There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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Laplacian Eigenmaps for dimensionality reduction and data representation

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

We present a real-time algorithm which can recover the 3D trajectory of a monocular camera, moving rapidly through a previously unknown scene. Our system, which we dub MonoSLAM, is the first successful application of the SLAM methodology from mobile robotics to the "pure vision" domain of a single uncontrolled camera, achieving real time but drift-free performance inaccessible to structure from motion approaches. The core of the approach is the online creation of a sparse but persistent map of natural landmarks within a probabilistic framework. Our key novel contributions include an active approach to mapping and measurement, the use of a general motion model for smooth camera movement, and solutions for monocular feature initialization and feature orientation estimation. Together, these add up to an extremely efficient and robust algorithm which runs at 30 Hz with standard PC and camera hardware. This work extends the range of robotic systems in which SLAM can be usefully applied, but also opens up new areas. We present applications of MonoSLAM to real-time 3D localization and mapping for a high-performance full-size humanoid robot and live augmented reality with a hand-held camera

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MonoSLAM: Real-Time Single Camera SLAM

This paper presents algorithms for vision-based detection and classification of vehicles in monocular image sequences of traffic scenes recorded by a stationary camera. Processing is done at three levels: raw images, region level, and vehicle level. Vehicles are modeled as rectangular patches with certain dynamic behavior. The proposed method is based on the establishment of correspondences between regions and vehicles, as the vehicles move through the image sequence. Experimental results from highway scenes are provided which demonstrate the effectiveness of the method. We also briefly describe an interactive camera calibration tool that we have developed for recovering the camera parameters using features in the image selected by the user.

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Detection and classification of vehicles

The authors present algorithms for robotic (eye-in-hand configuration) real-time visual tracking of arbitrary 3D objects traveling at unknown velocities in a 2D space (depth is given as known). Visual tracking is formulated as a problem of combining control with computer vision. A mathematical formulation of the control problem that includes information from a novel feedback vision sensor and represents everything with respect to the camera frame is presented. The sum-of-squared differences (SSD) optical flow is used to compute the vector of discrete displacements each instant of time. These displacements can be fed either directly to a PI (proportional-integral) controller or to a pole assignment controller or discrete steady-state Kalman filter. In the latter case, the Kalman filter calculates the estimated values of the system's states and the exogenous disturbances, and a discrete LQG (linear-quadratic Gaussian) controller computes the desired motion of the robotic system. The outputs of the controllers are sent to the Cartesian robotic controller. Performance results are presented. >

Visual tracking of a moving target by a camera mounted on a robot: a combination of control and vision

One of the principal bottlenecks in applying learning techniques to classification problems is the large amount of labeled training data required. Especially for images and video, providing training data is very expensive in terms of human time and effort. In this paper we propose an active learning approach to tackle the problem. Instead of passively accepting random training examples, the active learning algorithm iteratively selects unlabeled examples for the user to label, so that human effort is focused on labeling the most “useful” examples. Our method relies on the idea of uncertainty sampling, in which the algorithm selects unlabeled examples that it finds hardest to classify. Specifically, we propose an uncertainty measure that generalizes margin-based uncertainty to the multi-class case and is easy to compute, so that active learning can handle a large number of classes and large data sizes efficiently. We demonstrate results for letter and digit recognition on datasets from the UCI repository, object recognition results on the Caltech-101 dataset, and scene categorization results on a dataset of 13 natural scene categories. The proposed method gives large reductions in the number of training examples required over random selection to achieve similar classification accuracy, with little computational overhead.

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Multi-class active learning for image classification

The use of a vision sensor in the feedback loop is addressed within the controlled active vision framework. Algorithms are proposed for the solution of the robotic (eye-in-hand configuration) visual tracking and servoing problem. Visual tracking is stated as a problem of combining control with computer vision. The sum-of-squared differences optical flow is used to compute the vector of discrete displacements. The displacements are fed to an adaptive controller (self-tuning regulator) that creates commands for a robot control system. The procedure is based on the online estimation of the relative distance of the target from the camera, but only partial knowledge of the relative distance is required, obviating the need for offline calibration. Three different adaptive control schemes have been implemented, both in simulation and in experiments. The computational complexity and the experimental results demonstrate that the proposed algorithms can be implemented in real time. >

Adaptive robotic visual tracking: theory and experiments

An approach to intelligent PID (proportional integral derivative) control of industrial systems which is based on the application of fuzzy logic is presented. This approach assumes that one has available nominal controller parameter settings through some classical tuning technique (Ziegler-Nichols, Kalman, etc.). By using an appropriate fuzzy matrix (similar to Macvicar-Whelan matrix), it is possible to determine small changes on these values during the system operation, and these lead to improved performance of the transient and steady behavior of the closed-loop system. This is achieved at the expense of some small extra computational effort, which can be very easily undertaken by a microprocessor. Several experimental results illustrate the improvements achieved. >

Nikolaos Papanikolopoulos

Papers

Detection and classification of vehicles

Visual tracking of a moving target by a camera mounted on a robot: a combination of control and vision

Multi-class active learning for image classification

Adaptive robotic visual tracking: theory and experiments

Incremental fuzzy expert PID control