Data Visualization, Dimensionality Reduction, and Data Alignment via Manifold Learning

The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel manifold learning methods to recover a sensitive geometry, alongside the parametric structure of autoencoders. Manifold learning can also be useful to study data collected from different measurement instruments, conditions, or protocols of the same underlying system. In such cases the data is acquired in a multi-domain representation. The last two Chapters of this thesis are devoted to two new methods capable of aligning multi-domain data, leveraging their geometric structure alongside limited common information. First, we present DTA (Diffusion Transport Alignment), a semi-supervised manifold alignment method that exploits prior one-to-one correspondence knowledge between distinct data views and finds an aligned common representation. And finally, we introduce MALI (Manifold Alignment with Label Information). Here we drop the one-to-one prior correspondences assumption, since in many scenarios such information can not be provided, either due to the nature of the experimental design, or it becomes extremely costly. Instead, MALI only needs side-information in the form of discrete labels/classes present in both domains

Face Centered Image Analysis Using Saliency and Deep Learning Based Techniques

Image analysis starts with the purpose of configuring vision machines that can perceive like human to intelligently infer general principles and sense the surrounding situations from imagery. This dissertation studies the face centered image analysis as the core problem in high level computer vision research and addresses the problem by tackling three challenging subjects: Are there anything interesting in the image? If there is, what is/are that/they? If there is a person presenting, who is he/she? What kind of expression he/she is performing? Can we know his/her age? Answering these problems results in the saliency-based object detection, deep learning structured objects categorization and recognition, human facial landmark detection and multitask biometrics. To implement object detection, a three-level saliency detection based on the self-similarity technique (SMAP) is firstly proposed in the work. The first level of SMAP accommodates statistical methods to generate proto-background patches, followed by the second level that implements local contrast computation based on image self-similarity characteristics. At last, the spatial color distribution constraint is considered to realize the saliency detection. The outcome of the algorithm is a full resolution image with highlighted saliency objects and well-defined edges. In object recognition, the Adaptive Deconvolution Network (ADN) is implemented to categorize the objects extracted from saliency detection. To improve the system performance, L1/2 norm regularized ADN has been proposed and tested in different applications. The results demonstrate the efficiency and significance of the new structure. To fully understand the facial biometrics related activity contained in the image, the low rank matrix decomposition is introduced to help locate the landmark points on the face images. The natural extension of this work is beneficial in human facial expression recognition and facial feature parsing research. To facilitate the understanding of the detected facial image, the automatic facial image analysis becomes essential. We present a novel deeply learnt tree-structured face representation to uniformly model the human face with different semantic meanings. We show that the proposed feature yields unified representation in multi-task facial biometrics and the multi-task learning framework is applicable to many other computer vision tasks

Broad Learning for Healthcare

A broad spectrum of data from different modalities are generated in the healthcare domain every day, including scalar data (e.g., clinical measures collected at hospitals), tensor data (e.g., neuroimages analyzed by research institutes), graph data (e.g., brain connectivity networks), and sequence data (e.g., digital footprints recorded on smart sensors). Capability for modeling information from these heterogeneous data sources is potentially transformative for investigating disease mechanisms and for informing therapeutic interventions. Our works in this thesis attempt to facilitate healthcare applications in the setting of broad learning which focuses on fusing heterogeneous data sources for a variety of synergistic knowledge discovery and machine learning tasks. We are generally interested in computer-aided diagnosis, precision medicine, and mobile health by creating accurate user profiles which include important biomarkers, brain connectivity patterns, and latent representations. In particular, our works involve four different data mining problems with application to the healthcare domain: multi-view feature selection, subgraph pattern mining, brain network embedding, and multi-view sequence prediction.Comment: PhD Thesis, University of Illinois at Chicago, March 201

On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed

3D Shape Descriptor-Based Facial Landmark Detection: A Machine Learning Approach

Facial landmark detection on 3D human faces has had numerous applications in the literature such as establishing point-to-point correspondence between 3D face models which is itself a key step for a wide range of applications like 3D face detection and authentication, matching, reconstruction, and retrieval, to name a few. Two groups of approaches, namely knowledge-driven and data-driven approaches, have been employed for facial landmarking in the literature. Knowledge-driven techniques are the traditional approaches that have been widely used to locate landmarks on human faces. In these approaches, a user with sucient knowledge and experience usually denes features to be extracted as the landmarks. Data-driven techniques, on the other hand, take advantage of machine learning algorithms to detect prominent features on 3D face models. Besides the key advantages, each category of these techniques has limitations that prevent it from generating the most reliable results. In this work we propose to combine the strengths of the two approaches to detect facial landmarks in a more ecient and precise way. The suggested approach consists of two phases. First, some salient features of the faces are extracted using expert systems. Afterwards, these points are used as the initial control points in the well-known Thin Plate Spline (TPS) technique to deform the input face towards a reference face model. Second, by exploring and utilizing multiple machine learning algorithms another group of landmarks are extracted. The data-driven landmark detection step is performed in a supervised manner providing an information-rich set of training data in which a set of local descriptors are computed and used to train the algorithm. We then, use the detected landmarks for establishing point-to-point correspondence between the 3D human faces mainly using an improved version of Iterative Closest Point (ICP) algorithms. Furthermore, we propose to use the detected landmarks for 3D face matching applications