Applied data analytics : principles and applications / Johnson I. Agbinya.

Format:

Book

Author/Creator:

Agbinya, Johnson I., author.

Series:

River Publishers series in signal, image and speech processing.

River Publishers Series in Signal, Image and Speech Processing

Language:

English

Subjects (All):

Big data.

Data mining.

Quantitative research.

Physical Description:

1 online resource (370 pages)

Edition:

1st ed.

Place of Publication:

Gistrup, Denmark : River Publishers, [2020]

Summary:

This text provides some of the most sought after techniques in big data analytics. Establishing strong foundations in these topics provides practical ease when big data analyses are undertaken using the widely available open source and commercially orientated computation platforms, languages and visualization systems. The book, when combined with such platforms, provides a complete set of tools required to handle big data and can lead to fast implementations and applications. The book contains a mixture of machine learning foundations, deep learning, artificial intelligence, statistics and evo.

Contents:

Cover

Half Title

Sereis Page

Title Page

Copyright Page

Dedication

Table of Contents

Preface

Acknowledgement

List of Contributors

List of Figures

List of Tables

List of Abbreviations

1: Markov Chain and Its Applications

1.1 Introduction

1.2 Definitions

1.2.1 State Space

1.2.2 Trajectory

1.2.2.1 Transition Probability

1.2.2.2 State Transition Matrix

1.3 Prediction Using Markov Chain

1.3.1 Initial State

1.3.2 Long-Run Probability

1.3.2.1 Algebraic Solution

1.3.2.2 Matrix Method

1.4 Applications of Markov Chains

1.4.1 Absorbing Nodes in a Markov Chain

2: Hidden Markov Modelling (HMM)

