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1st Edition - January 6, 2023

Authors: Jingli Ren, Haiyan Wang

Language: EnglishPaperback ISBN:

9 7 8 - 0 - 4 4 3 - 1 8 6 7 9 - 0

eBook ISBN:

9 7 8 - 0 - 4 4 3 - 1 8 6 8 0 - 6

Mathematical Methods in Data Science covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probabili… Read more

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*Mathematical Methods in Data Science* covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. Based on the authors’ recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for data

analysis and prediction. With data science being used in virtually every aspect of our society, the book includes examples and problems arising in data science and the clear explanation of advanced mathematical concepts, especially data-driven differential equations, making it accessible to researchers and graduate students in mathematics and data science.

- Combines a broad spectrum of mathematics, including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science
- Written by two researchers who are actively applying mathematical and statistical methods as well as ODE and PDE for data analysis and prediction
- Highly interdisciplinary, with content spanning mathematics, data science, social media analysis, network science, financial markets, and more
- Presents a wide spectrum of topics in a logical order, including probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations

Advanced undergraduate students, graduate students and researchers. Background preparations and necessary references

Chapter 1 Linear Algebra

1.1 Introduction

1.2 Elements of Linear Algebra

1.2.1 Linear Spaces

1.2.2 Orthogonality

1.2.3 Gram-Schmidt Process

1.2.4 Eigenvalues and Eigenvectors

1.3 Linear Regression

1.3.1 QR Decomposition

1.3.2 Least-squares Problems

1.3.3 Linear Regression

1.4 Principal Component Analysis

1.4.1 Singular Value Decomposition

1.4.2 Low-Rank Matrix Approximations

1.4.3 Principal Component Analysis

Chapter 2 Probability

2.1 Introduction

2.2 Probability Distribution

2.2.1 Probability Axioms

2.2.2 Conditional Probability

2.2.3 Discrete Random Variables

2.2.4 Continues Random Variables

2.3 Independent Variables and Random Samples

2.3.1 Joint Probability Distributions

2.3.2 Correlation and Dependence

2.3.3 Random Samples

2.4 Maximum Likelihood Estimation

2.4.1 MLE for Random Samples

2.4.2 Linear Regression

Chapter 3 Calculus and Optimization

3.1 Introduction

3.2 Continuity and Differentiation

3.2.1 Limits and Continuity

3.2.2 Derivatives

3.2.3 Taylor’s Theorem

3.3 Unconstrained Optimization

3.3.1 Necessary and Suffcent Conditions of Local Minimizers

3.3.2 Convexity and Global Minimizers

3.3.3 Gradient Descent

3.4 Logistic Regression

3.5 *K*-means

3.6 Support Vector Machine

3.7 Neural Networks

3.7.1 Mathematical Formulation

3.7.2 Activation Functions

3.7.3 Cost Function

3.7.4 Backpropagation

3.7.5 Backpropagation Algorithm

Chapter 4 Network Analysis

4.1 Introduction

4.1.1 Graph Models

4.1.2 Laplacian Matrix

4.2 Spectral Graph Bipartitioning

4.3 Network Embedding

4.4 Network Based Influenza Prediction

4.4.1 Introduction

4.4.2 Data Analysis with Spatial Networks

4.4.3 ANN Method for Prediction

Chapter 5 Ordinary Differential Equations

5.1 Introduction

5.1.1 Logistic Differential Equations

5.2 Epidemical Model

5.3 Prediction of Daily PM2*.*5 Concentration

5.3.1 Introduction

5.3.2 Genetic Programming for ODE

5.3.3 Experimental Results and Prediction Analysis

5.4 Analysis of COVID-19

5.4.1 Introduction

5.4.2 Modeling and Parameter Estimation

5.4.3 Model Simulations

5.4.4 Conclusion and Perspective

5.5 Analysis of COVID-19 in Arizona

5.5.1 Introduction

5.5.2 Data Sources and Collection

5.5.3 Model Simulations

5.5.4 Remarks

Chapter 6 Partial Differential Equations

6.1 Introduction

6.1.1 Formulation of Partial Differential Equation Models

6.2 Bitcoin Price Prediction

6.2.1 Network Analysis for Bitcoin

6.2.2 PDE Modeling

6.2.3 Bitcoin Price Prediction

6.2.4 Remarks

6.3 Prediction of *PM*2*.*5 in China

6.3.1 Introduction

6.3.2 PDE model for *PM*2*.*5

6.3.3 Data Collection and Clustering

6.3.4 *PM*2*.*5 Prediction

6.3.5 Remarks

6.4 Prediction of COVID-19 in Arizona

6.4.1 Introduction

6.4.2 Arizona COVID Data

6.4.3 PDE Modeling of Arizona COVID-19

6.4.4 Model Prediction

6.4.5 Remarks

6.5 Compliance with COVID-19 Mitigation Policies in the US

6.5.1 Introduction

6.5.2 Dataset Sources and Collection

6.5.3 PDE Model for Quantifying Compliance with COVID-19 Policies

6.5.4 Model Prediction

6.5.5 Analysis of Compliance with the US COVID-19 Mitigation Policy

6.5.6 Remarks

- No. of pages: 258
- Language: English
- Edition: 1
- Published: January 6, 2023
- Imprint: Elsevier
- Paperback ISBN: 9780443186790
- eBook ISBN: 9780443186806

JR

She received the Ph.D. degree in applied mathematics from Beijing Institute of Technology, Beijing, China, in 2004. Her research interests include data science, applied mathematics, and applied statistics. She conducted five Projects of National Nature Science Foundation of China, one Alexander von Humboldt Fellowship for Experienced Researcher, and five Provincial Projects. She has published numerous articles in scholarly journals, such as Acta Mater.、Appl. Phys. Lett.、IEEE Trans. SMC、Infor. Sci.、J. Stat. Phys.、J. Nonlinear Sci.、 Phys. Rev. B、Phys. Rev. E、Sci. China Math.、Sci. China Phys. and Sci. China Mater., etc.

Affiliations and expertise

Professor, Zhengzhou University, ChinaHW

He completed his doctorate in mathematics, while also earning a master's degree in computer science at Michigan State University in 1997. He worked as a full-time software engineer in industry for almost ten years before joining Arizona State University. Dr. Wang’s research interests include applied mathematics, data science, differential equations, online social networks. He has published numerous articles in scholarly journals and a book entitled, “Modeling Information Diffusion in Online Social Networks with Partial Differential Equations”, Springer, 2020. Recently he developed and taught a course, Mathematical Methods in Data Science, at Arizona State University.

Affiliations and expertise

Arizona State University, USARead *Mathematical Methods in Data Science* on ScienceDirect