Computational Methods For Manifold Learning
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Author | : Xin Yang |
Publisher | : |
Total Pages | : 132 |
Release | : 2007 |
Genre | : |
ISBN | : |
In many real world applications, data samples lying in a high dimensional ambient space can be modeled by very low dimensional nonlinear manifolds. Manifold learning, as a new framework of machine learning, discovers this low dimensional structure from the collection of the high dimensional data. In this thesis, some novel manifold learning methods are proposed, including conical dimension, semi-supervised nonlinear dimensionality reduction, active learning for the semi-supervised manifold learning, and mesh-free manifold learning. {it Conical dimension} is proposed as a novel local intrinsic dimension estimator, for estimating the intrinsic dimension of a data set consisting of points lying in the proximity of a manifold. It can also be applied to intersection and boundary detection. The accuracy and robustness of the algorithm are illustrated by both synthetic and real-world data experiments. Both synthetic and real life examples are shown. We propose the {it semi-supervised nonlinear dimensionality reduction} by introducing the prior information into basic nonlinear dimensionality reduction method, such as LLE and LTSA. The sensitivity analysis of our algorithms shows that prior information will improve the stability of the solution. We demonstrate the usefulness of our algorithm by synthetic and real life examples. A principled approach for selecting the data points for labeling used in semi-supervised manifold learning is proposed as {it active learning} method. Experiments on both synthetic and real-world problems show that our proposed methods can substantially improve the accuracy of the computed global parameterizations over several alternative methods. In the last section, we propose an alternative dimensionality reduction method, namely mesh-free manifold learning, which introduce the phase field models into dimensionality reduction problem to track the data movement during the time step of the dimensionality reduction procedure.
Author | : Wei Qi Yan |
Publisher | : Springer Nature |
Total Pages | : 134 |
Release | : 2020-12-04 |
Genre | : Computers |
ISBN | : 3030610810 |
Integrating concepts from deep learning, machine learning, and artificial neural networks, this highly unique textbook presents content progressively from easy to more complex, orienting its content about knowledge transfer from the viewpoint of machine intelligence. It adopts the methodology from graphical theory, mathematical models, and algorithmic implementation, as well as covers datasets preparation, programming, results analysis and evaluations. Beginning with a grounding about artificial neural networks with neurons and the activation functions, the work then explains the mechanism of deep learning using advanced mathematics. In particular, it emphasizes how to use TensorFlow and the latest MATLAB deep-learning toolboxes for implementing deep learning algorithms. As a prerequisite, readers should have a solid understanding especially of mathematical analysis, linear algebra, numerical analysis, optimizations, differential geometry, manifold, and information theory, as well as basic algebra, functional analysis, and graphical models. This computational knowledge will assist in comprehending the subject matter not only of this text/reference, but also in relevant deep learning journal articles and conference papers. This textbook/guide is aimed at Computer Science research students and engineers, as well as scientists interested in deep learning for theoretic research and analysis. More generally, this book is also helpful for those researchers who are interested in machine intelligence, pattern analysis, natural language processing, and machine vision. Dr. Wei Qi Yan is an Associate Professor in the Department of Computer Science at Auckland University of Technology, New Zealand. His other publications include the Springer title, Visual Cryptography for Image Processing and Security.
Author | : Yunqian Ma |
Publisher | : CRC Press |
Total Pages | : 410 |
Release | : 2011-12-20 |
Genre | : Business & Economics |
ISBN | : 1466558873 |
Trained to extract actionable information from large volumes of high-dimensional data, engineers and scientists often have trouble isolating meaningful low-dimensional structures hidden in their high-dimensional observations. Manifold learning, a groundbreaking technique designed to tackle these issues of dimensionality reduction, finds widespread
Author | : Lodhi, Huma |
Publisher | : IGI Global |
Total Pages | : 418 |
Release | : 2010-07-31 |
Genre | : Computers |
ISBN | : 1615209123 |
"This book is a timely compendium of key elements that are crucial for the study of machine learning in chemoinformatics, giving an overview of current research in machine learning and their applications to chemoinformatics tasks"--Provided by publisher.
Author | : Jake VanderPlas |
Publisher | : "O'Reilly Media, Inc." |
Total Pages | : 743 |
Release | : 2016-11-21 |
Genre | : Computers |
ISBN | : 1491912138 |
For many researchers, Python is a first-class tool mainly because of its libraries for storing, manipulating, and gaining insight from data. Several resources exist for individual pieces of this data science stack, but only with the Python Data Science Handbook do you get them all—IPython, NumPy, Pandas, Matplotlib, Scikit-Learn, and other related tools. Working scientists and data crunchers familiar with reading and writing Python code will find this comprehensive desk reference ideal for tackling day-to-day issues: manipulating, transforming, and cleaning data; visualizing different types of data; and using data to build statistical or machine learning models. Quite simply, this is the must-have reference for scientific computing in Python. With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas: features the DataFrame for efficient storage and manipulation of labeled/columnar data in Python Matplotlib: includes capabilities for a flexible range of data visualizations in Python Scikit-Learn: for efficient and clean Python implementations of the most important and established machine learning algorithms
Author | : Ingwer Borg |
Publisher | : Springer Science & Business Media |
Total Pages | : 469 |
Release | : 2013-04-18 |
Genre | : Mathematics |
ISBN | : 1475727119 |
Multidimensional scaling (MDS) is a technique for the analysis of similarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices for a set of countries. MDS attempts to model such data as distances among points in a geometric space. The main reason for doing this is that one wants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to map the data, the mapping function, the algorithms used to find an optimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the different purposes for which MDS has been used, to various ways of looking at or "interpreting" an MDS representation, or to differences in the data required for the particular models. In this book, we give a fairly comprehensive presentation of MDS. For the reader with applied interests only, the first six chapters of Part I should be sufficient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.
Author | : Justin Solomon |
Publisher | : CRC Press |
Total Pages | : 400 |
Release | : 2015-06-24 |
Genre | : Computers |
ISBN | : 1482251892 |
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Author | : Wei Qi Yan |
Publisher | : Springer Nature |
Total Pages | : 235 |
Release | : 2023-10-17 |
Genre | : Computers |
ISBN | : 9819948231 |
The first edition of this textbook was published in 2021. Over the past two years, we have invested in enhancing all aspects of deep learning methods to ensure the book is comprehensive and impeccable. Taking into account feedback from our readers and audience, the author has diligently updated this book. The second edition of this textbook presents control theory, transformer models, and graph neural networks (GNN) in deep learning. We have incorporated the latest algorithmic advances and large-scale deep learning models, such as GPTs, to align with the current research trends. Through the second edition, this book showcases how computational methods in deep learning serve as a dynamic driving force in this era of artificial intelligence (AI). This book is intended for research students, engineers, as well as computer scientists with interest in computational methods in deep learning. Furthermore, it is also well-suited for researchers exploring topics such as machine intelligence, robotic control, and related areas.
Author | : Gilbert Strang |
Publisher | : Wellesley-Cambridge Press |
Total Pages | : 0 |
Release | : 2019-01-31 |
Genre | : Computers |
ISBN | : 9780692196380 |
Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.
Author | : |
Publisher | : Elsevier |
Total Pages | : 590 |
Release | : 2024-06-13 |
Genre | : Mathematics |
ISBN | : 0443239851 |
Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on the Numerical Analysis Meets Machine Learning