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E-raamat: Applied Data Analytics - Principles and Applications

(Melbourne Institute of Technology, Australia)
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The emergence of huge amounts of data which require analysis and in some cases real-time processing has forced exploration into fast algorithms for handling very lage data sizes. Analysis of x-ray images in medical applications, cyber security data, crime data, telecommunications and stock market data, health records and business analytics data are but a few areas of interest. Applications and platforms including R, RapidMiner and Weka provide the basis for analysis, often used by practitioners who pay little to no attention to the underlying mathematics and processes impacting the data. This often leads to an inability to explain results or correct mistakes, or to spot errors.

Applied Data Analytics - Principles and Applications seeks to bridge this missing gap by providing 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 visualisation 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 evolutionary learning mathematics written from the usage point of view with rich explanations on what the concepts mean. The author has thus avoided the complexities often associated with these concepts when found in research papers. The tutorial nature of the book and the applications provided are some of the reasons why the book is suitable for undergraduate, postgraduate and big data analytics enthusiasts.

This text should ease the fear of mathematics often associated with practical data analytics and support rapid applications in artificial intelligence, environmental sensor data modelling and analysis, health informatics, business data analytics, data from Internet of Things and deep learning applications.
Preface xix
Acknowledgement xxi
List of Contributors
xxiii
List of Figures
xxv
List of Tables
xxix
List of Abbreviations
xxxi
1 Markov Chain and its Applications
1(16)
1.1 Introduction
1(1)
1.2 Definitions
2(6)
1.2.1 State Space
2(1)
1.2.2 Trajectory
3(1)
1.2.2.1 Transition probability
3(2)
1.2.2.2 State transition matrix
5(3)
1.3 Prediction Using Markov Chain
8(5)
1.3.1 Initial State
8(3)
1.3.2 Long-run Probability
11(1)
1.3.2.1 Algebraic solution
11(1)
1.3.2.2 Matrix method
12(1)
1.4 Applications of Markov Chains
13(4)
1.4.1 Absorbing Nodes in a Markov Chain
14(3)
2 Hidden Markov Modelling (HMM)
17(18)
2.1 HMM Notation
17(1)
2.2 Emission Probabilities
18(2)
2.3 A Hidden Markov Model
20(6)
2.3.1 Setting up HMM Model
21(1)
2.3.2 HMM in Pictorial Form
22(4)
2.4 The Three Great Problems in HMM
26(5)
2.4.1 Notation
26(1)
2.4.1.1 Problem 1: Classification or the likelihood problem (find p(O|λ))
26(1)
2.4.1.2 Problems 2: Trajectory estimation problem
26(1)
2.4.1.3 Problem 3: System identification problem
26(1)
2.4.2 Solution to Problem 1: Estimation of Likelihood
26(1)
2.4.2.1 Naive solution
27(1)
2.4.2.2 Forward recursion
27(1)
2.4.2.3 Backward recursion
28(2)
2.4.2.4 Solution to Problem 2: Trajectory estimation problem
30(1)
2.5 State Transition Table
31(2)
2.5.1 Input Symbol Table
31(1)
2.5.2 Output Symbol Table
32(1)
2.6 Solution to Problem 3: Find the Optimal HMM
33(1)
2.6.1 The Algorithm
33(1)
2.7 Exercises
34(1)
3 Introduction to Kalman Filters
35(24)
3.1 Introduction
35(1)
3.2 Scalar Form
35(4)
3.2.1 Step (1): Calculate Kalman Gain
