed by this paper, this is mainly because the structure information of objects in computer vision research is a reasonable constraint to reduce the number of unknown parameters used to represent a learning model. Therefore, we apply this information to the vector-based learning ...

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchi...

This paper proposes a compensated algorithm to evaluate Bézier tensor product surfaces with floating-point coefficients and coordinates. This algorithm is based on the application of error-free transformations to improve the traditional de Casteljau tensor product algorithm. This compensated algorithm extends the compensated de Casteljau algorithm for the evaluation of a Bézier curve to the cas...

The tensor rank and border rank of the $3 \times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well. We also include an analysis of $5 \times 5$ and $7 \times 7$ determinant and permanent tensors, as well as the symmetric $3 \times 3$ permanent and determinant tensors. We end wit...

This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices and higher-order tensors. We propose to use an approach based on probabilistic interpretation of t...