Hyperspectral imagery is often associated with high storage and transmission costs. Dimensionality reduction aims to reduce the time and space complexity of hyperspectral imagery by projecting data into a low-dimensional space such that all the important information in the data is preserved. Dimensionality-reduction methods based on transforms are widely used and give a data-dependent representation that is unfortunately costly to compute. Recently, there has been a growing interest in data-independent representations for dimensionality reduction; of particular prominence are random projections which are attractive due to their computational efficiency and simplicity of implementation. This dissertation concentrates on exploring the realm of computationally fast and efficient random projections by considering projections based on a random Hadamard matrix. These Hadamard-based projections are offered as an alternative to more widely used random projections based on dense Gaussian matrices. Such Hadamard matrices are then coupled with a fast singular value decomposition in order to implement a two-stage dimensionality reduction that marries the computational benefits of the data-independent random projection to the structure-capturing capability of the data-dependent singular value transform. Finally, random projections are applied in conjunction with nonnegative least squares to provide a computationally lightweight methodology for the well-known spectral-unmixing problem. Overall, it is seen that random projections offer a computationally efficient framework for dimensionality reduction that permits hyperspectral-analysis tasks such as unmixing and classification to be conducted in a lower-dimensional space without sacrificing analysis performance while reducing computational costs significantly.

Cancer is a dangerous disease caused by mutations in the host's genome that makes the cells proliferateuncontrollably and disrupts bodily functions. The immune system tries to prevent this, but tumours have methods ofdisrupting the immune system's ability to combat the cancer. These immunosuppression events can for examplehappen when the immune system interacts with the tumour to recognise it or try and destroy it. The tumours can bychanging their displayed proteins on the cell surface avoid detection or by excreting proteins, they can neutralisedangerous immune cells. This happens within the tumour microenvironment (TME), the immediate surrounding of atumour where there is a plethora of different cells both aiding and suppressing the tumour. Some of these cells arenot cancer cells but can still aid the tumour due to how the tumour has influenced them. For example, throughangiogenesis, where new blood vessels are formed which feeds the tumour. The interactions in the TME can be used as a target for immunotherapy, a field of treatments which improves theimmune system's own ability at defending against cancer. Immunotherapy can for example help the immune systemby guiding immune cells towards the tumour. It is therefore essential to understand the complex system ofinteractions within the TME to be able to create new methods of immunotherapy and thus treat cancers moreefficiently. Concurrently new methods of mapping what happens in a tissue have been developed in recent years,namely spatial transcriptomics (ST). It allows for the retrieval of transcriptomic information of cells throughsequencing while still retaining spatial information. However, the ST methods which capture the wholetranscriptome of the cells and reveal the cell-to-cell interactions are not of single-cell resolution yet. They capturemultiple cells in each spot, creating a mix of cells in the sequencing. This mix of cells can be detangled, and theproportions of each cell type revealed through the process of deconvolution. Deconvolution works by mapping thesingle cell expression profile of different cell types onto the ST data and figuring out what proportions of expressioneach cell type produces the expression of the mix. This reveals the cellular composition of the microenvironment.But since the interactions in the TME depend on the cells current expression we need to deconvolute according tophenotype and not just cell type. In this project we were able to create a tool which automatically finds phenotypes in the single-cell data and usesthose phenotypes to deconvolute ST data. Phenotypes are found using dimensionality reduction methods todifferentiate cells according to their contribution to the variability in the data. The resulting deconvoluted data wasthen used as the foundation for describing the growth of a cancer as a system of phenotype proportions in the tumourmicroenvironment. From this system a mathematical model was created which predicts the growth and couldprovide insight into how the phenotypes interact. The tool created worked as intended and the model explains thegrowth of a tumour in the TME with not just cancer cells phenotypes but other cell phenotypes as well. However, nonew interaction could be discovered by the final model and no phenotype found could provide us with new insightsto the structure of the TME. But our analysis was able to identify structures we expect to see in a tumour, eventhough they might not be so obvious, so an improved version of our tools might be able to find even more detailsand perhaps new, more subtle interactions.

