generalized principal component analysis interdisciplinary applied mathematics

Download Book Generalized Principal Component Analysis Interdisciplinary Applied Mathematics in PDF format. You can Read Online Generalized Principal Component Analysis Interdisciplinary Applied Mathematics here in PDF, EPUB, Mobi or Docx formats.

Generalized Principal Component Analysis

Author : René Vidal
ISBN : 9780387878119
Genre : Science
File Size : 80. 17 MB
Format : PDF
Download : 915
Read : 526

Get This Book


This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Principal Component Analysis

Author : I.T. Jolliffe
ISBN : 9781475719048
Genre : Mathematics
File Size : 33. 70 MB
Format : PDF
Download : 374
Read : 232

Get This Book


Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.

Principal Component Analysis

Author : Virginia Gray
ISBN : 1536108898
Genre :
File Size : 72. 41 MB
Format : PDF, Kindle
Download : 695
Read : 915

Get This Book


This book provides new research on principal component analysis (PCA). Chapter One introduces typical PCA applications of transcriptomic, proteomic and metabolomic data. Chapter Two studies the factor analysis of an outcome measurement survey for science, technology and society. Chapter Three examines the application of PCA to performance enhancement of hyperspectral radiative transfer computations.

Generalized Principal Component Analysis

Author : Yi Ma
ISBN : 0387879250
Genre : Mathematics
File Size : 55. 83 MB
Format : PDF, Docs
Download : 738
Read : 1326

Get This Book


The main goal of this book is to introduce a new method to study hybrid models, referred to as generalized principal component analysis. The general problems that GPCA aims to address represents a fairly general class of unsupervised learning problems— many data clustering and modeling methods in machine learning can be viewed as special cases of this method. This book provides a comprehensive introduction of the fundamental statistical, geometric and algebraic concepts associated with the estimation (and segmentation) of the hybrid models, especially the hybrid linear models.

Nonlinear Dimensionality Reduction

Author : John A. Lee
ISBN : 9780387393513
Genre : Mathematics
File Size : 27. 61 MB
Format : PDF
Download : 908
Read : 637

Get This Book


This book describes established and advanced methods for reducing the dimensionality of numerical databases. Each description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. The text provides a lucid summary of facts and concepts relating to well-known methods as well as recent developments in nonlinear dimensionality reduction. Methods are all described from a unifying point of view, which helps to highlight their respective strengths and shortcomings. The presentation will appeal to statisticians, computer scientists and data analysts, and other practitioners having a basic background in statistics or computational learning.

Manifold Learning Theory And Applications

Author : Yunqian Ma
ISBN : 9781466558878
Genre : Business & Economics
File Size : 43. 21 MB
Format : PDF, ePub
Download : 649
Read : 1117

Get This Book


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 application in machine learning, neural networks, pattern recognition, image processing, and computer vision. Filling a void in the literature, Manifold Learning Theory and Applications incorporates state-of-the-art techniques in manifold learning with a solid theoretical and practical treatment of the subject. Comprehensive in its coverage, this pioneering work explores this novel modality from algorithm creation to successful implementation—offering examples of applications in medical, biometrics, multimedia, and computer vision. Emphasizing implementation, it highlights the various permutations of manifold learning in industry including manifold optimization, large scale manifold learning, semidefinite programming for embedding, manifold models for signal acquisition, compression and processing, and multi scale manifold. Beginning with an introduction to manifold learning theories and applications, the book includes discussions on the relevance to nonlinear dimensionality reduction, clustering, graph-based subspace learning, spectral learning and embedding, extensions, and multi-manifold modeling. It synergizes cross-domain knowledge for interdisciplinary instructions, offers a rich set of specialized topics contributed by expert professionals and researchers from a variety of fields. Finally, the book discusses specific algorithms and methodologies using case studies to apply manifold learning for real-world problems.

Principal Components Analysis

Author : George H. Dunteman
ISBN : 0803931042
Genre : Mathematics
File Size : 65. 9 MB
Format : PDF, Mobi
Download : 142
Read : 1181

Get This Book


For anyone in need of a concise, introductory guide to principal components analysis, this book is a must. Through an effective use of simple mathematical-geometrical and multiple real-life examples (such as crime statistics, indicators of drug abuse, and educational expenditures) -- and by minimizing the use of matrix algebra -- the reader can quickly master and put this technique to immediate use.

Principal Component Analysis Handbook

Author : Rebecca Cross
ISBN : 1632404168
Genre : Mathematics
File Size : 73. 71 MB
Format : PDF, Kindle
Download : 746
Read : 1022

Get This Book


This book on Principal component analysis (PCA) is a significant contribution to the field of data analysis. PCA involves a statistical procedure which orthogonally transforms a set of possibly correlated observations into set of values of linearly uncorrelated variables called principal components. The aim of this book is to enhance knowledge of scientists, engineers and researchers regarding the advantages of this technique in data analysis and includes information on the uses of PCA in distinct fields like multi-sensor data fusion, ecology, energy, agriculture, climate, image and video processing, gas chromatographic examination, color coating, materials science and automatic target identification.

Neural Networks And Deep Learning

Author : Charu C. Aggarwal
ISBN : 9783319944630
Genre : Computers
File Size : 77. 3 MB
Format : PDF, Mobi
Download : 223
Read : 1316

Get This Book


This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly important for understanding important concepts, so that one can understand the important design concepts of neural architectures in different applications. Why do neural networks work? When do they work better than off-the-shelf machine-learning models? When is depth useful? Why is training neural networks so hard? What are the pitfalls? The book is also rich in discussing different applications in order to give the practitioner a flavor of how neural architectures are designed for different types of problems. Applications associated with many different areas like recommender systems, machine translation, image captioning, image classification, reinforcement-learning based gaming, and text analytics are covered. The chapters of this book span three categories: The basics of neural networks: Many traditional machine learning models can be understood as special cases of neural networks. An emphasis is placed in the first two chapters on understanding the relationship between traditional machine learning and neural networks. Support vector machines, linear/logistic regression, singular value decomposition, matrix factorization, and recommender systems are shown to be special cases of neural networks. These methods are studied together with recent feature engineering methods like word2vec. Fundamentals of neural networks: A detailed discussion of training and regularization is provided in Chapters 3 and 4. Chapters 5 and 6 present radial-basis function (RBF) networks and restricted Boltzmann machines. Advanced topics in neural networks: Chapters 7 and 8 discuss recurrent neural networks and convolutional neural networks. Several advanced topics like deep reinforcement learning, neural Turing machines, Kohonen self-organizing maps, and generative adversarial networks are introduced in Chapters 9 and 10. The book is written for graduate students, researchers, and practitioners. Numerous exercises are available along with a solution manual to aid in classroom teaching. Where possible, an application-centric view is highlighted in order to provide an understanding of the practical uses of each class of techniques.

Diffusion And Ecological Problems Modern Perspectives

Author : Akira Okubo
ISBN : 9781475749786
Genre : Science
File Size : 71. 36 MB
Format : PDF, ePub
Download : 714
Read : 253

Get This Book


Surveying a wide variety of mathematical models of diffusion in the ecological context, this book is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background of the mathematics and physics of diffusion and how they can be applied to ecological problems. Equally, this is a specialized text book for graduates interested in mathematical ecology -- assuming no more than a basic knowledge of probability and differential equations. Each chapter in this new edition has been substantially updated by appopriate leading researchers in the field and contains much new material covering recent developments.

Top Download:

Best Books