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Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…
Many of the systems that appear in various signal processing applications are non-linear, for example, due to hardware impairments such as non-linear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular…
Inner product-based convolution has been a central component of convolutional neural networks (CNNs) and the key to learning visual representations. Inspired by the observation that CNN-learned features are naturally decoupled with the norm…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
Decoupling is a recent development in Fourier analysis, which has applications in harmonic analysis, PDE, and number theory. We survey some applications of decoupling and some of the ideas in the proof. This survey is aimed at a general…
Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…
We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…