Data that is represented with high dimensionality presents a computational complexity challenge for many existing algorithms. Limiting dimensionality by discarding attributes is sometimes a poor solution to this problem because significant high-level concepts may be encoded in the data across many or all of the attributes. Non-linear dimensionality reduction (NLDR) techniques have been successful with many problems at minimizing dimensionality while preserving intrinsic high-level concepts that are encoded with varying combinations of attributes. Unfortunately, many challenges remain with existing NLDR techniques, including excessive computational requirements, an inability to benefit from prior knowledge, and an inability to handle certain difficult conditions that occur in data with many real-world problems. Further, certain practical factors have limited advancement in NLDR, such as a lack of clarity regarding suitable applications for NLDR, and a general inavailability of efficient implementations of complex algorithms. This dissertation presents a collection of papers that advance the state of NLDR in each of these areas. Contributions of this dissertation include: • An NLDR algorithm, called Manifold Sculpting, that optimizes its solution using graduated optimization. This approach enables it to obtain better results than methods that only optimize an approximate problem. Additionally, Manifold Sculpting can benefit from prior knowledge about the problem. • An intelligent neighbor-finding technique called SAFFRON that improves the breadth of problems that existing NLDR techniques can handle. • A neighborhood refinement technique called CycleCut that further increases the robustness of existing NLDR techniques, and that can work in conjunction with SAFFRON to solve difficult problems. • Demonstrations of specific applications for NLDR techniques, including the estimation of state within dynamical systems, training of recurrent neural networks, and imputing missing values in data. • An open source toolkit containing each of the techniques described in this dissertation, as well as several existing NLDR algorithms, and other useful machine learning methods.

Many machine learning problems involve dealing with a large amount of high-dimensional data across diverse domains. In addition, annotating or labeling the data is expensive as it involves significant human effort. This dissertation explores a joint solution to both these problems by exploiting the property that high-dimensional data in real-world application domains often lies on a lower-dimensional structure, whose geometry can be modeled as a graph or manifold. In particular, we propose a set of novel manifold-alignment based approaches for transfer learning. The proposed approaches transfer knowledge across different domains by finding low-dimensional embeddings of the datasets to a common latent space, which simultaneously match corresponding instances while preserving local or global geometry of each input dataset. We develop a novel two-step transfer learning method called Procrustes alignment. Procrustes alignment first maps the datasets to low-dimensional latent spaces reflecting their intrinsic geometries and then removes the translational, rotational and scaling components from one set so that the optimal alignment between the two sets can be achieved. This approach can preserve either global geometry or local geometry depending on the dimensionality reduction approach used in the first step. We propose a general one-step manifold alignment framework called manifold projections that can find alignments, both across instances as well as across features, while preserving local domain geometry. We develop and mathematically analyze several extensions of this framework to more challenging situations, including (1) when no correspondences across domains are given; (2) when the global geometry of each input domain needs to be respected; (3) when label information rather than correspondence information is available. A final contribution of this thesis is the study of multiscale methods for manifold alignment. Multiscale alignment automatically generates alignment results at different levels by discovering the shared intrinsic multilevel structures of the given datasets, providing a common representation across all input datasets.

Myoelectric control schemes aim to utilize the surface electromyography (EMG) signals which are the electric potentials directly measured from skeletal muscles to control wearable robots such as exoskeletons and prostheses. The main challenge of myoelectric controls is to increase and preserve the signal quality by minimizing the effect of confounding factors such as muscle fatigue or electrode shift. Current research in myoelectric control schemes are developed to work in ideal laboratory conditions, but there is a persistent need to have these control schemes be more robust and work in real-world environments. Following the manifold hypothesis, complexity in the world can be broken down from a high-dimensional space to a lower-dimensional form or representation that can explain how the higher-dimensional real world operates. From this premise, the biological actions and their relevant multimodal signals can be compressed and optimally pertinent when performed in both laboratory and non-laboratory settings once the learned representation or manifold is discovered. This thesis outlines a method that incorporates the use of a contrastive variational autoencoder with an integrated classifier on multimodal sensor data to create a compressed latent space representation that can be used in future myoelectric control schemes.

To overcome the dimensionality curse of hyperspectral data, an investigation has been done on the use of grouping spectral bands, followed by feature level fusion and classifier decision fusion, to develop an automated target recognition (ATR) system for data reduction and enhanced classification. The entire span of spectral bands in the hyperspectral data is subdivided into groups based on performance metrics. Feature extraction is done using supervised methods as well as unsupervised methods. The effects of classification of the lower dimension data by parametric, as well as non-parametric, classifiers are studied. Further, multiclassifiers and decision level fusion using Qualified Majority Voting is applied to the features extracted from each group. The effectiveness of the ATR system is tested using the hyperspectral signatures of a target class, Cogongrass (Imperata Cylindrica), and a non-target class, Johnsongrass (Sorghum halepense). A comparison of target detection accuracies by before and after decision fusion illustrates the effect of the influence of each group on the final decision and the benefits of using decision fusion with multiclassifiers. Hence, the ATR system designed can be used to detect a target class while significantly reducing the dimensionality of the data.

