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abstract: Dimensionality reduction methods are examined for large-scale discrete problems, specifically for the solution of three-dimensional geophysics problems: the inversion of gravity and magnetic data. The matrices for the associated forward problems have beneficial structure for each depth layer of the volume domain, under mild assumptions, which facilitates the use of the two dimensional fast Fourier transform for evaluating forward and transpose matrix operations, providing considerable savings in both computational costs and storage requirements. Application of this approach for the magnetic problem is new in the geophysics literature. Further, the approach is extended for padded volume domains. Stabilized inversion is obtained efficiently by applying novel randomization techniques within each update of the iteratively reweighted scheme. For a general rectangular linear system, a randomization technique combined with preconditioning is introduced and investigated. This is shown to provide well-conditioned inversion, stabilized through truncation. Applying this approach, while implementing matrix operations using the two dimensional fast Fourier transform, yields computationally effective inversion, in memory and cost. Validation is provided via synthetic data sets, and the approach is contrasted with the well-known LSRN algorithm when applied to these data sets. The results demonstrate a significant reduction in computational cost with the new algorithm. Further, this new algorithm produces results for inversion of real magnetic data consistent with those provided in literature. Typically, the iteratively reweighted least squares algorithm depends on a standard Tikhonov formulation. Here, this is solved using both a randomized singular value de- composition and the iterative LSQR Krylov algorithm. The results demonstrate that the new algorithm is competitive with these approaches and offers the advantage that no regularization parameter needs to be found at each outer iteration. Given its efficiency, investigating the new algorithm for the joint inversion of these data sets may be fruitful. Initial research on joint inversion using the two dimensional fast Fourier transform has recently been submitted and provides the basis for future work. Several alternative directions for dimensionality reduction are also discussed, including iteratively applying an approximate pseudo-inverse and obtaining an approximate Kronecker product decomposition via randomization for a general matrix. These are also topics for future consideration. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

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The aim of this master’s thesis is analysis of the multidimensional data. Three dimensionality reduction algorithms are introduced. It is shown how to manipulate with text documents using basic methods of natural language processing. The goal of the practical part of the thesis is to process real-world data from the internet forum. Posted messages are transformed to the numerical representation, then to two-dimensional space and visualized. Later on, topics of the messages are discovered. In the last part, a few selected algorithms are compared.

abstract: The goal of reinforcement learning is to enable systems to autonomously solve tasks in the real world, even in the absence of prior data. To succeed in such situations, reinforcement learning algorithms collect new experience through interactions with the environment to further the learning process. The behaviour is optimized by maximizing a reward function, which assigns high numerical values to desired behaviours. Especially in robotics, such interactions with the environment are expensive in terms of the required execution time, human involvement, and mechanical degradation of the system itself. Therefore, this thesis aims to introduce sample-efficient reinforcement learning methods which are applicable to real-world settings and control tasks such as bimanual manipulation and locomotion. Sample efficiency is achieved through directed exploration, either by using dimensionality reduction or trajectory optimization methods. Finally, it is demonstrated how data-efficient reinforcement learning methods can be used to optimize the behaviour and morphology of robots at the same time. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2019

Predictive Maintenance (PM) has been increasingly adopted in the Automotive industry, in the recent decades along with conventional approaches such as the Preventive Maintenance and Diagnostic/Corrective Maintenance, since it provides many advantages to estimate the failure before the actual occurrence proactively, and also being adaptive to the present status of the vehicle, in turn allowing flexible maintenance schedules for efficient repair or replacing of faulty components. PM necessitates the storage and analysis of large amounts of sensor data. This requirement can be a challenge in deploying this method on-board the vehicles due to the limited storage and computational power on the hardware of the vehicle. Hence, this thesis seeks to obtain low dimensional descriptive features from high dimensional data using Representation Learning. This low dimensional representation will be used for predicting vehicle faults, specifically Turbocharger related failures. Since the Logged Vehicle Data (LVD) was base on all the data utilized in this thesis, it allowed for the evaluation of large populations of trucks without requiring additional measuring devices and facilities. The gradual degradation methodology is considered for describing vehicle condition, which allows for modeling the malfunction/ failure as a continuous process rather than a discrete flip from healthy to an unhealthy state. This approach eliminates the challenge of data imbalance of healthy and unhealthy samples. Two important hypotheses are presented. Firstly, Parallel StackedClassical Autoencoders would produce better representations com-pared to individual Autoencoders. Secondly, employing Learned Em-beddings on Categorical Variables would improve the performance of the Dimensionality reduction. Based on these hypotheses, a model architecture is proposed and is developed on the LVD. The model is shown to achieve good performance, and in close standards to the previous state-of-the-art research. This thesis, finally, illustrates the potential to apply parallel stacked architectures with Learned Embeddings for the Categorical features, and a combination of feature selection and extraction for numerical features, to predict the Remaining Useful Life (RUL) of a vehicle, in the context of the Turbocharger. A performance improvement of 21.68% with respect to the Mean Absolute Error (MAE) loss with an 80.42% reduction in the size of data was observed.

