In many real-world machine learning classification applications, well labeled training data can be difficult, expensive, or even impossible to obtain. In such situations, it is sometimes possible to label a small subset of data as belonging to the class of interest though it is impractical to manually label all data not of interest. The result is a small set of positive labeled data and a large set of unknown and unlabeled data. This is known as the Positive and Unlabeled learning (PU learning) problem, a type of semi-supervised learning. In this dissertation, the PU learning problem is rigorously defined, several common assumptions described, and a literature review of the field provided. A new family of effective PU learning algorithms, the MLR (Modified Logistic Regression) family of algorithms, is described. Theoretical and experimental justification for these algorithms is provided demonstrating their success and flexibility. Extensive experimentation and empirical evidence are provided comparing several new and existing PU learning evaluation estimation metrics in a wide variety of scenarios. The surprisingly clear advantage of a simple recall estimate as the best estimate for overall PU classifier performance is described. Finally, an application of PU learning to the field of solar fault detection, an area not previously explored in the field, demonstrates the advantage and potential of PU learning in new application domains.

A distributed wireless sensor network (WSN) is a network of a large number of lowcost,multi-functional sensors with power, bandwidth, and memory constraints, operating in remote environments with sensing and communication capabilities. WSNs are a source for a large amount of data and due to the inherent communication and resource constraints, developing a distributed algorithms to perform statistical parameter estimation and data analysis is necessary. In this work, consensus based distributed algorithms are developed for distributed estimation and processing over WSNs. Firstly, a distributed spectral clustering algorithm to group the sensors based on the location attributes is developed. Next, a distributed max consensus algorithm robust to additive noise in the network is designed. Furthermore, distributed spectral radius estimation algorithms for analog, as well as, digital communication models are developed. The proposed algorithms work for any connected graph topologies. Theoretical bounds are derived and simulation results supporting the theory are also presented.

The increasing demand for clean energy solutions requires more than just expansion, but also improvements in the efficiency of renewable sources, such as solar. This requires analytics for each panel regarding voltage, current, temperature, and irradiance. This project involves the development of machine learning algorithms along with a data logger for the purpose of photovoltaic (PV) monitoring and control. Machine learning is used for fault classification. Once a fault is detected, the system can change its reconfiguration to minimize the power losses. Accuracy in the fault detection was demonstrated to be at a level over 90% and topology reconfiguration showed to increase power output by as much as 5%.

Over the past decade, machine learning research has made great strides and significant impact in several fields. Its success is greatly attributed to the development of effective machine learning algorithms like deep neural networks (a.k.a. deep learning), availability of large-scale databases and access to specialized hardware like Graphic Processing Units. When designing and training machine learning systems, researchers often assume access to large quantities of data that capture different possible variations. Variations in the data is needed to incorporate desired invariance and robustness properties in the machine learning system, especially in the case of deep learning algorithms. However, it is very difficult to gather such data in a real-world setting. For example, in certain medical/healthcare applications, it is very challenging to have access to data from all possible scenarios or with the necessary amount of variations as required to train the system. Additionally, the over-parameterized and unconstrained nature of deep neural networks can cause them to be poorly trained and in many cases over-confident which, in turn, can hamper their reliability and generalizability. This dissertation is a compendium of my research efforts to address the above challenges. I propose building invariant feature representations by wedding concepts from topological data analysis and Riemannian geometry, that automatically incorporate the desired invariance properties for different computer vision applications. I discuss how deep learning can be used to address some of the common challenges faced when working with topological data analysis methods. I describe alternative learning strategies based on unsupervised learning and transfer learning to address issues like dataset shifts and limited training data. Finally, I discuss my preliminary work on applying simple orthogonal constraints on deep learning feature representations to help develop more reliable and better calibrated models.

The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution and quantity leaving a large data footprint. This dissertation is motivated by the need for equivalent representations of grid data in lower-dimensional feature spaces so that machine learning algorithms can be employed for a variety of purposes. To achieve that, without sacrificing the interpretation of the results, the dissertation leverages the physics behind power systems, well-known laws that underlie this man-made infrastructure, and the nature of the underlying stochastic phenomena that define the system operating conditions as the backbone for modeling data from the grid.

The first part of the dissertation introduces a new framework of graph signal processing (GSP) for the power grid, Grid-GSP, and applies it to voltage phasor measurements that characterize the overall system state of the power grid. Concepts from GSP are used in conjunction with known power system models in order to highlight the low-dimensional structure in data and present generative models for voltage phasors measurements. Applications such as identification of graphical communities, network inference, interpolation of missing data, detection of false data injection attacks and data compression are explored wherein Grid-GSP based generative models are used.

The second part of the dissertation develops a model for a joint statistical description of solar photo-voltaic (PV) power and the outdoor temperature which can lead to better management of power generation resources so that electricity demand such as air conditioning and supply from solar power are always matched in the face of stochasticity. The low-rank structure inherent in solar PV power data is used for forecasting and to detect partial-shading type of faults in solar panels.

