Data Science in Theory and Practice: Techniques for Big Data Analytics and Complex Data Sets

Cover
Title Page
Copyright
Contents
List of Figures
List of Tables
Preface
Chapter 1 Background of Data Science
	1.1 Introduction
	1.2 Origin of Data Science
	1.3 Who is a Data Scientist?
	1.4 Big Data
		1.4.1 Characteristics of Big Data
		1.4.2 Big Data Architectures
Chapter 2 Matrix Algebra and Random Vectors
	2.1 Introduction
	2.2 Some Basics of Matrix Algebra
		2.2.1 Vectors
		2.2.2 Matrices
	2.3 Random Variables and Distribution Functions
		2.3.1 The Dirichlet Distribution
		2.3.2 Multinomial Distribution
		2.3.3 Multivariate Normal Distribution
	2.4 Problems
Chapter 3 Multivariate Analysis
	3.1 Introduction
	3.2 Multivariate Analysis: Overview
	3.3 Mean Vectors
	3.4 Variance–Covariance Matrices
	3.5 Correlation Matrices
	3.6 Linear Combinations of Variables
		3.6.1 Linear Combinations of Sample Means
		3.6.2 Linear Combinations of Sample Variance and Covariance
		3.6.3 Linear Combinations of Sample Correlation
	3.7 Problems
Chapter 4 Time Series Forecasting
	4.1 Introduction
	4.2 Terminologies
	4.3 Components of Time Series
		4.3.1 Seasonal
		4.3.2 Trend
		4.3.3 Cyclical
		4.3.4 Random
	4.4 Transformations to Achieve Stationarity
	4.5 Elimination of Seasonality via Differencing
	4.6 Additive and Multiplicative Models
	4.7 Measuring Accuracy of Different Time Series Techniques
		4.7.1 Mean Absolute Deviation
		4.7.2 Mean Absolute Percent Error
		4.7.3 Mean Square Error
		4.7.4 Root Mean Square Error
	4.8 Averaging and Exponential Smoothing Forecasting Methods
		4.8.1 Averaging Methods
			4.8.1.1 Simple Moving Averages
			4.8.1.2 Weighted Moving Averages
		4.8.2 Exponential Smoothing Methods
			4.8.2.1 Simple Exponential Smoothing
			4.8.2.2 Adjusted Exponential Smoothing
	4.9 Problems
Chapter 5 Introduction to R
	5.1 Introduction
	5.2 Basic Data Types
		5.2.1 Numeric Data Type
		5.2.2 Integer Data Type
		5.2.3 Character
		5.2.4 Complex Data Types
		5.2.5 Logical Data Types
	5.3 Simple Manipulations – Numbers and Vectors
		5.3.1 Vectors and Assignment
		5.3.2 Vector Arithmetic
		5.3.3 Vector Index
		5.3.4 Logical Vectors
		5.3.5 Missing Values
		5.3.6 Index Vectors
			5.3.6.1 Indexing with Logicals
			5.3.6.2 A Vector of Positive Integral Quantities
			5.3.6.3 A Vector of Negative Integral Quantities
			5.3.6.4 Named Indexing
		5.3.7 Other Types of Objects
			5.3.7.1 Matrices
			5.3.7.2 List
			5.3.7.3 Factor
			5.3.7.4 Data Frames
		5.3.8 Data Import
			5.3.8.1 Excel File
			5.3.8.2 CSV File
			5.3.8.3 Table File
			5.3.8.4 Minitab File
			5.3.8.5 SPSS File
	5.4 Problems
Chapter 6 Introduction to Python
	6.1 Introduction
	6.2 Basic Data Types
		6.2.1 Number Data Type
			6.2.1.1 Integer
			6.2.1.2 Floating‐Point Numbers
			6.2.1.3 Complex Numbers
		6.2.2 Strings
		6.2.3 Lists
		6.2.4 Tuples
		6.2.5 Dictionaries
	6.3 Number Type Conversion
	6.4 Python Conditions
		6.4.1 If Statements
		6.4.2 The Else and Elif Clauses
		6.4.3 The While Loop
