The purpose of the overall project is to create a simulated environment similar to Google map and traffic but simplified for education purposes. Students can choose different traffic patterns and program a car to navigate through the traffic dynamically based on the changing traffic. The environment used in the project is ASU VIPLE (Visual IoT/Robotics Programming Language Environment). It is a visual programming environment for Computer Science education. VIPLE supports a number of devices and platforms, including a traffic simulator developed using Unity game engine. This thesis focuses on creating realistic traffic data for the traffic simulator and implementing dynamic routing algorithm in VIPLE. The traffic data is generated from the recorded real traffic data published at Arizona Maricopa County website. Based on the generated traffic data, VIPLE programs are developed to implement the traffic simulation based on dynamic changing traffic data.

Communicating with computers through thought has been a remarkable achievement in recent years. This was made possible by the use of Electroencephalography (EEG). Brain-computer interface (BCI) relies heavily on Electroencephalography (EEG) signals for communication between humans and computers. With the advent ofdeep learning, many studies recently applied these techniques to EEG data to perform various tasks like emotion recognition, motor imagery classification, sleep analysis, and many more. Despite the rise of interest in EEG signal classification, very few studies have explored the MindBigData dataset, which collects EEG signals recorded at the stimulus of seeing a digit and thinking about it. This dataset takes us closer to realizing the idea of mind-reading or communication via thought. Thus classifying these signals into the respective digit that the user thinks about is a challenging task. This serves as a motivation to study this dataset and apply existing deep learning techniques to study it. Given the recent success of transformer architecture in different domains like Computer Vision and Natural language processing, this thesis studies transformer architecture for EEG signal classification. Also, it explores other deep learning techniques for the same. As a result, the proposed classification pipeline achieves comparable performance with the existing methods.

Graph matching is a fundamental but notoriously difficult problem due to its NP-hard nature, and serves as a cornerstone for a series of applications in machine learning and computer vision, such as image matching, dynamic routing, drug design, to name a few. Although there has been massive previous investigation on high-performance graph matching solvers, it still remains a challenging task to tackle the matching problem under real-world scenarios with severe graph uncertainty (e.g., noise, outlier, misleading or ambiguous link).In this dissertation, a main focus is to investigate the essence and propose solutions to graph matching with higher reliability under such uncertainty. To this end, the proposed research was conducted taking into account three perspectives related to reliable graph matching: modeling, optimization and learning. For modeling, graph matching is extended from typical quadratic assignment problem to a more generic mathematical model by introducing a specific family of separable function, achieving higher capacity and reliability. In terms of optimization, a novel high gradient-efficient determinant-based regularization technique is proposed in this research, showing high robustness against outliers. Then learning paradigm for graph matching under intrinsic combinatorial characteristics is explored. First, a study is conducted on the way of filling the gap between discrete problem and its continuous approximation under a deep learning framework. Then this dissertation continues to investigate the necessity of more reliable latent topology of graphs for matching, and propose an effective and flexible framework to obtain it. Coherent findings in this dissertation include theoretical study and several novel algorithms, with rich experiments demonstrating the effectiveness.

Graph matching is a fundamental but notoriously difficult problem due to its NP-hard nature, and serves as a cornerstone for a series of applications in machine learning and computer vision, such as image matching, dynamic routing, drug design, to name a few. Although there has been massive previous investigation on high-performance graph matching solvers, it still remains a challenging task to tackle the matching problem under real-world scenarios with severe graph uncertainty (e.g., noise, outlier, misleading or ambiguous link).In this dissertation, a main focus is to investigate the essence and propose solutions to graph matching with higher reliability under such uncertainty. To this end, the proposed research was conducted taking into account three perspectives related to reliable graph matching: modeling, optimization and learning. For modeling, graph matching is extended from typical quadratic assignment problem to a more generic mathematical model by introducing a specific family of separable function, achieving higher capacity and reliability. In terms of optimization, a novel high gradient-efficient determinant-based regularization technique is proposed in this research, showing high robustness against outliers. Then learning paradigm for graph matching under intrinsic combinatorial characteristics is explored. First, a study is conducted on the way of filling the gap between discrete problem and its continuous approximation under a deep learning framework. Then this dissertation continues to investigate the necessity of more reliable latent topology of graphs for matching, and propose an effective and flexible framework to obtain it. Coherent findings in this dissertation include theoretical study and several novel algorithms, with rich experiments demonstrating the effectiveness.