This thesis investigates the use of sequential parametric projection pursuits (SPPP) for hyperspectral dimensionality reduction and invasive species target recognition. The SPPP method is implemented in a top-down fashion, where hyperspectral bands are used to form an increasing number of smaller groups, with each group being projected onto a subspace of dimensionality one. Both supervised and unsupervised potential projections are investigated for their use in the SPPP method. Fisher?s linear discriminant analysis (LDA) is used as a potential supervised projection. Average, Gaussian-weighted average, and principal component analysis (PCA) are used as potential unsupervised projections. The Bhattacharyya distance is used as the SPPP performance index. The performance of the SPPP method is compared to two other currently used dimensionality reduction techniques, namely best spectral band selection (BSBS) and best wavelet coefficient selection (BWCS). The SPPP dimensionality reduction method is combined with a nearest mean classifier to form an automated target recognition (ATR) system. The ATR system is tested on two invasive species hyperspectral datasets: a terrestrial case study of Cogongrass versus Johnsongrass and an aquatic case study of Waterhyacinth versus American Lotus. For both case studies, the SPPP approach either outperforms or performs on par with the BSBS and BWCS methods in terms of classification accuracy; however, the SPPP approach requires significantly less computational time. For the Cogongrass and Waterhyacinth applications, the SPPP method results in overall classification accuracy in the mid to upper 90?s.

The ongoing development and increased affordability of hyperspectral sensors are increasing their utilization in a variety of applications, such as agricultural monitoring and decision making. Hyperspectral Automated Target Recognition (ATR) systems typically rely heavily on dimensionality reduction methods, and particularly intelligent reduction methods referred to as feature extraction techniques. This dissertation reports on the development, implementation, and testing of new hyperspectral analysis techniques for ATR systems, including their use in agricultural applications where ground truthed observations available for training the ATR system are typically very limited. This dissertation reports the design of effective methods for grouping and down-selecting Discrete Wavelet Transform (DWT) coefficients and the design of automated Wavelet Packet Decomposition (WPD) filter tree pruning methods for use within the framework of a Multiclassifiers and Decision Fusion (MCDF) ATR system. The efficacy of the DWT MCDF and WPD MCDF systems are compared to existing ATR methods commonly used in hyperspectral remote sensing applications. The newly developed methods’ sensitivity to operating conditions, such as mother wavelet selection, decomposition level, and quantity and quality of available training data are also investigated. The newly developed ATR systems are applied to the problem of hyperspectral remote sensing of agricultural food crop contaminations either by airborne chemical application, specifically Glufosinate herbicide at varying concentrations applied to corn crops, or by biological infestation, specifically soybean rust disease in soybean crops. The DWT MCDF and WPD MCDF methods significantly outperform conventional hyperspectral ATR methods. For example, when detecting and classifying varying levels of soybean rust infestation, stepwise linear discriminant analysis, results in accuracies of approximately 30%-40%, but WPD MCDF methods result in accuracies of approximately 70%-80%.

In general, the consumer must depend on others to provide their software solutions. However, this outsourcing of software development has caused it to become more and more abstract as to where the software is actually being developed and by whom, and it poses a potentially large security problem for the consumer as it opens up the possibility for rogue functionality to be injected into an application without the consumer’s knowledge or consent. This begs the question of ‘How do we know that the software we use can be trusted?’ or ‘How can we have assurance that the software we use is doing only the tasks that we ask it to do?’ Traditional methods for thwarting such activities, such as virus detection engines, are far too antiquated for today’s adversary. More sophisticated research needs to be conducted in this area to combat these more technically advanced enemies. To combat the ever increasing problem of rogue applications, this dissertation has successfully applied and extended the information retrieval techniques of n-gram analysis and document similarity and the data mining techniques of dimensionality reduction and attribute extraction. This combination of techniques has generated a more effective Trojan horse, rogue application detection capability tool suite that can detect not only standalone rogue applications but also those that are embedded within other applications. This research provides several major contributions to the field including a unique combination of techniques that have provided a new tool for the administrator’s multi-pronged defense to combat the infestation of rogue applications. Another contribution involves a unique method of slicing the potential rogue applications that has proven to provide a more robust rogue application classifier. Through experimental research this effort has shown that a viable and worthy rogue application detection tool suite can be developed. Experimental results have shown that in some cases as much as a 28% increase in overall accuracy can be achieved when comparing the accepted feature selection practice of mutual information with the feature extraction method presented in this effort called randomized projection.

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