A kernel-based embedding framework for high-dimensional data analysis

The world is essentially multidimensional, e.g., neurons, computer networks, Internet traffic, and financial markets. The challenge is to discover and extract information that lies hidden in these high-dimensional datasets to support classification, regression, clustering, and visualization tasks. As a result, dimensionality reduction aims to provide a faithful representation of data in a low-dimensional space. This removes noise and redundant features, which is useful to understand and visualize the structure of complex datasets. The focus of this work is the analysis of high-dimensional data to support regression tasks and exploratory data analysis in real-world scenarios. Firstly, we propose an online framework to predict longterm future behavior of time-series. Secondly, we propose a new dimensionality reduction method to preserve the significant structure of high-dimensional data in a low-dimensional space. Lastly, we propose an sparsification strategy based on dimensionality reduction to avoid overfitting and reduce computational complexity in online applicationsEl mundo es esencialmente multidimensional, por ejemplo, neuronas, redes computacionales, tráfico de internet y los mercados financieros. El desafío es descubrir y extraer información que permanece oculta en estos conjuntos de datos de alta dimensión para apoyar tareas de clasificación, regresión, agrupamiento y visualización. Como resultado de ello, los métodos de reducción de dimensión pretenden suministrar una fiel representación de los datos en un espacio de baja dimensión. Esto permite eliminar ruido y características redundantes, lo que es útil para entender y visualizar la estructura de conjuntos de datos complejos. Este trabajo se enfoca en el análisis de datos de alta dimensión para apoyar tareas de regresión y el análisis exploratorio de datos en escenarios del mundo real. En primer lugar, proponemos un marco para la predicción del comportamiento a largo plazo de series de tiempo. En segundo lugar, se propone un nuevo método de reducción de dimensión para preservar la estructura significativa de datos de alta dimensión en un espacio de baja dimensión. Finalmente, proponemos una estrategia de esparsificacion que utiliza reducción de dimensional dad para evitar sobre ajuste y reducir la complejidad computacional de aplicaciones en líneaDoctorad

Interactions between gaussian processes and bayesian estimation

L’apprentissage (machine) de modèle et l’estimation d’état sont cruciaux pour interpréter les phénomènes sous-jacents à de nombreuses applications du monde réel. Toutefois, il est souvent difficile d’apprendre le modèle d’un système et de capturer les états latents, efficacement et avec précision, en raison du fait que la connaissance du monde est généralement incertaine. Au cours des dernières années, les approches d’estimation et de modélisation bayésiennes ont été extensivement étudiées afin que l’incertain soit réduit élégamment et de manière flexible. Dans la pratique cependant, différentes limitations au niveau de la modélisation et de l’estimation bayésiennes peuvent détériorer le pouvoir d’interprétation bayésienne. Ainsi, la performance de l’estimation est souvent limitée lorsque le modèle de système manque de souplesse ou/et est partiellement inconnu. De même, la performance de la modélisation est souvent restreinte lorsque l’estimateur Bayésien est inefficace. Inspiré par ces faits, nous proposons d’étudier dans cette thèse, les connections possibles entre modélisation bayésienne (via le processus gaussien) et l’estimation bayésienne (via le filtre de Kalman et les méthodes de Monte Carlo) et comment on pourrait améliorer l’une en utilisant l’autre. À cet effet, nous avons d’abord vu de plus près comment utiliser les processus gaussiens pour l’estimation bayésienne. Dans ce contexte, nous avons utilisé le processus gaussien comme un prior non-paramétrique des modèles et nous avons montré comment cela permettait d’améliorer l’efficacité et la précision de l’estimation bayésienne. Ensuite, nous nous somme intéressé au fait de savoir comment utiliser l’estimation bayésienne pour le processus gaussien. Dans ce cadre, nous avons utilisé différentes estimations bayésiennes comme le filtre de Kalman et les filtres particulaires en vue d’améliorer l’inférence au niveau du processus gaussien. Ceci nous a aussi permis de capturer différentes propriétés au niveau des données d’entrée. Finalement, on s’est intéressé aux interactions dynamiques entre estimation bayésienne et processus gaussien. On s’est en particulier penché sur comment l’estimation bayésienne et le processus gaussien peuvent ”travailler” de manière interactive et complémentaire de façon à améliorer à la fois le modèle et l’estimation. L’efficacité de nos approches, qui contribuent à la fois au processus gaussien et à l’estimation bayésienne, est montrée au travers d’une analyse mathématique rigoureuse et validée au moyen de différentes expérimentations reflétant des applications réelles.Model learning and state estimation are crucial to interpret the underlying phenomena in many real-world applications. However, it is often challenging to learn the system model and capture the latent states accurately and efficiently due to the fact that the knowledge of the world is highly uncertain. During the past years, Bayesian modeling and estimation approaches have been significantly investigated so that the uncertainty can be elegantly reduced in a flexible probabilistic manner. In practice, however, several drawbacks in both Bayesian modeling and estimation approaches deteriorate the power of Bayesian interpretation. On one hand, the estimation performance is often limited when the system model lacks in flexibility and/or is partially unknown. On the other hand, the modeling performance is often restricted when a Bayesian estimator is not efficient and/or accurate. Inspired by these facts, we propose Interactions Between Gaussian Processes and Bayesian Estimation where we investigate the novel connections between Bayesian model (Gaussian processes) and Bayesian estimator (Kalman filter and Monte Carlo methods) in different directions to address a number of potential difficulties in modeling and estimation tasks. Concretely, we first pay our attention to Gaussian Processes for Bayesian Estimation where a Gaussian process (GP) is used as an expressive nonparametric prior for system models to improve the accuracy and efficiency of Bayesian estimation. Then, we work on Bayesian Estimation for Gaussian Processes where a number of Bayesian estimation approaches, especially Kalman filter and particle filters, are used to speed up the inference efficiency of GP and also capture the distinct input-dependent data properties. Finally, we investigate Dynamical Interaction Between Gaussian Processes and Bayesian Estimation where GP modeling and Bayesian estimation work in a dynamically interactive manner so that GP learner and Bayesian estimator are positively complementary to improve the performance of both modeling and estimation. Through a number of mathematical analysis and experimental demonstrations, we show the effectiveness of our approaches which contribute to both GP and Bayesian estimation