			6.4.3.1 The Break Statement
			6.4.3.2 The Continue Statement
		6.4.4 For Loops
			6.4.4.1 Nested Loops
	6.5 Python File Handling: Open, Read, and Close
	6.6 Python Functions
		6.6.1 Calling a Function in Python
		6.6.2 Scope and Lifetime of Variables
	6.7 Problems
Chapter 7 Algorithms
	7.1 Introduction
	7.2 Algorithm – Definition
	7.3 How to Write an Algorithm
		7.3.1 Algorithm Analysis
		7.3.2 Algorithm Complexity
		7.3.3 Space Complexity
		7.3.4 Time Complexity
	7.4 Asymptotic Analysis of an Algorithm
		7.4.1 Asymptotic Notations
			7.4.1.1 Big O Notation
			7.4.1.2 The Omega Notation, Ω
			7.4.1.3 The Θ Notation
	7.5 Examples of Algorithms
	7.6 Flowchart
	7.7 Problems
Chapter 8 Data Preprocessing and Data Validations
	8.1 Introduction
	8.2 Definition – Data Preprocessing
	8.3 Data Cleaning
		8.3.1 Handling Missing Data
		8.3.2 Types of Missing Data
			8.3.2.1 Missing Completely at Random
			8.3.2.2 Missing at Random
			8.3.2.3 Missing Not at Random
		8.3.3 Techniques for Handling the Missing Data
			8.3.3.1 Listwise Deletion
			8.3.3.2 Pairwise Deletion
			8.3.3.3 Mean Substitution
			8.3.3.4 Regression Imputation
			8.3.3.5 Multiple Imputation
		8.3.4 Identifying Outliers and Noisy Data
			8.3.4.1 Binning
			8.3.4.2 Box and Whisker plot
	8.4 Data Transformations
		8.4.1 Min–Max Normalization
		8.4.2 Z‐score Normalization
	8.5 Data Reduction
	8.6 Data Validations
		8.6.1 Methods for Data Validation
			8.6.1.1 Simple Statistical Criterion
			8.6.1.2 Fourier Series Modeling and SSC
			8.6.1.3 Principal Component Analysis and SSC
	8.7 Problems
Chapter 9 Data Visualizations
	9.1 Introduction
	9.2 Definition – Data Visualization
		9.2.1 Scientific Visualization
		9.2.2 Information Visualization
		9.2.3 Visual Analytics
	9.3 Data Visualization Techniques
		9.3.1 Time Series Data
		9.3.2 Statistical Distributions
			9.3.2.1 Stem‐and‐Leaf Plots
			9.3.2.2 Q–Q Plots
	9.4 Data Visualization Tools
		9.4.1 Tableau
		9.4.2 Infogram
		9.4.3 Google Charts
	9.5 Problems
Chapter 10 Binomial and Trinomial Trees
	10.1 Introduction
	10.2 The Binomial Tree Method
		10.2.1 One Step Binomial Tree
		10.2.2 Using the Tree to Price a European Option
		10.2.3 Using the Tree to Price an American Option
		10.2.4 Using the Tree to Price Any Path Dependent Option
	10.3 Binomial Discrete Model
		10.3.1 One‐Step Method
		10.3.2 Multi‐step Method
			10.3.2.1 Example: European Call Option
	10.4 Trinomial Tree Method
		10.4.1 What is the Meaning of Little o and Big O?
	10.5 Problems
Chapter 11 Principal Component Analysis
	11.1 Introduction
	11.2 Background of Principal Component Analysis
	11.3 Motivation
		11.3.1 Correlation and Redundancy
		11.3.2 Visualization
	11.4 The Mathematics of PCA
		11.4.1 The Eigenvalues and Eigenvectors
	11.5 How PCA Works
		11.5.1 Algorithm
	11.6 Application
	11.7 Problems
Chapter 12 Discriminant and Cluster Analysis
	12.1 Introduction
	12.2 Distance
	12.3 Discriminant Analysis
		12.3.1 Kullback–Leibler Divergence
		12.3.2 Chernoff Distance