37(2)
3.3 Matrix Form
39(9)
3.3.1 Models of the State Variables
42(1)
3.3.1.1 Using prediction and measurements in Kalman filters
42(2)
3.3.2 Gaussian Representation of State
44(4)
3.4 The State Matrix
48(8)
3.4.1 State Matrix for Object Moving in a Single Direction
48(4)
3.4.1.1 Tracking including measurements
52(1)
3.4.2 State Matrix of an Object Moving in Two Dimensions
52(2)
3.4.3 Objects Moving in Three-Dimensional Space
54(2)
3.5 Kalman Filter Models with Noise
56(3)
References
57(2)
4 Kalman Filter II
59(16)
4.1 Introduction
59(1)
4.2 Processing Steps in Kalman Filter
59(16)
4.2.1 Covariance Matrices
59(3)
4.2.2 Computation Methods for Covariance Matrix
62(1)
4.2.2.1 Manual method
62(3)
4.2.2.2 Deviation matrix computation method
65(2)
4.2.3 Iterations in Kalman Filter
67(8)
5 Genetic Algorithm
75(18)
5.1 Introduction
75(1)
5.2 Steps in Genetic Algorithm
75(1)
5.3 Terminology of Genetic Algorithms (GAs)
76(2)
5.4 Fitness Function
78(3)
5.4.1 Generic Requirements of a Fitness Function
78(3)
5.5 Selection
81(3)
5.5.1 The Roulette Wheel
81(1)
5.5.2 Crossover
82(1)
5.5.2.1 Single-position crossover
82(1)
5.5.2.2 Double crossover
83(1)
5.5.2.3 Mutation
83(1)
5.5.2.4 Inversion
84(1)
5.6 Maximizing a Function of a Single Variable
84(3)
5.7 Continuous Genetic Algorithms
87(6)
5.7.1 Lowest Elevation on Topographical Maps
87(3)
5.7.2 Application of GA to Temperature Recording with Sensors
90(1)
References
91(2)
6 Calculus on Computational Graphs
93(12)
6.1 Introduction
93(2)
6.1.1 Elements of Computational Graphs
94(1)
6.2 Compound Expressions
95(1)
6.3 Computing Partial Derivatives
96(3)
6.3.1 Partial Derivatives: Two Cases of the Chain Rule
97(1)
6.3.1.1 Linear chain rule
98(1)
6.3.1.2 Loop chain rule
98(1)
6.3.1.3 Multiple loop chain rule
99(1)
6.4 Computing of Integrals
99(3)
6.4.1 Trapezoidal Rule
100(1)
6.4.2 Simpson Rule
100(2)
6.5 Multipath Compound Derivatives
102(3)
7 Support Vector Machines
105(34)
7.1 Introduction
105(1)
7.2 Essential Mathematics of SVM
106(5)
7.2.1 Introduction to Hyperplanes
107(3)
7.2.2 Parallel Hyperplanes
110(1)
7.2.3 Distance between Two Parallel Planes
110(1)
7.3 Support Vector Machines
111(3)
7.3.1 Problem Definition
111(1)
7.3.2 Linearly Separable Case
112(2)
7.4 Location of Optimal Hyperplane (Primal Problem)
114(4)
7.4.1 Finding the Margin
114(2)
7.4.2 Distance of a Point xi from Separating Hyperplane
116(1)
7.4.2.1 Margin for support vector points
117(1)
7.4.3 Finding Optimal Hyperplane Problem
117(1)
7.4.3.1 Hard margin
117(1)
7.5 The Lagrangian Optimization Function
118(6)
7.5.1 Optimization Involving Single Constraint
119(1)
7.5.2 Optimization with Multiple Constraints
120(1)
7.5.2.1 Single inequality constraint
121(1)
7.5.2.2 Multiple inequality constraints
122(1)
7.5.3 Karush--Kuhn--Tucker Conditions
123(1)
7.6 SVM Optimization Problems
124(5)
7.6.1 The Primal SVM Optimization Problem
124(1)
7.6.2 The Dual Optimization Problem
125(1)
7.6.2.1 Reformulation of the dual algorithm
126(3)
7.7 Linear SVM (Non-linearly Separable) Data
129(10)
7.7.1 Slack Variables
129(1)
7.7.1.1 Primal formulation including slack variable
130(1)
7.7.1.2 Dual formulation including slack variable
130(1)
7.7.1.3 Choosing C in soft margin cases
131(1)
7.7.2 Non-linear Data Classification Using Kernels
132(3)
7.7.2.1 Polynomial kernel function
135(1)
7.7.2.2 Multi-layer perceptron (Sigmoidal) kernel
136(1)