Sparse Bayesian information filters for localization and mapping

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008This thesis formulates an estimation framework for Simultaneous Localization and Mapping (SLAM) that addresses the problem of scalability in large environments. We describe an estimation-theoretic algorithm that achieves significant gains in computational efficiency while maintaining consistent estimates for the vehicle pose and the map of the environment. We specifically address the feature-based SLAM problem in which the robot represents the environment as a collection of landmarks. The thesis takes a Bayesian approach whereby we maintain a joint posterior over the vehicle pose and feature states, conditioned upon measurement data. We model the distribution as Gaussian and parametrize the posterior in the canonical form, in terms of the information (inverse covariance) matrix. When sparse, this representation is amenable to computationally efficient Bayesian SLAM filtering. However, while a large majority of the elements within the normalized information matrix are very small in magnitude, it is fully populated nonetheless. Recent feature-based SLAM filters achieve the scalability benefits of a sparse parametrization by explicitly pruning these weak links in an effort to enforce sparsity. We analyze one such algorithm, the Sparse Extended Information Filter (SEIF), which has laid much of the groundwork concerning the computational benefits of the sparse canonical form. The thesis performs a detailed analysis of the process by which the SEIF approximates the sparsity of the information matrix and reveals key insights into the consequences of different sparsification strategies. We demonstrate that the SEIF yields a sparse approximation to the posterior that is inconsistent, suffering from exaggerated confidence estimates. This overconfidence has detrimental effects on important aspects of the SLAM process and affects the higher level goal of producing accurate maps for subsequent localization and path planning. This thesis proposes an alternative scalable filter that maintains sparsity while preserving the consistency of the distribution. We leverage insights into the natural structure of the feature-based canonical parametrization and derive a method that actively maintains an exactly sparse posterior. Our algorithm exploits the structure of the parametrization to achieve gains in efficiency, with a computational cost that scales linearly with the size of the map. Unlike similar techniques that sacrifice consistency for improved scalability, our algorithm performs inference over a posterior that is conservative relative to the nominal Gaussian distribution. Consequently, we preserve the consistency of the pose and map estimates and avoid the effects of an overconfident posterior. We demonstrate our filter alongside the SEIF and the standard EKF both in simulation as well as on two real-world datasets. While we maintain the computational advantages of an exactly sparse representation, the results show convincingly that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the original Gaussian distribution as produced by the EKF, but at much less computational expense. The thesis concludes with an extension of our SLAM filter to a complex underwater environment. We describe a systems-level framework for localization and mapping relative to a ship hull with an Autonomous Underwater Vehicle (AUV) equipped with a forward-looking sonar. The approach utilizes our filter to fuse measurements of vehicle attitude and motion from onboard sensors with data from sonar images of the hull. We employ the system to perform three-dimensional, 6-DOF SLAM on a ship hull

