Braman [1] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear transformations over vectors with real-valued scalars. This result is based upon a circulant-based tensor multiplication due to Kilmer et al. [4]. In this work,...

Generalized multilinear model for dimensionality reduction of binary tensors (GMM-DR-BT) is a technique for computing low-rank approximations of multi-dimensional data objects, tensors. The model exposes a latent structure that represents dominant trends in the binary tensorial data while retaining as much information as possible. Recently, there exist several models for computing the low-rank ...

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we build upon a novel framework called FEAST(Feature ExtrAction using Score function Tensors) which incorporates generative models for discriminative learning. FEAST considers a novel class of matrix and tensor-valued featur...

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

Abstract In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank in three space dimensions. So great body of works have been devoted to this specific class tensors and their physical applications that review would perhaps be welcome by number students. Here, we endeavour place into broader perspective, considering non-vanishing traces non-fully as well....

Matrix fields are becoming increasingly important in digital imaging. In order to perform shape analysis, enhancement or segmentation of such matrix fields, appropriate image processing tools must be developed. This paper extends fundamental morphological operations to the setting of matrices, in the literature sometimes referred to as tensors despite the fact that matrices are only rank two te...

Few-shot segmentation (FSS) aims to segment unseen classes given only a few annotated samples. Encouraging progress has been made for FSS by leveraging semantic features learned from base with sufficient training samples represent novel classes. The correlation-based methods lack the ability consider interaction of two subspace matching scores due inherent nature real-valued 2D convolutions. In...

It has been shown that a best rank-R approximation of an order-k tensor may not exist when R ≥ 2 and k ≥ 3. This poses a serious problem to data analysts using tensor decompositions. It has been observed numerically that, generally, this issue cannot be solved by consecutively computing and subtracting best rank-1 approximations. The reason for this is that subtracting a best rank-1 approximati...

In recent joint work with András Vasy [19], we analyze the low energy behavior of differential form-valued waves on black hole spacetimes. In order to deduce asymptotics and decay from this, one in addition needs high energy estimates for the wave operator acting on sections of the form bundle. The present paper provides these on perturbations of Schwarzschild-de Sitter spaces in all spacetime ...

Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are 3×3 symmetric positive definite (SPD) matrices, along fiber bundles. This paper develops a functional data analysis framework to model diffusion tensors along fiber tracts as functional data in a Riemannian manifold...