The recent increase in users of cellular networks necessitates the use of new technologies to meet this demand. Massive multiple input multiple output (MIMO) communication systems have great potential for increasing the network capacity of the emerging 5G+ cellular networks. However, leveraging the multiplexing and beamforming gains from these large-scale MIMO systems requires the channel knowlege between each antenna and each user. Obtaining channel information on such a massive scale is not feasible with the current technology available due to the complexity of such large systems. Recent research shows that deep learning methods can lead to interesting gains for massive MIMO systems by mapping the channel information from the uplink frequency band to the channel information for the downlink frequency band as well as between antennas at nearby locations. This thesis presents the research to develop a deep learning based channel mapping proof-of-concept prototype.



Due to deep neural networks' need of large training sets for accurate performance, this thesis outlines the design and implementation of an autonomous channel measurement system to analyze the performance of the proposed deep learning based channel mapping concept. This system obtains channel magnitude measurements from eight antennas autonomously using a mobile robot carrying a transmitter which receives wireless commands from the central computer connected to the static receiver system. The developed autonomous channel measurement system is capable of obtaining accurate and repeatable channel magnitude measurements. It is shown that the proposed deep learning based channel mapping system accurately predicts channel information containing few multi-path effects.

In many biological research studies, including speech analysis, clinical research, and prediction studies, the validity of the study is dependent on the effectiveness of the training data set to represent the target population. For example, in speech analysis, if one is performing emotion classification based on speech, the performance of the classifier is mainly dependent on the number and quality of the training data set. For small sample sizes and unbalanced data, classifiers developed in this context may be focusing on the differences in the training data set rather than emotion (e.g., focusing on gender, age, and dialect).

This thesis evaluates several sampling methods and a non-parametric approach to sample sizes required to minimize the effect of these nuisance variables on classification performance. This work specifically focused on speech analysis applications, and hence the work was done with speech features like Mel-Frequency Cepstral Coefficients (MFCC) and Filter Bank Cepstral Coefficients (FBCC). The non-parametric divergence (D_p divergence) measure was used to study the difference between different sampling schemes (Stratified and Multistage sampling) and the changes due to the sentence types in the sampling set for the process.

Over the last decade, deep neural networks also known as deep learning, combined with large databases and specialized hardware for computation, have made major strides in important areas such as computer vision, computational imaging and natural language processing. However, such frameworks currently suffer from some drawbacks. For example, it is generally not clear how the architectures are to be designed for different applications, or how the neural networks behave under different input perturbations and it is not easy to make the internal representations and parameters more interpretable. In this dissertation, I propose building constraints into feature maps, parameters and and design of algorithms involving neural networks for applications in low-level vision problems such as compressive imaging and multi-spectral image fusion, and high-level inference problems including activity and face recognition. Depending on the application, such constraints can be used to design architectures which are invariant/robust to certain nuisance factors, more efficient and, in some cases, more interpretable. Through extensive experiments on real-world datasets, I demonstrate these advantages of the proposed methods over conventional frameworks.

The depth richness of a scene translates into a spatially variable defocus blur in the acquired image. Blurring can mislead computational image understanding; therefore, blur detection can be used for selective image enhancement of blurred regions and the application of image understanding algorithms to sharp regions. This work focuses on blur detection and its application to image enhancement.

This work proposes a spatially-varying defocus blur detection based on the quotient of spectral bands; additionally, to avoid the use of computationally intensive algorithms for the segmentation of foreground and background regions, a global threshold defined using weak textured regions on the input image is proposed. Quantitative results expressed in the precision-recall space as well as qualitative results overperform current state-of-the-art algorithms while keeping the computational requirements at competitive levels.

Imperfections in the curvature of lenses can lead to image radial distortion (IRD). Computer vision applications can be drastically affected by IRD. This work proposes a novel robust radial distortion correction algorithm based on alternate optimization using two cost functions tailored for the estimation of the center of distortion and radial distortion coefficients. Qualitative and quantitative results show the competitiveness of the proposed algorithm.

Blur is one of the causes of visual discomfort in stereopsis. Sharpening applying traditional algorithms can produce an interdifference which causes eyestrain and visual fatigue for the viewer. A sharpness enhancement method for stereo images that incorporates binocular vision cues and depth information is presented. Perceptual evaluation and quantitative results based on the metric of interdifference deviation are reported; results of the proposed algorithm are competitive with state-of-the-art stereo algorithms.

Digital images and videos are produced every day in astonishing amounts. Consequently, the market-driven demand for higher quality content is constantly increasing which leads to the need of image quality assessment (IQA) methods. A training-free, no-reference image sharpness assessment method based on the singular value decomposition of perceptually-weighted normalized-gradients of relevant pixels in the input image is proposed. Results over six subject-rated publicly available databases show competitive performance when compared with state-of-the-art algorithms.