7.7.2.3 Gaussian radial basis function
136(1)
7.7.2.4 Creating new kernels
137(1)
References
137(2)
8 Artificial Neural Networks
139(14)
8.1 Introduction
139(1)
8.2 Neuron
139(14)
8.2.1 Activation Functions
143(1)
8.2.1.1 Sigmoid
143(1)
8.2.1.2 Hyperbolic tangent
144(1)
8.2.1.3 Rectified Linear Unit (ReLU)
144(1)
8.2.1.4 Leaky ReLU
145(1)
8.2.1.5 Parametric rectifier
145(1)
8.2.1.6 Maxout neuron
146(1)
8.2.1.7 The Gaussian
146(1)
8.2.1.8 Error calculation
146(3)
8.2.1.9 Output layer node
149(1)
8.2.1.10 Hidden layer nodes
150(1)
8.2.1.11 Summary of derivations
151(2)
9 Training of Neural Networks
153(18)
9.1 Introduction
153(1)
9.2 Practical Neural Network
153(1)
9.3 Backpropagation Model
154(3)
9.3.1 Computational Graph
154(3)
9.4 Backpropagation Example with Computational Graphs
157(1)
9.5 Back Propagation
158(2)
9.6 Practical Training of Neural Networks
160(6)
9.6.1 Forward Propagation
161(2)
9.6.2 Backward Propagation
163(1)
9.6.2.1 Adapting the weights
164(2)
9.7 Initialisation of Weights Methods
166(3)
9.7.1 Xavier Initialisation
167(2)
9.7.2 Batch Normalisation
169(1)
9.8 Conclusion
169(2)
References
170(1)
10 Recurrent Neural Networks
171(14)
10.1 Introduction
171(1)
10.2 Introduction to Recurrent Neural Networks
171(3)
10.3 Recurrent Neural Network
174(11)
11 Convolutional Neural Networks
185(20)
11.1 Introduction
185(1)
11.2 Convolution Matrices
185(2)
11.2.1 Three-Dimensional Convolution in CNN
187(1)
11.3 Convolution Kernels
187(6)
11.3.1 Design of Convolution Kernel
190(1)
11.3.1.1 Separable Gaussian kernel
191(1)
11.3.1.2 Separable Sobel kernel
192(1)
11.3.1.3 Computation advantage
192(1)
11.4 Convolutional Neural Networks
193(8)
11.4.1 Concepts and Hyperparameters
193(1)
11.4.1.1 Depth (D)
193(1)
11.4.1.2 Zero-padding (P)
193(2)
11.4.1.3 Receptive field (R)
195(1)
11.4.1.4 Stride (S)
195(1)
11.4.1.5 Activation function using rectified linear unit
195(1)
11.4.2 CNN Processing Stages
196(1)
11.4.2.1 Convolution layer
196(3)
11.4.3 The Pooling Layer
199(2)
11.4.4 The Fully Connected Layer
201(1)
11.5 CNN Design Principles
201(1)
11.6 Conclusion
202(3)
Reference
203(2)
12 Principal Component Analysis
205(16)
12.1 Introduction
205(1)
12.2 Definitions
205(8)
12.2.1 Co variance Matrices
209(4)
12.3 Computation of Principal Components
213(8)
12.3.1 PCA Using Vector Projection
213(1)
12.3.2 PCA Computation Using Covariance Matrices
214(3)
12.3.3 PCA Using Singular-Value Decomposition
217(1)
12.3.4 Applications of PCA
218(1)
12.3.4.1 Face recognition
219(1)
Reference
220(1)
13 Moment-Generating Functions
221(18)
13.1 Moments of Random Variables
221(3)
13.1.1 Central Moments of Random Variables
222(1)
13.1.2 Properties of Moments
222(2)
13.2 Univariate Moment-Generating Functions
224(2)
13.3 Series Representation of MGF
226(2)
13.3.1 Properties of Probability Mass Functions
227(1)
13.3.2 Properties of Probability Distribution Functions fnof;(x)
227(1)
13.4 Moment-Generating Functions of Discrete Random Variables
228(4)
13.4.1 Bernoulli Random Variable
228(1)
13.4.2 Binomial Random Variables
229(2)
13.4.3 Geometric Random Variables
231(1)
13.4.4 Poisson Random Variable
232(1)
13.5 Moment-Generating Functions of Continuous Random Variables
232(4)
13.5.1 Exponential Distributions
232(1)
13.5.2 Normal Distribution
233(2)
13.5.3 Gamma Distribution
235(1)
13.6 Properties of Moment-Generating Functions
236(1)
13.7 Multivariate Moment-Generating Functions
