Linear Algebra With Machine Learning and Data

图书简介

This book takes a deep dive into several key linear algebra subjects as they apply to data analytics and data mining. The book offers a case study approach where each case will be grounded in a real-world application. This text is meant to be used for a second course in applications of Linear Algebra to Data Analytics, with a supplemental chapter on Decision Trees and their applications in regression analysis. The text can be considered in two different but overlapping general data analytics categories, clustering and interpolation. Knowledge of mathematical techniques related to data analytics, and exposure to interpretation of results within a data analytics context, are particularly valuable for students studying undergraduate mathematics. Each chapter of this text takes the reader through several relevant and case studies using real world data. All data sets, as well as Python and R syntax are provided to the reader through links to Github documentation. Following each chapter is a short exercise set in which students are encouraged to use technology to apply their expanding knowledge of linear algebra as it is applied to data analytics. A basic knowledge of the concepts in a first Linear Algebra course are assumed; however, an overview of key concepts are presented in the Introduction and as needed throughout the text.

Acknowledgments Introduction 1 Graph Theory 1.1 Basic Terminology 1.2 The Power of the Adjacency Matrix 1.3 Eigenvalues and Eigenvectors as Key Players 1.4 CASE STUDY: Applications in Sport Ranking 1.5 CASE STUDY: Gerrymandering 1.6 Exercises 2. Stochastic Processes 2.1 Markov Chain Basics 2.2 Hidden Markov Models 2.2.1 The Likelihood Problem 2.2.2 The Decoding Problem 2.2.3 The Learning Problem 2.3 CASE STUDY: Spread of Infectious Disease 2.4 CASE STUDY: Text Analysis and Autocorrect 2.5 CASE STUDY: Tweets and Time Series 2.6 Exercises 3. SVD and PCA 3.1 Vector and Inner Product Spaces 3.2 Singular Values 3.3 Singular Value Decomposition 3.4 Compression of Data Using Principal Component Analysis (PCA) 3.5 PCA, Covariance, and Correlation 3.6 Linear Discriminant Analysis 3.7 CASE STUDY: Digital Humanities 3.8 CASE STUDY: Facial Recognition Using PCA and LDA 3.9 Exercises 4. Interpolation 4.1 Lagrange Interpolation 4.2 Orthogonal Families of Polynomials 4.3 Newton’s Divided Difference 4.3.1 Newton’s interpolation via divided difference 4.3.2 Newton’s interpolation via the Vandermonde matrix 4.4 Chebyshev interpolation 4.5 Hermite interpolation 4.6 Least Squares Regression 4.7 CASE STUDY : Chebyshev Polynomials and Cryptography 4.8 CASE STUDY: Racial Disparities in Marijuana Arrests 4.9 CASE STUDY : Interpolation in Higher Education Data 4.10 Exercises 5. Optimization and Learning Techniques for Regression 5.1 Basics of Probability Theory 5.2 Introduction to Matrix Calculus 5.2.1 Matrix Differentiation 5.2.2 Matrix Integration 5.3 Maximum Likeli

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Linear Algebra With Machine Learning and Data（Textbooks in Mathematics） 具有机器学习和数据的线性代数 数学史

Linear Algebra With Machine Learning and Data（Textbooks in Mathematics）

具有机器学习和数据的线性代数
数学史