Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Author: Jianzhong Wang

Publisher: Springer Science & Business Media

Published: 2012-04-28

Total Pages: 363

ISBN-13: 3642274978

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"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.


Dimension Reduction

Dimension Reduction

Author: Christopher J. C. Burges

Publisher: Now Publishers Inc

Published: 2010

Total Pages: 104

ISBN-13: 1601983786

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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.


High-Dimensional Probability

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.


Machine Learning Approaches for Urban Computing

Machine Learning Approaches for Urban Computing

Author: Mainak Bandyopadhyay

Publisher: Springer Nature

Published: 2021-04-28

Total Pages: 208

ISBN-13: 9811609357

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This book discusses various machine learning applications and models, developed using heterogeneous data, which helps in a comprehensive prediction, optimization, association analysis, cluster analysis and classification-related applications for various activities in urban area. It details multiple types of data generating from urban activities and suitability of various machine learning algorithms for handling urban data. The book is helpful for researchers, academicians, faculties, scientists and geospatial industry professionals for their research work and sets new ideas in the field of urban computing.


Modern Dimension Reduction

Modern Dimension Reduction

Author: Philip D. Waggoner

Publisher: Cambridge University Press

Published: 2021-08-05

Total Pages: 98

ISBN-13: 1108991645

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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.


17th International Conference on Information Technology–New Generations (ITNG 2020)

17th International Conference on Information Technology–New Generations (ITNG 2020)

Author: Shahram Latifi

Publisher: Springer Nature

Published: 2020-05-11

Total Pages: 691

ISBN-13: 3030430200

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This volume presents the 17th International Conference on Information Technology—New Generations (ITNG), and chronicles an annual event on state of the art technologies for digital information and communications. The application of advanced information technology to such domains as astronomy, biology, education, geosciences, security, and healthcare are among the themes explored by the ITNG proceedings. Visionary ideas, theoretical and experimental results, as well as prototypes, designs, and tools that help information flow to end users are of special interest. Specific topics include Machine Learning, Robotics, High Performance Computing, and Innovative Methods of Computing. The conference features keynote speakers; a best student contribution award, poster award, and service award; a technical open panel, and workshops/exhibits from industry, government, and academia.


Data Classification

Data Classification

Author: Charu C. Aggarwal

Publisher: CRC Press

Published: 2014-07-25

Total Pages: 710

ISBN-13: 1498760589

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Comprehensive Coverage of the Entire Area of ClassificationResearch on the problem of classification tends to be fragmented across such areas as pattern recognition, database, data mining, and machine learning. Addressing the work of these different communities in a unified way, Data Classification: Algorithms and Applications explores the underlyi


Structural, Syntactic, and Statistical Pattern Recognition

Structural, Syntactic, and Statistical Pattern Recognition

Author: Niels da Vitoria Lobo

Publisher: Springer

Published: 2008-12-02

Total Pages: 1029

ISBN-13: 3540896899

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This volume in the Springer Lecture Notes in Computer Science (LNCS) series contains 98 papers presented at the S+SSPR 2008 workshops. S+SSPR 2008 was the sixth time that the SPR and SSPR workshops organized by Technical Committees, TC1 and TC2, of the International Association for Pattern Rec- nition (IAPR) wereheld as joint workshops. S+SSPR 2008was held in Orlando, Florida, the family entertainment capital of the world, on the beautiful campus of the University of Central Florida, one of the up and coming metropolitan universities in the USA. S+SSPR 2008 was held during December 4–6, 2008 only a few days before the 19th International Conference on Pattern Recog- tion(ICPR2008),whichwasheldin Tampa,onlytwo hoursawayfromOrlando, thus giving the opportunity of both conferences to attendees to enjoy the many attractions o?ered by two neighboring cities in the state of Florida. SPR 2008 and SSPR 2008 received a total of 175 paper submissions from many di?erent countries around the world, thus giving the workshop an int- national clout, as was the case for past workshops. This volume contains 98 accepted papers: 56 for oral presentations and 42 for poster presentations. In addition to parallel oral sessions for SPR and SSPR, there was also one joint oral session with papers of interest to both the SPR and SSPR communities. A recent trend that has emerged in the pattern recognition and machine lea- ing research communities is the study of graph-based methods that integrate statistical andstructural approaches.


Recent Applications in Data Clustering

Recent Applications in Data Clustering

Author: Harun Pirim

Publisher: BoD – Books on Demand

Published: 2018-08-01

Total Pages: 250

ISBN-13: 178923526X

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Clustering has emerged as one of the more fertile fields within data analytics, widely adopted by companies, research institutions, and educational entities as a tool to describe similar/different groups. The book Recent Applications in Data Clustering aims to provide an outlook of recent contributions to the vast clustering literature that offers useful insights within the context of modern applications for professionals, academics, and students. The book spans the domains of clustering in image analysis, lexical analysis of texts, replacement of missing values in data, temporal clustering in smart cities, comparison of artificial neural network variations, graph theoretical approaches, spectral clustering, multiview clustering, and model-based clustering in an R package. Applications of image, text, face recognition, speech (synthetic and simulated), and smart city datasets are presented.


Large-scale Kernel Machines

Large-scale Kernel Machines

Author: Léon Bottou

Publisher: MIT Press

Published: 2007

Total Pages: 409

ISBN-13: 0262026252

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Solutions for learning from large scale datasets, including kernel learning algorithms that scale linearly with the volume of the data and experiments carried out on realistically large datasets. Pervasive and networked computers have dramatically reduced the cost of collecting and distributing large datasets. In this context, machine learning algorithms that scale poorly could simply become irrelevant. We need learning algorithms that scale linearly with the volume of the data while maintaining enough statistical efficiency to outperform algorithms that simply process a random subset of the data. This volume offers researchers and engineers practical solutions for learning from large scale datasets, with detailed descriptions of algorithms and experiments carried out on realistically large datasets. At the same time it offers researchers information that can address the relative lack of theoretical grounding for many useful algorithms. After a detailed description of state-of-the-art support vector machine technology, an introduction of the essential concepts discussed in the volume, and a comparison of primal and dual optimization techniques, the book progresses from well-understood techniques to more novel and controversial approaches. Many contributors have made their code and data available online for further experimentation. Topics covered include fast implementations of known algorithms, approximations that are amenable to theoretical guarantees, and algorithms that perform well in practice but are difficult to analyze theoretically. Contributors Léon Bottou, Yoshua Bengio, Stéphane Canu, Eric Cosatto, Olivier Chapelle, Ronan Collobert, Dennis DeCoste, Ramani Duraiswami, Igor Durdanovic, Hans-Peter Graf, Arthur Gretton, Patrick Haffner, Stefanie Jegelka, Stephan Kanthak, S. Sathiya Keerthi, Yann LeCun, Chih-Jen Lin, Gaëlle Loosli, Joaquin Quiñonero-Candela, Carl Edward Rasmussen, Gunnar Rätsch, Vikas Chandrakant Raykar, Konrad Rieck, Vikas Sindhwani, Fabian Sinz, Sören Sonnenburg, Jason Weston, Christopher K. I. Williams, Elad Yom-Tov