		12.3.3 Application – Seismic Time Series
		12.3.4 Application – Financial Time Series
	12.4 Cluster Analysis
		12.4.1 Partitioning Algorithms
		12.4.2 k‐Means Algorithm
		12.4.3 k‐Medoids Algorithm
		12.4.4 Application – Seismic Time Series
		12.4.5 Application – Financial Time Series
	12.5 Problems
Chapter 13 Multidimensional Scaling
	13.1 Introduction
	13.2 Motivation
	13.3 Number of Dimensions and Goodness of Fit
	13.4 Proximity Measures
	13.5 Metric Multidimensional Scaling
		13.5.1 The Classical Solution
	13.6 Nonmetric Multidimensional Scaling
		13.6.1 Shepard–Kruskal Algorithm
	13.7 Problems
Chapter 14 Classification and Tree‐Based Methods
	14.1 Introduction
	14.2 An Overview of Classification
		14.2.1 The Classification Problem
		14.2.2 Logistic Regression Model
			14.2.2.1 l1 Regularization
			14.2.2.2 l2 Regularization
	14.3 Linear Discriminant Analysis
		14.3.1 Optimal Classification and Estimation of Gaussian Distribution
	14.4 Tree‐Based Methods
		14.4.1 One Single Decision Tree
		14.4.2 Random Forest
	14.5 Applications
	14.6 Problems
Chapter 15 Association Rules
	15.1 Introduction
	15.2 Market Basket Analysis
	15.3 Terminologies
		15.3.1 Itemset and Support Count
		15.3.2 Frequent Itemset
		15.3.3 Closed Frequent Itemset
		15.3.4 Maximal Frequent Itemset
		15.3.5 Association Rule
		15.3.6 Rule Evaluation Metrics
	15.4 The Apriori Algorithm
		15.4.1 An example of the Apriori Algorithm
	15.5 Applications
		15.5.1 Confidence
		15.5.2 Lift
		15.5.3 Conviction
	15.6 Problems
Chapter 16 Support Vector Machines
	16.1 Introduction
	16.2 The Maximal Margin Classifier
	16.3 Classification Using a Separating Hyperplane
	16.4 Kernel Functions
	16.5 Applications
	16.6 Problems
Chapter 17 Neural Networks
	17.1 Introduction
	17.2 Perceptrons
	17.3 Feed Forward Neural Network
	17.4 Recurrent Neural Networks
	17.5 Long Short‐Term Memory
		17.5.1 Residual Connections
		17.5.2 Loss Functions
		17.5.3 Stochastic Gradient Descent
		17.5.4 Regularization – Ensemble Learning
	17.6 Application
		17.6.1 Emergent and Developed Market
		17.6.2 The Lehman Brothers Collapse
		17.6.3 Methodology
		17.6.4 Analyses of Data
			17.6.4.1 Results of the Emergent Market Index
			17.6.4.2 Results of the Developed Market Index
	17.7 Significance of Study
	17.8 Problems
Chapter 18 Fourier Analysis
	18.1 Introduction
	18.2 Definition
	18.3 Discrete Fourier Transform
	18.4 The Fast Fourier Transform (FFT) Method
	18.5 Dynamic Fourier Analysis
		18.5.1 Tapering
		18.5.2 Daniell Kernel Estimation
	18.6 Applications of the Fourier Transform
		18.6.1 Modeling Power Spectrum of Financial Returns Using Fourier Transforms
		18.6.2 Image Compression
	18.7 Problems
Chapter 19 Wavelets Analysis
	19.1 Introduction
		19.1.1 Wavelets Transform
	19.2 Discrete Wavelets Transforms
		19.2.1 Haar Wavelets
			19.2.1.1 Haar Functions
			19.2.1.2 Haar Transform Matrix
		19.2.2 Daubechies Wavelets
	19.3 Applications of the Wavelets Transform
		19.3.1 Discriminating Between Mining Explosions and Cluster of Earthquakes
			19.3.1.1 Background of Data
			19.3.1.2 Results
		19.3.2 Finance
		19.3.3 Damage Detection in Frame Structures
		19.3.4 Image Compression
		19.3.5 Seismic Signals
	19.4 Problems
Chapter 20 Stochastic Analysis
	20.1 Introduction
	20.2 Necessary Definitions from Probability Theory
	20.3 Stochastic Processes
		20.3.1 The Index Set I
		20.3.2 The State Space S
		20.3.3 Stationary and Independent Components
		20.3.4 Stationary and Independent Increments
		20.3.5 Filtration and Standard Filtration
	20.4 Examples of Stochastic Processes
		20.4.1 Markov Chains
			20.4.1.1 Examples of Markov Processes
			20.4.1.2 The Chapman–Kolmogorov Equation
			20.4.1.3 Classification of States
			20.4.1.4 Limiting Probabilities
			20.4.1.5 Branching Processes
			20.4.1.6 Time Homogeneous Chains
		20.4.2 Martingales
		20.4.3 Simple Random Walk
		20.4.4 The Brownian Motion (Wiener Process)
	20.5 Measurable Functions and Expectations
		20.5.1 Radon–Nikodym Theorem and Conditional Expectation
	20.6 Problems
Chapter 21 Fractal Analysis – Lévy, Hurst, DFA, DEA
	21.1 Introduction and Definitions
	21.2 Lévy Processes
		21.2.1 Examples of Lévy Processes
			21.2.1.1 The Poisson Process (Jumps)
			21.2.1.2 The Compound Poisson Process
			21.2.1.3 Inverse Gaussian (IG) Process
			21.2.1.4 The Gamma Process
		21.2.2 Exponential Lévy Models
		21.2.3 Subordination of Lévy Processes
		21.2.4 Stable Distributions
	21.3 Lévy Flight Models
	21.4 Rescaled Range Analysis (Hurst Analysis)
	21.5 Detrended Fluctuation Analysis (DFA)
	21.6 Diffusion Entropy Analysis (DEA)
		21.6.1 Estimation Procedure
			21.6.1.1 The Shannon Entropy
		21.6.2 The H–α Relationship for the Truncated Lévy Flight
	21.7 Application – Characterization of Volcanic Time Series
		21.7.1 Background of Volcanic Data
		21.7.2 Results
	21.8 Problems
Chapter 22 Stochastic Differential Equations
	22.1 Introduction
	22.2 Stochastic Differential Equations
		22.2.1 Solution Methods of SDEs
	22.3 Examples
		22.3.1 Modeling Asset Prices
		22.3.2 Modeling Magnitude of Earthquake Series
	22.4 Multidimensional Stochastic Differential Equations
		22.4.1 The multidimensional Ornstein–Uhlenbeck Processes
		22.4.2 Solution of the Ornstein–Uhlenbeck Process
	22.5 Simulation of Stochastic Differential Equations
		22.5.1 Euler–Maruyama Scheme for Approximating Stochastic Differential Equations
		22.5.2 Euler–Milstein Scheme for Approximating Stochastic Differential Equations
	22.6 Problems
Chapter 23 Ethics: With Great Power Comes Great Responsibility
	23.1 Introduction
	23.2 Data Science Ethical Principles
		23.2.1 Enhance Value in Society
		23.2.2 Avoiding Harm
		23.2.3 Professional Competence
		23.2.4 Increasing Trustworthiness
		23.2.5 Maintaining Accountability and Oversight
	23.3 Data Science Code of Professional Conduct
	23.4 Application
		23.4.1 Project Planning
		23.4.2 Data Preprocessing
		23.4.3 Data Management
		23.4.4 Analysis and Development
	23.5 Problems
Bibliography
Index
EULA