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...

Graph Regularized Tensor Decomposition for Recommender Systems

Humans make decisions when presented with choices based on influences. The Internet today presents people with abundant choices to choose from. Recommending choices with an emphasis on people's preferences has become increasingly sought. Grundy (1979), the first computer librarian Recommender System (RS), provided users with book recommendations...

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...

Improving the Computational Speed of a Tensor-Networked Kalman Filter for Streaming Video Completion

Streaming video completion is the practice that aims to fill in missing or corrupted pixels in a video stream by using past uncorrupted data. A method to tackle this problem is recently introduced called a Tensor Networked Kalman Filter (TNKF). It shows promising results in terms of performance compared to state-of-the-art methods for high...

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.

Tensor-Networked Square-Root Kalman Filter for Online Video Completion

Online video completion aims to complete corrupted frames of a video in an online fashion. Consider a surveillance camera that suddenly outputs corrupted data, where up to 95% of the pixels per frame are corrupted. Real time video completion and correction is often desirable in such scenarios. Therefore, this thesis improves the Tensor-Networked...

Batch Bayesian Learning of Large-Scale LS-SVMs Based on Low-rank Tensor Networks

Least Squares Support Vector Machines (LS-SVMs) are state-of-the-art learning algorithms that have been widely used for pattern recognition. The solution for an LS-SVM is found by solving a system of linear equations, which involves the computational complexity of O(N^3). When datasets get larger, solving LS-SVM problems with standard methods...

Non-Linear Bayesian System Identification of Cortical Responses Using Volterra Series

The human sensorimotor system can be seen as a complex network in which the brain plays an important role, resulting in a difficult-to-understand relation between proprioceptive stimuli and cortical responses. However, understanding this relationship is of added value for understanding various diseases which cause dysfunctionality. In recent...

Nonnegative Robust PCA for Background and Foreground Image Decomposition

Nowadays, video surveillance and motion detection system are widely used in various environments. With the relatively low-price cameras and highly automated monitoring system, video and image analysis on road, highway and skies becomes realistic. The key process in the analysis is to separate the useful information such as moving foreground...

Recursive Tensor Network Bayesian Learning of Large-Scale LS-SVMs

Least-squares support-vector-machines are a frequently used supervised learning method for nonlinear regression and classification. The method can be implemented by solving either its primal problem or dual problem. In the dual problem a linear system needs to be solved, yet for large-scale problems this can be impractical as current methods...

Development of a Computational Model of Respiratory Mechanics in Mechanical Ventilation

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...

Precise Data-Driven Modelling of Reticle Heating Induced Spatial Deformations for Correcting Non-Moving Average Effects

In the thesis, the challenge of precisely developing a data-driven Linear Time Invariant MIMO Reticle Heating Induced Deformation Prediction (RHIDP) model for ASML's DUV systems is presented. The model is developed for two inputs, namely airflow temperature and dose for full field exposures. A reduced order data-driven based approach for...