Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Graph-based Methods for Visualization and Clustering

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: it is complex and deprived of semantical context. A common step to address those issues is to embed raw data in lower dimensions, by finding a mapping which preserves the similarity between data points from their original space to a new one. Measuring similarity between large sets of high-dimensional objects is, however, problematic for two main reasons: first, high-dimensional points are subject to the curse of dimensionality and second, the number of pairwise distances between points is quadratic with respect to the amount of data points. Both problems can be addressed by using nearest neighbours graphs to understand the structure in data. As a matter of fact, most dimensionality reduction methods use similarity matrices that can be interpreted as graph adjacency matrices. Yet, despite recent progresses, dimensionality reduction is still very challenging when applied to very large datasets. Indeed, although recent methods specifically address the problem of scaleability, processing datasets of millions of elements remain a very lengthy process. In this thesis, we propose new contributions which address the problem of scaleability using the framework of Graph Signal Processing, which extends traditional signal processing to graphs. We do so motivated by the premise that graphs are well suited to represent the structure of the data. In the first part of this thesis, we look at quantitative measures for the evaluation of dimensionality reduction methods. Using tools from graph theory and Graph Signal Processing, we show that specific characteristics related to quality can be assessed by taking measures on the graph, which indirectly validates the hypothesis relating graph to structure. The second contribution is a new method for a fast eigenspace approximation of the graph Laplacian. Using principles of GSP and random matrices, we show that an approximated eigensubpace can be recovered very efficiently, which be used for fast spectral clustering or visualization. Next, we propose a compressive scheme to accelerate any dimensionality reduction technique. The idea is based on compressive sampling and transductive learning on graphs: after computing the embedding for a small subset of data points, we propagate the information everywhere using transductive inference. The key components of this technique are a good sampling strategy to select the subset and the application of transductive learning on graphs. Finally, we address the problem of over-discriminative feature spaces by proposing a hierarchical clustering structure combined with multi-resolution graphs. Using efficient coarsening and refinement procedures on this structure, we show that dimensionality reduction algorithms can be run on intermediate levels and up-sampled to all points leading to a very fast dimensionality reduction method. For all contributions, we provide extensive experiments on both synthetic and natural datasets, including large-scale problems. This allows us to show the pertinence of our models and the validity of our proposed algorithms. Following reproducible principles, we provide everything needed to repeat the examples and the experiments presented in this work

Graphical models for visual object recognition and tracking

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 277-301).We develop statistical methods which allow effective visual detection, categorization, and tracking of objects in complex scenes. Such computer vision systems must be robust to wide variations in object appearance, the often small size of training databases, and ambiguities induced by articulated or partially occluded objects. Graphical models provide a powerful framework for encoding the statistical structure of visual scenes, and developing corresponding learning and inference algorithms. In this thesis, we describe several models which integrate graphical representations with nonparametric statistical methods. This approach leads to inference algorithms which tractably recover high-dimensional, continuous object pose variations, and learning procedures which transfer knowledge among related recognition tasks. Motivated by visual tracking problems, we first develop a nonparametric extension of the belief propagation (BP) algorithm. Using Monte Carlo methods, we provide general procedures for recursively updating particle-based approximations of continuous sufficient statistics. Efficient multiscale sampling methods then allow this nonparametric BP algorithm to be flexibly adapted to many different applications.(cont.) As a particular example, we consider a graphical model describing the hand's three-dimensional (3D) structure, kinematics, and dynamics. This graph encodes global hand pose via the 3D position and orientation of several rigid components, and thus exposes local structure in a high-dimensional articulated model. Applying nonparametric BP, we recover a hand tracking algorithm which is robust to outliers and local visual ambiguities. Via a set of latent occupancy masks, we also extend our approach to consistently infer occlusion events in a distributed fashion. In the second half of this thesis, we develop methods for learning hierarchical models of objects, the parts composing them, and the scenes surrounding them. Our approach couples topic models originally developed for text analysis with spatial transformations, and thus consistently accounts for geometric constraints. By building integrated scene models, we may discover contextual relationships, and better exploit partially labeled training images. We first consider images of isolated objects, and show that sharing parts among object categories improves accuracy when learning from few examples.(cont.) Turning to multiple object scenes, we propose nonparametric models which use Dirichlet processes to automatically learn the number of parts underlying each object category, and objects composing each scene. Adapting these transformed Dirichlet processes to images taken with a binocular stereo camera, we learn integrated, 3D models of object geometry and appearance. This leads to a Monte Carlo algorithm which automatically infers 3D scene structure from the predictable geometry of known object categories.by Erik B. Sudderth.Ph.D

Modeling, Predicting and Capturing Human Mobility

Realistic models of human mobility are critical for modern day applications, specifically for recommendation systems, resource planning and process optimization domains. Given the rapid proliferation of mobile devices equipped with Internet connectivity and GPS functionality today, aggregating large sums of individual geolocation data is feasible. The thesis focuses on methodologies to facilitate data-driven mobility modeling by drawing parallels between the inherent nature of mobility trajectories, statistical physics and information theory. On the applied side, the thesis contributions lie in leveraging the formulated mobility models to construct prediction workflows by adopting a privacy-by-design perspective. This enables end users to derive utility from location-based services while preserving their location privacy. Finally, the thesis presents several approaches to generate large-scale synthetic mobility datasets by applying machine learning approaches to facilitate experimental reproducibility

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Visualizing multidimensional data similarities:Improvements and applications

Multidimensional data is increasingly more prominent and important in many application domains. Such data typically consist of a large set of elements, each of which described by several measurements (dimensions). During the design of techniques and tools to process this data, a key component is to gather insights into their structure and patterns, which can be described by the notion of similarity between elements. Among these techniques, multidimensional projections and similarity trees can effectively capture similarity patterns and handle a large number of data elements and dimensions. However, understanding and interpreting these patterns in terms of the original data dimensions is still hard. This thesis addresses the development of visual explanatory techniques for the easy interpretation of similarity patterns present in multidimensional projections and similarity trees, by several contributions. First, we propose methods that make the computation of similarity trees efficient for large datasets, and also enhance its visual representation to allow the exploration of more data in a limited screen. Secondly, we propose methods for the visual explanation of multidimensional projections in terms of groups of similar elements. These are automatically annotated to describe which dimensions are more important to define their notion of group similarity. We show next how these explanatory mechanisms can be adapted to handle both static and time-dependent data. Our proposed techniques are designed to be easy to use, work nearly automatically, and are demonstrated on a variety of real-world large data obtained from image collections, text archives, scientific measurements, and software engineering

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum