Tensor decomposition for Independent Component Analysis: Through implicit cumulant tensor manipulation

Blind Source Separation (BSS), the separation of latent source components from observed mixtures, is relevant to many fields of expertise such as neuro-imaging, economics and machine learning. Reliable estimates of the sources can be obtained through diagonalization of the cumulant tensor, i.e., a fourth-order symmetric multi-linear array...

Compression of the embedding layer in an LSTM model using tensor train decomposition for NLP

Natural Language Processing (NLP) deals with understanding and processing human text by any computer software. There are several network architectures in the fields of deep learning and artificial intelligence that are used for NLP. Deep learning techniques like recurrent neural networks and feed-forward neural networks are used to develop...

All-at-once optimization for kernel machines with canonical polyadic decompositions: Enabling large scale learning for kernel machines

This thesis studies the Canonical Polyadic Decomposition (CPD) constrained kernel machine for large scale learning, i.e. learning with a large number of samples. The kernel machine optimization problem is solved in the primal space, such that the complexity of the problem scales linearly in the number of samples as opposed to scaling cubically...

Symmetric Canonical Polyadic Decomposition And Gauss-Newton Optimizer For Nonlinear Volterra System Identification

This thesis applies the Gauss-Newton optimizer to estimate the parameter values of the Volterra-PARAFAC model by minimizing a nonlinear least square cost (NLS) function given the input and output measurements of the MISO Volterra system.

performance of the low-rank TT-SVD for large dense tensors on modern multicore CPUs

There are several factorizations of multidimensional tensors into lower-dimensional components, known as ``tensor networks."" We consider the popular ``tensor-train"" (TT) format and ask, How efficiently can we compute a low-rank approximation from a full tensor on current multicore CPUs? Compared to sparse and dense linear algebra, kernel...

Alternating linear scheme in a bayesian framework for low-rank tensor approximation

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets can be facilitated. In this paper, we find a low-rank representation for a given tensor by solving a...

Streaming Video Completion using a Tensor-Networked Kalman Filter

In streaming video completion one aims to fill in missing pixels in streaming video data. This is a problem that naturally arises in the context of surveillance videos. Since these are streaming videos, they must be completed online and in real-time. This makes the streaming video completion problem significantly more difficult than the related...

Tensor Network B-splines for high-dimensional function approximation

B-splines are basis functions for the spline function space and are extensively used in applications requiring function approximation. The generalization of B-splines to multiple dimensions is done through tensor products of their univariate basis functions. The number of basis functions and weights that define a multivariate B-spline surface,...

Tensor Network Kalman Filter for Large-Scale MIMO Systems: With Application to Adaptive Optics

For large-scale system with tens of thousands of states and outputs the computation in the conventional Kalman filter becomes time-consuming such that Kalman filtering in large-scale real-time application is practically infeasible. A possible mathematical framework to lift the curse of dimensionality is to lift the problem in higher dimensions...

A tensor approach to linear parameter varying system identification

Multiway Component Analysis for the Removal of Far Ventricular Signal in Unipolar Epicardial Electrograms of Patients with Atrial Fibrillation

Atrial fibrillation (AF) is one of the more common clinical arrhythmias with a high morbidity and mortality. Despite this, the electrophysiological and pathological mechanisms associated with AF largely remain a mystery, encouraging the use of ever more sophisticated techniques to extract vital information for diagnostic and therapeutic purposes...

Flow-based dissimilarity measures for reservoir models: a spatial-temporal tensor approach

In reservoir engineering, it is attractive to characterize the difference between reservoir models in metrics that relate to the economic performance of the reservoir as well as to the underlying geological structure. In this paper, we develop a dissimilarity measure that is based on reservoir flow patterns under a particular operational...