2.1 HMM Notation

2.2 Emission Probabilities

2.3 A Hidden Markov Model

2.3.1 Setting up HMM Model

2.3.2 HMM in Pictorial Form

2.4 The Three Great Problems in HMM

2.4.1 Notation

2.4.1.1 Problem 1: Classification or the Likelihood Problem (Find p(Oj . .))

2.4.1.2 Problems 2: Trajectory Estimation Problem

2.4.1.3 Problem 3: System Identification Problem

2.4.2 Solution to Problem 1: Estimation of Likelihood

2.4.2.1 Naïve Solution

2.4.2.2 Forward Recursion

2.4.2.3 Backward Recursion

2.4.2.4 Solution to Problem 2: Trajectory Estimation Problem

2.5 State Transition Table

2.5.1 Input Symbol Table

2.5.2 Output Symbol Table

2.6 Solution to Problem 3: Find the Optimal HMM

2.6.1 The Algorithm

2.7 Exercises

3: Introduction to Kalman Filters

3.1 Introduction

3.2 Scalar Form

3.2.1 Step (1): Calculate Kalman Gain

3.3 Matrix Form

3.3.1 Models of the State Variables

3.3.1.1 Using Prediction and Measurements in Kalman Filters

3.3.2 Gaussian Representation of State

3.4 The State Matrix

3.4.1 State Matrix for Object Moving in a Single Direction

3.4.1.1 Tracking Including Measurements.

3.4.2 State Matrix of an Object Moving in Two Dimensions

3.4.3 Objects Moving in Three-Dimensional Space

3.5 Kalman Filter Models with Noise

References

4: Kalman Filter II

4.1 Introduction

4.2 Processing Steps in Kalman Filter

4.2.1 Covariance Matrices

4.2.2 Computation Methods for Covariance Matrix

4.2.2.1 Manual method

4.2.2.2 Deviation Matrix Computation Method

4.2.3. Iterations in Kalman Filter

5: Genetic Algorithm

5.1 Introduction

5.2 Steps in Genetic Algorithm

5.3 Terminology of Genetic Algorithms (GAs)

5.4 Fitness Function

5.4.1 Generic Requirements of a Fitness Function

5.5 Selection

5.5.1 The Roulette Wheel

5.5.2 Crossover

5.5.2.1 Single-Position Crossover

5.2.2.2 Double Crossover

5.2.2.3 Mutation

5.2.2.4 Inversion

5.6 Maximizing a Function of a Single Variable

5.7 Continuous Genetic Algorithms

5.7.1 Lowest Elevation on Topographical Maps

5.7.2 Application of GA to Temperature Recording with Sensors

6: Calculus on Computational Graphs

6.1 Introduction

6.1.1 Elements of Computational Graphs

6.2 Compound Expressions

6.3 Computing Partial Derivatives

6.3.1 Partial Derivatives: Two Cases of the Chain Rule

6.3.1.1 Linear Chain Rule

6.3.1.2 Loop Chain Rule

6.3.1.3 Multiple Loop Chain Rule

6.4 Computing of Integrals

6.4.1 Trapezoidal Rule

6.4.2 Simpson Rule

6.5 Multipath Compound Derivatives

7: Support Vector Machines

7.1 Introduction

7.2 Essential Mathematics of SVM

7.2.1 Introduction to Hyperplanes

7.2.2 Parallel Hyperplanes

7.2.3 Distance Between Two Parallel Planes

7.3 Support Vector Machines

7.3.1 Problem Definition

7.3.2 Linearly Separable Case

7.4 Location of Optimal Hyperplane (Primal Problem)

7.4.1 Finding the Margin.

7.4.2 Distance of a Point xi from Separating Hyperplane

7.4.2.1 Margin for Support Vector Points

7.4.3 Finding Optimal Hyperplane Problem

7.4.3.1 Hard margin

7.5 The Lagrangian Optimization Function

7.5.1 Optimization Involving Single Constraint

7.5.2 Optimization with Multiple Constraints

7.5.2.1 Single Inequality Constraint

7.5.2.2 Multiple Inequality Constraints

7.5.3 Karush-Kuhn-Tucker Conditions

7.6 SVM Optimization Problems

7.6.1 The Primal SVM Optimization Problem

7.6.2 The Dual Optimization Problem

7.6.2.1 Reformulation of the Dual Algorithm

7.7 Linear SVM (Non-Linearly Separable) Data

7.7.1 Slack Variables

7.7.1.1 Primal Formulation Including Slack Variable

7.7.1.2 Dual Formulation Including Slack Variable

7.7.1.3 Choosing C in Soft Margin Cases

7.7.2 Non-linear Data Classification Using Kernels

7.7.2.1 Polynomial Kernel Function

7.7.2.2 Multi-Layer Perceptron (Sigmoidal) Kernel

7.7.2.3 Gaussian Radial Basis Function

7.2.2.4 Creating New Kernels

8: Artificial Neural Networks

8.1 Introduction

8.2 Neuron

8.2.1 Activation Functions

8.2.1.1 Sigmoid

8.2.1.2 Hyperbolic Tangent

8.2.1.3 Rectified Linear Unit (ReLU)

8.2.1.4 Leaky ReLU

8.2.1.5 Parametric Rectifier

8.2.1.6 Maxout Neuron

8.2.1.7 The Gaussian

8.2.1.8 Error Calculation

8.2.1.9 Output Layer Node

8.2.1.10 Hidden Layer Nodes

