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Dimension Reduction And High Dimensional Data
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Book Synopsis Geometric Structure of High-Dimensional Data and Dimensionality Reduction by : Jianzhong Wang
Download or read book Geometric Structure of High-Dimensional Data and Dimensionality Reduction written by Jianzhong Wang and published by Springer Science & Business Media. This book was released on 2012-04-28 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Statistical Methods in Molecular Biology by : Heejung Bang
Download or read book Statistical Methods in Molecular Biology written by Heejung Bang and published by Humana. This book was released on 2016-08-23 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modern Dimension Reduction by : Philip D. Waggoner
Download or read book Modern Dimension Reduction written by Philip D. Waggoner and published by Cambridge University Press. This book was released on 2021-08-05 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Machine Learning Techniques for Multimedia by : Matthieu Cord
Download or read book Machine Learning Techniques for Multimedia written by Matthieu Cord and published by Springer Science & Business Media. This book was released on 2008-02-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classification, Regression and Dimension Reduction with High-Dimensional Data by : Yin Jen Chen
Download or read book Classification, Regression and Dimension Reduction with High-Dimensional Data written by Yin Jen Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dimension Reduction and High-dimensional Data by : Maxime Turgeon
Download or read book Dimension Reduction and High-dimensional Data written by Maxime Turgeon and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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." --
Book Synopsis Principal Manifolds for Data Visualization and Dimension Reduction by : Alexander N. Gorban
Download or read book Principal Manifolds for Data Visualization and Dimension Reduction written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2007-09-11 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.
Book Synopsis Dimension Reduction for Clustered High-dimensional Data by : Enikö Melinda Székely
Download or read book Dimension Reduction for Clustered High-dimensional Data written by Enikö Melinda Székely and published by . This book was released on 2011 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dimension Reduction by : Christopher J. C. Burges
Download or read book Dimension Reduction written by Christopher J. C. Burges and published by Now Publishers Inc. This book was released on 2010 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although the review focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nystr m method, which links several of the manifold algorithms, is also reviewed. We use a publicly available dataset to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.
Book Synopsis Advanced Prognostic Predictive Modelling in Healthcare Data Analytics by : Sudipta Roy
Download or read book Advanced Prognostic Predictive Modelling in Healthcare Data Analytics written by Sudipta Roy and published by Springer. This book was released on 2022-04-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses major technical advancements and research findings in the field of prognostic modelling in healthcare image and data analysis. The use of prognostic modelling as predictive models to solve complex problems of data mining and analysis in health care is the feature of this book. The book examines the recent technologies and studies that reached the practical level and becoming available in preclinical and clinical practices in computational intelligence. The main areas of interest covered in this book are highest quality, original work that contributes to the basic science of processing, analysing and utilizing all aspects of advanced computational prognostic modelling in healthcare image and data analysis.
Book Synopsis Statistical Learning with Sparsity by : Trevor Hastie
Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Computational Genomics with R by : Altuna Akalin
Download or read book Computational Genomics with R written by Altuna Akalin and published by CRC Press. This book was released on 2020-12-16 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sufficient Dimension Reduction by : Bing Li
Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :Tianwen Tony Cai Publisher :World Scientific Publishing Company Incorporated ISBN 13 :9789814324854 Total Pages :307 pages Book Rating :4.3/5 (248 download)
Book Synopsis High-dimensional Data Analysis by : Tianwen Tony Cai
Download or read book High-dimensional Data Analysis written by Tianwen Tony Cai and published by World Scientific Publishing Company Incorporated. This book was released on 2011 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. In particular, substantial advances have been made in the areas of feature selection, covariance estimation, classification and regression. This book intends to examine important issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research. The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in high-dimensional data analysis.
Book Synopsis Advances in Neural Networks - ISNN 2007 by : Derong Liu
Download or read book Advances in Neural Networks - ISNN 2007 written by Derong Liu and published by Springer. This book was released on 2007-07-14 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a three volume set that constitutes the refereed proceedings of the 4th International Symposium on Neural Networks, ISNN 2007, held in Nanjing, China in June 2007. Coverage includes neural networks for control applications, robotics, data mining and feature extraction, chaos and synchronization, support vector machines, fault diagnosis/detection, image/video processing, and applications of neural networks.
Book Synopsis Modeling High Dimensional Data by : Chinghway Lim
Download or read book Modeling High Dimensional Data written by Chinghway Lim and published by . This book was released on 2011 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is on high dimensional data and their associated regularization through dimension reduction and penalization. We start with two real world problems to illustrate the practical difficulties and remedies in analyzing high dimensional data. In Chapter 1, we are tasked with modeling and predicting the U.S. stock market, where the number of stocks far exceeds the number of days relevant to the current market. Through an existing statistical arbitrage framework, we reduce the dimension of our problem with the use of correspondence analysis. We develop a data driven regression model and highlight some common statistical methods that improve our predictions. In Chapter 2, we attempt to detect and predict system anomalies in large enterprise telephony systems. We do this by processing large amounts of unstructured log files, again with dimension reduction methods, allowing effective visualization and automatic filtering of results. We then move on to more general methodology and analysis in high dimensions. In Chapter 3, we consider regularization methods, often used in dealing with high dimensional data, and tackle the problem of selecting the associated regularization parameter. We introduce SSCV, a selection criterion based on statistical stability, but also incorporating model fit, and show that it can often outperform the popular cross validation. Finally, we explore robust methods in the high dimensional setting in Chapter 4. We focus on the relative performance and distributional robustness of the estimators optimizing L1 and L2 loss functions respectively. We verify some expected results and also highlight cases where results from classical asymptotics fail, setting the stage for future theoretical work.