The Population Receptive Field (pRF) model is widely used to predict the location (retinotopy) and size of receptive fields on the visual space. Doing so allows for the creation of a mapping from locations in the visual field to the associated groups of neurons in the cortical region (within the visual cortex of the brain). However, using the pRF model is very time consuming. Past research has focused on the creation of Convolutional Neural Networks (CNN) to mimic the pRF model in a fraction of the time, and they have worked well under highly controlled conditions. However, these models have not been thoroughly tested on real human data. This thesis focused on adapting one of these CNNs to accurately predict the retinotopy of a real human subject using a dataset from the Human Connectome Project. The results show promise towards creating a fully functioning CNN, but they also expose new challenges that must be overcome before the model could be used to predict the retinotopy of new human subjects.

Statistical Shape Modeling is widely used to study the morphometrics of deformable objects in computer vision and biomedical studies. There are mainly two viewpoints to understand the shapes. On one hand, the outer surface of the shape can be taken as a two-dimensional embedding in space. On the other hand, the outer surface along with its enclosed internal volume can be taken as a three-dimensional embedding of interests. Most studies focus on the surface-based perspective by leveraging the intrinsic features on the tangent plane. But a two-dimensional model may fail to fully represent the realistic properties of shapes with both intrinsic and extrinsic properties. In this thesis, severalStochastic Partial Differential Equations (SPDEs) are thoroughly investigated and several methods are originated from these SPDEs to try to solve the problem of both two-dimensional and three-dimensional shape analyses. The unique physical meanings of these SPDEs inspired the findings of features, shape descriptors, metrics, and kernels in this series of works. Initially, the data generation of high-dimensional shapes, here, the tetrahedral meshes, is introduced. The cerebral cortex is taken as the study target and an automatic pipeline of generating the gray matter tetrahedral mesh is introduced. Then, a discretized Laplace-Beltrami operator (LBO) and a Hamiltonian operator (HO) in tetrahedral domain with Finite Element Method (FEM) are derived. Two high-dimensional shape descriptors are defined based on the solution of the heat equation and Schrödinger’s equation. Considering the fact that high-dimensional shape models usually contain massive redundancies, and the demands on effective landmarks in many applications, a Gaussian process landmarking on tetrahedral meshes is further studied. A SIWKS-based metric space is used to define a geometry-aware Gaussian process. The study of the periodic potential diffusion process further inspired the idea of a new kernel call the geometry-aware convolutional kernel. A series of Bayesian learning methods are then introduced to tackle the problem of shape retrieval and classification. Experiments of every single item are demonstrated. From the popular SPDE such as the heat equation and Schrödinger’s equation to the general potential diffusion equation and the specific periodic potential diffusion equation, it clearly shows that classical SPDEs play an important role in discovering new features, metrics, shape descriptors and kernels. I hope this thesis could be an example of using interdisciplinary knowledge to solve problems.