8.2.1.11 Summary of Derivations

9: Training of Neural Networks

9.1 Introduction

9.2 Practical Neural Network

9.3 Backpropagation Model

9.3.1 Computational Graph

9.4 Backpropagation Example with Computational Graphs

9.5 Back Propagation

9.6 Practical Training of Neural Networks

9.6.1 Forward Propagation

9.6.2 Backward Propagation

9.6.2.1 Adapting the Weights

9.7 Initialisation of Weights Methods.

9.7.1 Xavier Initialisation

9.7.2 Batch Normalisation

9.8 Conclusion

10: Recurrent Neural Networks

10.1 Introduction

10.2 Introduction to Recurrent Neural Networks

10.3 Recurrent Neural Network

11: Convolutional Neural Networks

11.1 Introduction

11.2 Convolution Matrices

11.2.1 Three-Dimensional Convolution in CNN

11.3 Convolution Kernels

11.3.1 Design of Convolution Kernel

11.3.1.1 Separable Gaussian Kernel

11.3.1.2 Separable Sobel Kernel

11.3.1.3 Computation Advantage

11.4 Convolutional Neural Networks

11.4.1 Concepts and Hyperparameters

11.4.1.1 Depth (D)

11.4.1.2 Zero-Padding (P)

11.4.1.3 Receptive Field (R)

11.4.1.4 Stride (S)

11.4.1.5 Activation Function using Rectified Linear Unit

11.4.2 CNN Processing Stages

11.4.2.1 Convolution Layer

11.4.3 The Pooling Layer

11.4.4 The Fully Connected Layer

11.5 CNN Design Principles

11.6 Conclusion

Reference

12: Principal Component Analysis

12.1 Introduction

12.2 Definitions

12.2.1 Covariance Matrices

12.3 Computation of Principal Components

12.3.1 PCA Using Vector Projection

12.3.2 PCA Computation Using Covariance Matrices

12.3.3 PCA Using Singular-Value Decomposition

12.3.4 Applications of PCA

12.3.4.1 Face Recognition

13: Moment-Generating Functions

13.1 Moments of Random Variables

13.1.1 Central Moments of Random Variables

13.1.2 Properties of Moments

13.2 Univariate Moment-Generating Functions

13.3 Series Representation of MGF

13.3.1 Properties of Probability Mass Functions

13.3.2 Properties of Probability Distribution Functions f(x)

13.4 Moment-Generating Functions of Discrete Random Variables

13.4.1 Bernoulli Random Variable

13.4.2 Binomial Random Variables

13.4.3 Geometric Random Variables

13.4.4 Poisson Random Variable.

13.5 Moment-Generating Functions of Continuous Random Variables

13.5.1 Exponential Distributions

13.5.2 Normal Distribution

13.5.3 Gamma Distribution

13.6 Properties of Moment-Generating Functions

13.7 Multivariate Moment-Generating Functions

13.7.1 The Law of Large Numbers

13.8 Applications of MGF

14: Characteristic Functions

14.1 Characteristic Functions

14.1.1 Properties of Characteristic Functions

14.2 Characteristic Functions of Discrete Single Random Variables

14.2.1 Characteristic Function of a Poisson Random Variable

14.2.2 Characteristic Function of Binomial Random Variable

14.2.3 Characteristic Functions of Continuous Random Variables

15: Probability-Generating Functions

15.1 Probability-Generating Functions

15.2 Discrete Probability-Generating Functions

15.2.1 Properties of PGF

15.2.2 Probability-Generating Function of Bernoulli Random Variable

15.2.3 Probability-Generating Function for Binomial Random Variables

15.2.4 Probability-Generating Function for Poisson Random Variable

15.2.5 Probability-Generating Functions of Geometric Random Variables

15.2.6 Probability-Generating Function of Negative Binomial Random Variable

15.2.6.1 Negative binomial probability law

15.3 Applications of Probability-Generating Functions in Data Analytics

15.3.1 Discrete Event Applications

15.3.1.1 Coin tossing

15.3.1.2 Rolling a Die

15.3.2 Modelling of Infectious Diseases

15.3.2.1 Early Extinction Probability

15.3.2.1.1 Models of Extinction Probability

16: Digital Identity Management System Using Artificial Neural Networks

16.1 Introduction

16.2 Digital Identity Metrics

16.3 Identity Resolution

16.3.1 Fingerprint and Face Verification Challenges

16.3.1.1 Fingerprint

16.3.1.2 Face

16.4 Biometrics System Architecture.

16.4.1 Fingerprint Recognition.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version:

ISBN:

1-000-79221-8

1-00-333722-8

1-003-33722-8

1-000-79553-5

1-5231-3892-0

87-7022-095-6

OCLC:

1163958139