Background. Hyperplane folding was introduced by Lars Lundberg et al. in Hyperplane folding increased the margin while suffering from a flaw, referred to asover-rotation in this thesis. The aim of this thesis is to introduce a new different technique thatwould not over-rotate data points. This novel technique is referred to as RubberBand folding in the thesis. The following research questions are addressed: 1) DoesRubber Band folding increases classification accuracy? 2) Does Rubber Band fold-ing increase the Margin? 3) How does Rubber Band folding effect execution time? Rubber Band folding was implemented and its result was compared toHyperplane folding and the Support-vector machine. This comparison was done byapplying Stratified ten-fold cross-validation on four data sets for research question1 & 2. Four folds were applied for both Hyperplane folding and Rubber Band fold-ing, as more folds can lead to over-fitting. While research question 3 used 15 folds,in order to see trends and is not affected by over-fitting. One BMI data set, wasartificially made for the initial Hyperplane folding paper. Another data set labeled patients with, or without a liver disorder. Another data set predicted if patients havebenign- or malign cancer cells. Finally, a data set predicted if a hepatitis patient isalive within five years.Results.Rubber Band folding achieved a higher classification accuracy when com-pared to Hyperplane folding in all data sets. Rubber Band folding increased theclassification in the BMI data set and cancer data set while the accuracy for Rub-ber Band folding decreased in liver and hepatitis data sets. Hyperplane folding’saccuracy decreased in all data sets.Both Rubber Band folding and Hyperplane folding increases the margin for alldata sets tested. Rubber Band folding achieved a margin higher than Hyperplanefolding’s in the BMI and Liver data sets. Execution time for both the classification ofdata points and the training time for the classifier increases linearly per fold. RubberBand folding has slower growth in classification time when compared to Hyperplanefolding. Rubber Band folding can increase the classification accuracy, in whichexact cases are unknown. It is howevered believed to be when the data is none-linearly seperable.Rubber Band folding increases the margin. When compared to Hyperplane fold-ing, Rubber Band folding can in some cases, achieve a higher increase in marginwhile in some cases Hyperplane folding achieves a higher margin.Both Hyperplane folding and Rubber Band folding increases training time andclassification time linearly. The difference between Hyperplane folding and RubberBand folding in training time was negligible while Rubber bands increase in classifi-cation time was lower. This was attributed to Rubber Band folding rotating fewerpoints after 15 folds.

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Current x-ray technologies provide security personnel with non-invasive sub-surface imaging and contraband detection in various portal screening applications such as checked and carry-on baggage as well as cargo. Computed tomography (CT) scanners generate detailed 3D imagery in checked bags; however, these scanners often require significant power, cost, and space. These tomography machines are impractical for many applications where space and power are often limited such as checkpoint areas. Reducing the amount of data acquired would help reduce the physical demands of these systems. Unfortunately this leads to the formation of artifacts in various applications, thus presenting significant challenges in reconstruction and classification. As a result, the goal is to maintain a certain level of image quality but reduce the amount of data gathered. For the security domain this would allow for faster and cheaper screening in existing systems or allow for previously infeasible screening options due to other operational constraints. While our focus is predominantly on security applications, many of the techniques can be extended to other fields such as the medical domain where a reduction of dose can allow for safer and more frequent examinations. This dissertation aims to advance data reduction algorithms for security motivated x-ray imaging in three main areas: (i) development of a sensing aware dimensionality reduction framework, (ii) creation of linear motion tomographic method of object scanning and associated reconstruction algorithms for carry-on baggage screening, and (iii) the application of coded aperture techniques to improve and extend imaging performance of nuclear resonance fluorescence in cargo screening. The sensing aware dimensionality reduction framework extends existing dimensionality reduction methods to include knowledge of an underlying sensing mechanism of a latent variable. This method provides an improved classification rate over classical methods on both a synthetic case and a popular face classification dataset. The linear tomographic method is based on non-rotational scanning of baggage moved by a conveyor belt, and can thus be simpler, smaller, and more reliable than existing rotational tomography systems at the expense of more challenging image formation problems that require special model-based methods. The reconstructions for this approach are comparable to existing tomographic systems. Finally our coded aperture extension of existing nuclear resonance fluorescence cargo scanning provides improved observation signal-to-noise ratios. We analyze, discuss, and demonstrate the strengths and challenges of using coded aperture techniques in this application and provide guidance on regimes where these methods can yield gains over conventional methods.

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