Image super-resolution (SR) is a low-level image processing task, which has manyapplications such as medical imaging, satellite image processing, and video enhancement,
etc. Given a low resolution image, it aims to reconstruct a high resolution
image. The problem is ill-posed since there can be more than one high resolution
image corresponding to the same low-resolution image. To address this problem, a
number of machine learning-based approaches have been proposed.
In this dissertation, I present my works on single image super-resolution (SISR)
and accelerated magnetic resonance imaging (MRI) (a.k.a. super-resolution on MR
images), followed by the investigation on transfer learning for accelerated MRI reconstruction.
For the SISR, a dictionary-based approach and two reconstruction based
approaches are presented. To be precise, a convex dictionary learning (CDL)
algorithm is proposed by constraining the dictionary atoms to be formed by nonnegative
linear combination of the training data, which is a natural, desired property.
Also, two reconstruction-based single methods are presented, which make use
of (i)the joint regularization, where a group-residual-based regularization (GRR) and
a ridge-regression-based regularization (3R) are combined; (ii)the collaborative representation
and non-local self-similarity. After that, two deep learning approaches
are proposed, aiming at reconstructing high-quality images from accelerated MRI
acquisition. Residual Dense Block (RDB) and feedback connection are introduced
in the proposed models. In the last chapter, the feasibility of transfer learning for
accelerated MRI reconstruction is discussed.

The rapid development in acquiring multimodal neuroimaging data provides opportunities to systematically characterize human brain structures and functions. For example, in the brain magnetic resonance imaging (MRI), a typical non-invasive imaging technique, different acquisition sequences (modalities) lead to the different descriptions of brain functional activities, or anatomical biomarkers. Nowadays, in addition to the traditional voxel-level analysis of images, there is a trend to process and investigate the cross-modality relationship in a high dimensional level of images, e.g. surfaces and networks.

In this study, I aim to achieve multimodal brain image fusion by referring to some intrinsic properties of data, e.g. geometry of embedding structures where the commonly used image features reside. Since the image features investigated in this study share an identical embedding space, i.e. either defined on a brain surface or brain atlas, where a graph structure is easy to define, it is straightforward to consider the mathematically meaningful properties of the shared structures from the geometry perspective.

I first introduce the background of multimodal fusion of brain image data and insights of geometric properties playing a potential role to link different modalities. Then, several proposed computational frameworks either using the solid and efficient geometric algorithms or current geometric deep learning models are be fully discussed. I show how these designed frameworks deal with distinct geometric properties respectively, and their applications in the real healthcare scenarios, e.g. to enhanced detections of fetal brain diseases or abnormal brain development.

This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing.

Recently, a well-designed and well-trained neural network can yield state-of-the-art results across many domains, including data mining, computer vision, and medical image analysis. But progress has been limited for tasks where labels are difficult or impossible to obtain. This reliance on exhaustive labeling is a critical limitation in the rapid deployment of neural networks. Besides, the current research scales poorly to a large number of unseen concepts and is passively spoon-fed with data and supervision.

To overcome the above data scarcity and generalization issues, in my dissertation, I first propose two unsupervised conventional machine learning algorithms, hyperbolic stochastic coding, and multi-resemble multi-target low-rank coding, to solve the incomplete data and missing label problem. I further introduce a deep multi-domain adaptation network to leverage the power of deep learning by transferring the rich knowledge from a large-amount labeled source dataset. I also invent a novel time-sequence dynamically hierarchical network that adaptively simplifies the network to cope with the scarce data.

To learn a large number of unseen concepts, lifelong machine learning enjoys many advantages, including abstracting knowledge from prior learning and using the experience to help future learning, regardless of how much data is currently available. Incorporating this capability and making it versatile, I propose deep multi-task weight consolidation to accumulate knowledge continuously and significantly reduce data requirements in a variety of domains. Inspired by the recent breakthroughs in automatically learning suitable neural network architectures (AutoML), I develop a nonexpansive AutoML framework to train an online model without the abundance of labeled data. This work automatically expands the network to increase model capability when necessary, then compresses the model to maintain the model efficiency.

In my current ongoing work, I propose an alternative method of supervised learning that does not require direct labels. This could utilize various supervision from an image/object as a target value for supervising the target tasks without labels, and it turns out to be surprisingly effective. The proposed method only requires few-shot labeled data to train, and can self-supervised learn the information it needs and generalize to datasets not seen during training.