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Author : Michael W. Mahoney,John C. Duchi,Anna C. Gilbert
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 47,6 Mb
Release : 2018-11-15
Category : Big data
ISBN : 9781470435752
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Author : I.R. Goodman,R.P. Mahler,Hung T. Nguyen
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 51,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589291
Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of random set theory and conditional and relational event algebra. This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional and relational event algebra. Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.
Author : Daniela Calvetti,Erkki Somersalo
Publisher : SIAM
Page : 199 pages
File Size : 40,9 Mb
Release : 2020-11-20
Category : Mathematics
ISBN : 9781611976373
This textbook provides a solid mathematical basis for understanding popular data science algorithms for clustering and classification and shows that an in-depth understanding of the mathematics powering these algorithms gives insight into the underlying data. It presents a step-by-step derivation of these algorithms, outlining their implementation from scratch in a computationally sound way. Mathematics of Data Science: A Computational Approach to Clustering and Classification proposes different ways of visualizing high-dimensional data to unveil hidden internal structures, and nearly every chapter includes graphical explanations and computed examples using publicly available data sets to highlight similarities and differences among the algorithms. This self-contained book is geared toward advanced undergraduate and beginning graduate students in the mathematical sciences, engineering, and computer science and can be used as the main text in a semester course. Researchers in any application area where data science methods are used will also find the book of interest. No advanced mathematical or statistical background is assumed.
Author : Jeremy Kepner,Hayden Jananthan
Publisher : MIT Press
Page : 443 pages
File Size : 47,8 Mb
Release : 2018-08-07
Category : Computers
ISBN : 9780262347914
The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.
Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 50,5 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author : Jeff M. Phillips
Publisher : Springer Nature
Page : 299 pages
File Size : 45,6 Mb
Release : 2021-03-29
Category : Mathematics
ISBN : 9783030623418
This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.
Author : Michael W. Mahoney,John Duchi,Anna Catherine Gilbert
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470449900
Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book gives an introduction to the mathematical methods that form the foundations of machine learning and data science, presented by leading experts in computer science, statistics, and applied mathematics. Although the chapters can be read independently, they are designed to be read together as they lay out algorithmic, statistical, and numerical approaches in diverse but complementary ways. This book can be used both a.
Author : Kody Law,Andrew Stuart,Konstantinos Zygalakis
Publisher : Springer
Page : 242 pages
File Size : 52,9 Mb
Release : 2015-09-05
Category : Mathematics
ISBN : 9783319203256
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.
Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 40,5 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Author : Cathy O'Neil
Publisher : Crown Publishing Group (NY)
Page : 274 pages
File Size : 51,6 Mb
Release : 2016
Category : Business & Economics
ISBN : 9780553418811
"A former Wall Street quantitative analyst sounds an alarm on mathematical modeling, a pervasive new force in society that threatens to undermine democracy and widen inequality,"--NoveList.
Author : Barbara Canton
Publisher : Toronto. : McGraw-Hill Ryerson
Page : 227 pages
File Size : 48,9 Mb
Release : 2002
Category : Combinations
ISBN : 0075529130
Author : Dirk P. Kroese,Zdravko Botev,Thomas Taimre,Radislav Vaisman
Publisher : CRC Press
Page : 538 pages
File Size : 46,6 Mb
Release : 2019-11-20
Category : Business & Economics
ISBN : 9781000730777
Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code
Author : Vladimir Shikhman,David Müller
Publisher : Springer Nature
Page : 273 pages
File Size : 45,7 Mb
Release : 2021-02-11
Category : Computers
ISBN : 9783662625217
In this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary context. Exercises serve to improve understanding of the underlying theory. Complete solutions for exercises can be consulted by the interested reader at the end of the textbook; for some which have to be solved numerically, we provide descriptions of algorithms in Python code as supplementary material.This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.
Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Page : 615 pages
File Size : 41,5 Mb
Release : 2022-05-05
Category : Computers
ISBN : 9781009098489
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author : Frederick Mosteller,Stephen E. Fienberg,Robert E.K. Rourke
Publisher : Courier Corporation
Page : 608 pages
File Size : 48,5 Mb
Release : 2013-11-20
Category : Mathematics
ISBN : 9780486782256
This introduction to the world of statistics covers exploratory data analysis, methods for collecting data, formal statistical inference, and techniques of regression and analysis of variance. 1983 edition.