Local selection of features and its applications to image search and annotation

In multimedia applications, direct representations of data objects typically involve hundreds or thousands of features. Given a query object, the similarity between the query object and a database object can be computed as the distance between their feature vectors. The neighborhood of the query object consists of those database objects that are close to the query object. The semantic quality of the neighborhood, which can be measured as the proportion of neighboring objects that share the same class label as the query object, is crucial for many applications, such as content-based image retrieval and automated image annotation. However, due to the existence of noisy or irrelevant features, errors introduced into similarity measurements are detrimental to the neighborhood quality of data objects. One way to alleviate the negative impact of noisy features is to use feature selection techniques in data preprocessing. From the original vector space, feature selection techniques select a subset of features, which can be used subsequently in supervised or unsupervised learning algorithms for better performance. However, their performance on improving the quality of data neighborhoods is rarely evaluated in the literature. In addition, most traditional feature selection techniques are global, in the sense that they compute a single set of features across the entire database. As a consequence, the possibility that the feature importance may vary across different data objects or classes of objects is neglected. To compute a better neighborhood structure for objects in high-dimensional feature spaces, this dissertation proposes several techniques for selecting features that are important to the local neighborhood of individual objects. These techniques are then applied to image applications such as content-based image retrieval and image label propagation. Firstly, an iterative K-NN graph construction method for image databases is proposed. A local variant of the Laplacian Score is designed for the selection of features for individual images. Noisy features are detected and sparsified iteratively from the original standardized feature vectors. This technique is incorporated into an approximate K-NN graph construction method so as to improve the semantic quality of the graph. Secondly, in a content-based image retrieval system, a generalized version of the Laplacian Score is used to compute different feature subspaces for images in the database. For online search, a query image is ranked in the feature spaces of database images. Those database images for which the query image is ranked highly are selected as the query results. Finally, a supervised method for the local selection of image features is proposed, for refining the similarity graph used in an image label propagation framework. By using only the selected features to compute the edges leading from labeled image nodes to unlabeled image nodes, better annotation accuracy can be achieved. Experimental results on several datasets are provided in this dissertation, to demonstrate the effectiveness of the proposed techniques for the local selection of features, and for the image applications under consideration

Design and analysis of algorithms for similarity search based on intrinsic dimension

One of the most fundamental operations employed in data mining tasks such as classification, cluster analysis, and anomaly detection, is that of similarity search. It has been used in numerous fields of application such as multimedia, information retrieval, recommender systems and pattern recognition. Specifically, a similarity query aims to retrieve from the database the most similar objects to a query object, where the underlying similarity measure is usually expressed as a distance function. The cost of processing similarity queries has been typically assessed in terms of the representational dimension of the data involved, that is, the number of features used to represent individual data objects. It is generally the case that high representational dimension would result in a significant increase in the processing cost of similarity queries. This relation is often attributed to an amalgamation of phenomena, collectively referred to as the curse of dimensionality. However, the observed effects of dimensionality in practice may not be as severe as expected. This has led to the development of models quantifying the complexity of data in terms of some measure of the intrinsic dimensionality. The generalized expansion dimension (GED) is one of such models, which estimates the intrinsic dimension in the vicinity of a query point q through the observation of the ranks and distances of pairs of neighbors with respect to q. This dissertation is mainly concerned with the design and analysis of search algorithms, based on the GED model. In particular, three variants of similarity search problem are considered, including adaptive similarity search, flexible aggregate similarity search, and subspace similarity search. The good practical performance of the proposed algorithms demonstrates the effectiveness of dimensionality-driven design of search algorithms

Exactly Sparse Delayed-State Filters for View-Based SLAM

This paper reports the novel insight that the simultaneous localization and mapping (SLAM) information matrix is exactly sparse in a delayed-state framework. Such a framework is used in view-based representations of the environment that rely upon scan-matching raw sensor data to obtain virtual observations of robot motion with respect to a place it has previously been. The exact sparseness of the delayed-state information matrix is in contrast to other recent feature-based SLAM information algorithms, such as sparse extended information filter or thin junction-tree filter, since these methods have to make approximations in order to force the feature-based SLAM information matrix to be sparse. The benefit of the exact sparsity of the delayed-state framework is that it allows one to take advantage of the information space parameterization without incurring any sparse approximation error. Therefore, it can produce equivalent results to the full-covariance solution. The approach is validated experimentally using monocular imagery for two datasets: a test-tank experiment with ground truth, and a remotely operated vehicle survey of the RMS Titanic.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86062/1/reustice-25.pd

