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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: 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: Heejung Bang Publisher: Humana ISBN: 9781493961245 Category : Science Languages : en Pages : 636
Book Description
This progressive book presents the basic principles of proper statistical analyses. It progresses to more advanced statistical methods in response to rapidly developing technologies and methodologies in the field of molecular biology.
Author: Matthieu Cord Publisher: Springer Science & Business Media ISBN: 3540751718 Category : Computers Languages : en Pages : 297
Book Description
Processing multimedia content has emerged as a key area for the application of machine learning techniques, where the objectives are to provide insight into the domain from which the data is drawn, and to organize that data and improve the performance of the processes manipulating it. Arising from the EU MUSCLE network, this multidisciplinary book provides a comprehensive coverage of the most important machine learning techniques used and their application in this domain.
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: Altuna Akalin Publisher: CRC Press ISBN: 1498781861 Category : Mathematics Languages : en Pages : 463
Book Description
Computational Genomics with R provides a starting point for beginners in genomic data analysis and also guides more advanced practitioners to sophisticated data analysis techniques in genomics. The book covers topics from R programming, to machine learning and statistics, to the latest genomic data analysis techniques. The text provides accessible information and explanations, always with the genomics context in the background. This also contains practical and well-documented examples in R so readers can analyze their data by simply reusing the code presented. As the field of computational genomics is interdisciplinary, it requires different starting points for people with different backgrounds. For example, a biologist might skip sections on basic genome biology and start with R programming, whereas a computer scientist might want to start with genome biology. After reading: You will have the basics of R and be able to dive right into specialized uses of R for computational genomics such as using Bioconductor packages. You will be familiar with statistics, supervised and unsupervised learning techniques that are important in data modeling, and exploratory analysis of high-dimensional data. You will understand genomic intervals and operations on them that are used for tasks such as aligned read counting and genomic feature annotation. You will know the basics of processing and quality checking high-throughput sequencing data. You will be able to do sequence analysis, such as calculating GC content for parts of a genome or finding transcription factor binding sites. You will know about visualization techniques used in genomics, such as heatmaps, meta-gene plots, and genomic track visualization. You will be familiar with analysis of different high-throughput sequencing data sets, such as RNA-seq, ChIP-seq, and BS-seq. You will know basic techniques for integrating and interpreting multi-omics datasets. Altuna Akalin is a group leader and head of the Bioinformatics and Omics Data Science Platform at the Berlin Institute of Medical Systems Biology, Max Delbrück Center, Berlin. He has been developing computational methods for analyzing and integrating large-scale genomics data sets since 2002. He has published an extensive body of work in this area. The framework for this book grew out of the yearly computational genomics courses he has been organizing and teaching since 2015.
Author: Trevor Hastie Publisher: CRC Press ISBN: 1498712177 Category : Business & Economics Languages : en Pages : 354
Book Description
Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Author: Bing Li Publisher: CRC Press ISBN: 1351645730 Category : Mathematics Languages : en Pages : 362
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: Maxime Turgeon Publisher: ISBN: Category : Languages : en Pages :
Book Description
"Recent technological advances in many domains including both genomics and brain imaging have led to an abundance of high-dimensional and correlated data being routinely collected. A widespread analytical goal in these fields is to investigate the relationships between, on the one hand, a group of genomic markers or anatomical brain measurements and, on theother hand, a set of clinical variables or phenotypes. To leverage the correlation within each set of measurements, and to improve the interpretability of a measure of the association, one can use dimension reduction techniques: one, or both, group of variables can be summarised by a small set of latent features that summarise the structure of interest andcapture association through an appropriately chosen statistic. But the high-dimensionality of contemporary datasets brings many computational and theoretical challenges, and most classical multivariate methods cannot be used directly.This thesis is comprised primarily of three manuscripts that investigate the issues related to measuring association in high dimensional datasets. In the first manuscript, I explore the optimality properties of a dimension reduction method known as Principal Component of Explained Variance (PCEV). This method seeks a linear combination of the outcome variablesthat maximises the proportion of variance explained by a set of covariates of interest. I then explain how PCEV can be extended to a computationally simple and efficient estimation strategy for high-dimensional outcomes (p > n) that relies on a "block-independence" assumption. In the second manuscript, I study the problem of inference with high-dimensional datasets: given two datasets Y and X, with one or both being high-dimensional, how can we perform a test of association in a computationally efficient way? Specifically, I look at the set of multivariate methods that can be described as a double Wishart problem; PCEV, Canonical Correlation Analysis (CCA), and Multivariate Analysis of Variance (MANOVA) are all examples of double Wishart problems. I show that valid high-dimensional p-values can be derived using an empirical estimator of the null distribution. This is achieved by performing a small number of permutations, and then fitting a location-scale family of the Tracy-Widom distribution of order 1 to the test statistics computed from the permuted data. Finally, in the third manuscript, I apply the concepts developed in the two other manuscripts to a data analysis of targeted custom capture bisulfite methylation data. I show how PCEV can be used in conjunction with the ideas in the second manuscript to test for a region-level association between the methylation levels of CpG dinucleotides and levels of anti-citrullinated protein antibody (ACPA), an antigen thought to be a predictor of rheumatoid arthritis onset. In this study, the CpG dinucleotides are naturally grouped by design, and several of these groups contain a number of methylation measurements that is larger than the samplesize." --
Author: Jianzhong Wang
Author: Jianzhong Wang
Author: Heejung Bang
Author: Matthieu Cord
Author: Philip D. Waggoner
Author: Yin Jen Chen
Author: Roman Vershynin
Author: Altuna Akalin
Author: Trevor Hastie
Author: Bing Li
Author: Maxime Turgeon