Theory and Algorithms for Reliable Multimodal Data Analysis, Machine Learning, and Signal Processing

Modern engineering systems collect large volumes of data measurements across diverse sensing modalities. These measurements can naturally be arranged in higher-order arrays of scalars which are commonly referred to as tensors. Tucker decomposition (TD) is a standard method for tensor analysis with applications in diverse fields of science and engineering. Despite its success, TD exhibits severe sensitivity against outliers —i.e., heavily corrupted entries that appear sporadically in modern datasets. We study L1-norm TD (L1-TD), a reformulation of TD that promotes robustness. For 3-way tensors, we show, for the first time, that L1-TD admits an exact solution via combinatorial optimization and present algorithms for its solution. We propose two novel algorithmic frameworks for approximating the exact solution to L1-TD, for general N-way tensors. We propose a novel algorithm for dynamic L1-TD —i.e., efficient and joint analysis of streaming tensors. Principal-Component Analysis (PCA) (a special case of TD) is also outlier responsive. We consider Lp-quasinorm PCA (Lp-PCA) for

Efficient method of estimating Direction of Arrival (DOA) in communications systems.

Masters Degree. University of KwaZulu- Natal, Durban.In wireless communications systems, estimation of Direction of Arrival (DOA) has been used both for military and commercial purposes. The signal whose DOA is being estimated, could be a signal that has been reflected from a moving or stationary object, or a signal that has been generated from unwanted or illegal transmitter. When combined with estimating time of arrival, it is also possible to pinpoint the location of a target in space. Localization in space can also be achieved by estimating DOA using two receiving nodes with capability of estimating DOA. The beamforming pattern in smart antenna system is adjusted to emphasize the desired signal and to minimize the interference signal. Therefore, DOA estimation algorithms are critical for estimating the Angle of Arrival (AOA) and beamforming in smart antennas. This dissertation investigates the performance, angular accuracy and resolution of the Minimum Variance Distortionless Response (MVDR), Multiple Signal Classification (MUSIC) and our proposed method Advanced Multiple Signal Classification (A-MUSIC) as DOA algorithms on both Non-Uniform Array (NLA) and Uniform Linear Array (ULA). DOA is critical in antenna design for emphasizing the desired signal and minimizing interference. The scarcity of radio spectrum has fuelled the migration of communication networks to higher frequencies. This has resulted into radio propagation challenges due to the adverse environmental elements otherwise unexperienced at lower frequencies. In rainfall-impacted environments, DOA estimation is greatly affected by signal attenuation and scattering at the higher frequencies. Therefore, new DOA algorithms cognisant of these factors need to be developed and the performance of the existing algorithms quantified. This work investigates the performance of the Conventional Minimum Variance Distortion-less Look (MVDL), Subspace DOA Estimation Methods of Multiple Signal Classification (MUSIC) and the developed hybrid DOA algorithm on a weather impacted wireless channel. The performance of the proposed Advanced-MUSIC (A-MUSIC) algorithm is compared to the conventional DOA estimation algorithms of Minimum Variance Distortionless Response (MVDR) and the Multiple Signal Classification (MUSIC) algorithms for both NLA and ULA antenna arrays. The developed simulation results show that A-MUSIC shows superior performance compared to the two other algorithms in terms of Signal Noise Ratio (SNR) and the number of antenna elements. The results show performance degradation in a rainfall impacted communication network with the developed algorithm showing better performance degradation