Author: Paul G. Constantine Publisher: SIAM ISBN: 1611973864 Category : Computers Languages : en Pages : 105
Book Description
Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
Author: Jianzhong Wang Publisher: Springer Science & Business Media ISBN: 3642274978 Category : Computers Languages : en Pages : 363
Book Description
"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.
Author: Bing Li Publisher: CRC Press ISBN: 1498704484 Category : Mathematics Languages : en Pages : 307
Book Description
Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.
Author: Charu C. Aggarwal Publisher: Springer Science & Business Media ISBN: 1461432235 Category : Computers Languages : en Pages : 527
Book Description
Text mining applications have experienced tremendous advances because of web 2.0 and social networking applications. Recent advances in hardware and software technology have lead to a number of unique scenarios where text mining algorithms are learned. Mining Text Data introduces an important niche in the text analytics field, and is an edited volume contributed by leading international researchers and practitioners focused on social networks & data mining. This book contains a wide swath in topics across social networks & data mining. Each chapter contains a comprehensive survey including the key research content on the topic, and the future directions of research in the field. There is a special focus on Text Embedded with Heterogeneous and Multimedia Data which makes the mining process much more challenging. A number of methods have been designed such as transfer learning and cross-lingual mining for such cases. Mining Text Data simplifies the content, so that advanced-level students, practitioners and researchers in computer science can benefit from this book. Academic and corporate libraries, as well as ACM, IEEE, and Management Science focused on information security, electronic commerce, databases, data mining, machine learning, and statistics are the primary buyers for this reference book.
Author: Yura A. Kubyshin Publisher: Springer ISBN: 9783662137529 Category : Science Languages : en Pages : 80
Book Description
This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
Author: Peter Benner Publisher: Springer Science & Business Media ISBN: 3540279091 Category : Technology & Engineering Languages : en Pages : 397
Book Description
In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.
Author: Philip D. Waggoner Publisher: Cambridge University Press ISBN: 1108991645 Category : Political Science Languages : en Pages : 98
Book Description
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github.
Author: John A. Lee Publisher: Springer Science & Business Media ISBN: 038739351X Category : Mathematics Languages : en Pages : 316
Book Description
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.
Author: Liang Sun Publisher: CRC Press ISBN: 1439806160 Category : Business & Economics Languages : en Pages : 206
Book Description
Similar to other data mining and machine learning tasks, multi-label learning suffers from dimensionality. An effective way to mitigate this problem is through dimensionality reduction, which extracts a small number of features by removing irrelevant, redundant, and noisy information. The data mining and machine learning literature currently lacks
Author: Marianna Bolla Publisher: CRC Press ISBN: 1000392392 Category : Mathematics Languages : en Pages : 318
Book Description
This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix. Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.
Author: Paul G. Constantine
Author: Jianzhong Wang
Author: Bing Li
Author: Charu C. Aggarwal
Author: Yura A. Kubyshin
Author: Peter Benner
Author: Philip D. Waggoner
Author: John A. Lee
Author: Liang Sun
Author: Marianna Bolla