Laguerre's method in global iterative zero-finding.

by Kwok, Wong-chuen Tony.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves [85-86]).AcknowledgementAbstractChapter I --- Laguerre's Method in Polynomial Zero-findingChapter 1 --- Background --- p.1Chapter 2 --- Introduction and Problems of Laguerre´ةs Method --- p.3Chapter 2.1 --- Laguerre´ةs Method in Symmetrie-Cluster ProblemChapter 2.2 --- Cyclic BehaviourChapter 2.3 --- Supercluster ProblemChapter 3 --- Proposed Enhancement to Laguerre 's Method --- p.9Chapter 3.1 --- Analysis of Adding a Zero or PoleChapter 3.2 --- Proposed AlgorithmChapter 4 --- Conclusion --- p.17Chapter II --- Homotopy Methods applied to Polynomial Zero-findingChapter 1 --- Introduction --- p.18Chapter 2 --- Overcoming Bifurcation --- p.22Chapter 3 --- Comparison of Homotopy Algorithms --- p.27Chapter 4 --- Conclusion --- p.29AppendicesChapter I --- Laguerre's Method in Polynomial Zero-findingChapter 0 --- Naming of Testing PolynomialsChapter 1 --- Finding All Zeros using Proposed Laguerre's MethodChapter 2 --- Experiments: Selected Pictures of Comparison of Proposed Strategy with Other StrategyChapter 3 --- Experiments: Tables of Comparison of Proposed Strategy with Other StrategyChapter 4 --- Distance Colorations and Target ColorationsChapter II --- Homotopy Methods applied to Polynomial Zero-findingChapter 1 --- Comparison of Algorithms using Homotopy MethodChapter 2 --- Experiments: Selected Pictorial ComparisonChapter III --- An Example Demonstrating Effect of Round-off Errors Reference

Semi-supervised and unsupervised kernel-based novelty detection with application to remote sensing images

The main challenge of new information technologies is to retrieve intelligible information from the large volume of digital data gathered every day. Among the variety of existing data sources, the satellites continuously observing the surface of the Earth are key to the monitoring of our environment. The new generation of satellite sensors are tremendously increasing the possibilities of applications but also increasing the need for efficient processing methodologies in order to extract information relevant to the users' needs in an automatic or semi-automatic way. This is where machine learning comes into play to transform complex data into simplified products such as maps of land-cover changes or classes by learning from data examples annotated by experts. These annotations, also called labels, may actually be difficult or costly to obtain since they are established on the basis of ground surveys. As an example, it is extremely difficult to access a region recently flooded or affected by wildfires. In these situations, the detection of changes has to be done with only annotations from unaffected regions. In a similar way, it is difficult to have information on all the land-cover classes present in an image while being interested in the detection of a single one of interest. These challenging situations are called novelty detection or one-class classification in machine learning. In these situations, the learning phase has to rely only on a very limited set of annotations, but can exploit the large set of unlabeled pixels available in the images. This setting, called semi-supervised learning, allows significantly improving the detection. In this Thesis we address the development of methods for novelty detection and one-class classification with few or no labeled information. The proposed methodologies build upon the kernel methods, which take place within a principled but flexible framework for learning with data showing potentially non-linear feature relations. The thesis is divided into two parts, each one having a different assumption on the data structure and both addressing unsupervised (automatic) and semi-supervised (semi-automatic) learning settings. The first part assumes the data to be formed by arbitrary-shaped and overlapping clusters and studies the use of kernel machines, such as Support Vector Machines or Gaussian Processes. An emphasis is put on the robustness to noise and outliers and on the automatic retrieval of parameters. Experiments on multi-temporal multispectral images for change detection are carried out using only information from unchanged regions or none at all. The second part assumes high-dimensional data to lie on multiple low dimensional structures, called manifolds. We propose a method seeking a sparse and low-rank representation of the data mapped in a non-linear feature space. This representation allows us to build a graph, which is cut into several groups using spectral clustering. For the semi-supervised case where few labels of one class of interest are available, we study several approaches incorporating the graph information. The class labels can either be propagated on the graph, constrain spectral clustering or used to train a one-class classifier regularized by the given graph. Experiments on the unsupervised and oneclass classification of hyperspectral images demonstrate the effectiveness of the proposed approaches

Handbook of Vascular Biometrics

This open access handbook provides the first comprehensive overview of biometrics exploiting the shape of human blood vessels for biometric recognition, i.e. vascular biometrics, including finger vein recognition, hand/palm vein recognition, retina recognition, and sclera recognition. After an introductory chapter summarizing the state of the art in and availability of commercial systems and open datasets/open source software, individual chapters focus on specific aspects of one of the biometric modalities, including questions of usability, security, and privacy. The book features contributions from both academia and major industrial manufacturers