Distributed Estimation for Formation Flying Spacecraft

Formation flying is a critical technology for future space missions. Distributed estimation architectures will play a key role in achieving multi-spacecraft mission objectives. In the distributed framework, each spacecraft has access only to its local measurement data and the goal is to perform collaborative estimation via information exchange with the neighboring spacecraft. This dissertation develops two types of estimation algorithms, namely, a distributed batch filter for static parameter estimation and a distributed real-time filter for dynamic state estimation. The Least Squares (LS) technique is a popular approach for batch filtering. This method finds the solution of an overdetermined system of linear equations by minimizing the sum of squares of the residuals. While the LS estimator is known to be optimal for Gaussian measurement errors, its performance degrades in the presence of gross errors (outliers) in the measurements. The Least Absolute Deviations (LAD) technique, on the other hand, finds the solution that minimizes the sum of absolute values of the residuals and is known to be robust to measurement outliers. In this dissertation, we begin by formulating a linear programming-based solution to the LAD estimation problem. The LAD solution for linear systems is implemented in a nonlinear framework to solve an orbit determination problem. Further, an estimate of the error covariance matrix for the LAD estimates is also derived. For applications in multi-agent systems, a distributed form of the LAD estimator is formulated. In the Distributed (D-) LAD algorithm, individual agents utilize local measurement data and iteratively exchange information with their immediate neighbors via single-hop communications to collaboratively compute the LAD estimate. The distributed algorithm retains the robustness properties of the central LAD estimator. The D-LAD solution for linear systems is implemented in a nonlinear framework to solve the problem of distributed orbit determination of a target body using a formation of spacecraft. For distributed real-time filtering, the problem of autonomous inertial localization of spacecraft formations is considered. In the case of large formation sizes, each spacecraft may not be able to track or communicate with all other spacecraft. Further, for formations deployed in deep space, the unavailability of the Global Navigation Satellite System makes inertial state estimation challenging. We propose the Distributed Absolute and Relative Estimation (DARE) algorithm for autonomous inertial estimation of spacecraft formations. The algorithm enables each spacecraft to maintain an accurate inertial estimate of the entire formation even in the presence of observability and communication constraints. A modified version of the algorithm called the Sparse (S-) DARE algorithm is also derived. This algorithm is computationally more efficient at the expense of estimation accuracy making it suitable for implementation on nano-satellites where resources are limited

IMPROVING EFFICIENCY AND SCALABILITY IN VISUAL SURVEILLANCE APPLICATIONS

We present four contributions to visual surveillance: (a) an action recognition method based on the characteristics of human motion in image space; (b) a study of the strengths of five regression techniques for monocular pose estimation that highlights the advantages of kernel PLS; (c) a learning-based method for detecting objects carried by humans requiring minimal annotation; (d) an interactive video segmentation system that reduces supervision by using occlusion and long term spatio-temporal structure information. We propose a representation for human actions that is based solely on motion information and that leverages the characteristics of human movement in the image space. The representation is best suited to visual surveillance settings in which the actions of interest are highly constrained, but also works on more general problems if the actions are ballistic in nature. Our computationally efficient representation achieves good recognition performance on both a commonly used action recognition dataset and on a dataset we collected to simulate a checkout counter. We study discriminative methods for 3D human pose estimation from single images, which build a map from image features to pose. The main difficulty with these methods is the insufficiency of training data due to the high dimensionality of the pose space. However, real datasets can be augmented with data from character animation software, so the scalability of existing approaches becomes important. We argue that Kernel Partial Least Squares approximates Gaussian Process regression robustly, enabling the use of larger datasets, and we show in experiments that kPLS outperforms two state-of-the-art methods based on GP. The high variability in the appearance of carried objects suggests using their relation to the human silhouette to detect them. We adopt a generate-and-test approach that produces candidate regions from protrusion, color contrast and occlusion boundary cues and then filters them with a kernel SVM classifier on context features. Our method exceeds state of the art accuracy and has good generalization capability. We also propose a Multiple Instance Learning framework for the classifier that reduces annotation effort by two orders of magnitude while maintaining comparable accuracy. Finally, we present an interactive video segmentation system that trades off a small amount of segmentation quality for significantly less supervision than necessary in systems in the literature. While applications like video editing could not directly use the output of our system, reasoning about the trajectories of objects in a scene or learning coarse appearance models is still possible. The unsupervised segmentation component at the base of our system effectively employs occlusion boundary cues and achieves competitive results on an unsupervised segmentation dataset. On videos used to evaluate interactive methods, our system requires less interaction time than others, does not rely on appearance information and can extract multiple objects at the same time