236(2)
13.7.1 The Law of Large Numbers
237(1)
13.8 Applications of MGF
238(1)
14 Characteristic Functions
239(4)
14.1 Characteristic Functions
239(1)
14.1.1 Properties of Characteristic Functions
240(1)
14.2 Characteristic Functions of Discrete Single Random Variables
240(3)
14.2.1 Characteristic Function of a Poisson Random Variable
240(1)
14.2.2 Characteristic Function of Binomial Random Variable
241(1)
14.2.3 Characteristic Functions of Continuous Random Variables
242(1)
15 Probability-Generating Functions
243(16)
15.1 Probability-Generating Functions
243(1)
15.2 Discrete Probability-Generating Functions
243(10)
15.2.1 Properties of PGF
244(2)
15.2.2 Probability-Generating Function of Bernoulli Random Variable
246(1)
15.2.3 Probability-Generating Function for Binomial Random Variable
246(1)
15.2.4 Probability-Generating Function for Poisson Random Variable
247(1)
15.2.5 Probability-Generating Functions of Geometric Random Variables
248(2)
15.2.6 Probability-Generating Function of Negative Binomial Random Variables
250(1)
15.2.6.1 Negative binomial probability law
251(2)
15.3 Applications of Probability-Generating Functions in Data Analytics
253(6)
15.3.1 Discrete Event Applications
253(1)
15.3.1.1 Coin tossing
253(1)
15.3.1.2 Rolling a die
253(1)
15.3.2 Modelling of Infectious Diseases
254(1)
15.3.2.1 Early extinction probability
255(1)
15.3.2.1.1 Models of extinction probability
256(1)
References
257(2)
16 Digital Identity Management System Using Artificial Neural Networks
259(18)
Johnson I. Agbinya
Rumana Islam
16.1 Introduction
259(1)
16.2 Digital Identity Metrics
259(2)
16.3 Identity Resolution
261(2)
16.3.1 Fingerprint and Face Verification Challenges
261(1)
16.3.1.1 Fingerprint
262(1)
16.3.1.2 Face
262(1)
16.4 Biometrics System Architecture
263(3)
16.4.1 Fingerprint Recognition
264(1)
16.4.2 Face Recognition
264(2)
16.5 Information Fusion
266(1)
16.6 Artificial Neural Networks
267(2)
16.6.1 Artificial Neural Networks Implementation
268(1)
16.7 Multimodal Digital Identity Management System Implementation
269(3)
16.7.1 Terminal, Fingerprint Scanner and Camera
269(1)
16.7.2 Fingerprint and Face Recognition SDKs
270(1)
16.7.3 Database
271(1)
16.7.4 Verification: Connect to Host and Select Verification
271(1)
16.7.4.1 Verifying user
271(1)
16.7.4.2 Successful verification
271(1)
16.8 Conclusion
272(5)
References
272(5)
17 Probabilistic Neural Network Classifiers for IoT Data Classification
277(14)
Tony Jan
17.1 Introduction
277(1)
17.2 Probabilistic Neural Network (PNN)
278(2)
17.3 Generalized Regression Neural Network (GRNN)
280(2)
17.4 Vector Quantized GRNN (VQ-GRNN)
282(4)
17.5 Experimental Works
286(1)
17.6 Conclusion and Future Works
287(4)
References
288(3)
18 MML Learning and Inference of Hierarchical Probabilistic Finite State Machines
291(36)
Vidya Saikrishna
D. L. Dowe
Sid Ray
18.1 Introduction
291(1)
18.2 Finite State Machines (FSMs) and PFSMs
292(4)
18.2.1 Mathematical Definition of a Finite State Machine
293(1)
18.2.2 Representation of an FSM in a State Diagram
293(3)
18.3 MML Encoding and Inference of PFSMs
296(11)
18.3.1 Modelling a PFSM
297(1)
18.3.1.1 Assertion code for hypothesis H
297(3)
18.3.1.2 Assertion code for data D generated by hypothesis H
300(1)
18.3.2 Inference of PFSM Using MML
301(1)
18.3.2.1 Inference of PFSM by ordered merging (OM)
302(1)
18.3.2.1.1 First stage merge
302(1)
18.3.2.1.2 Second stage merge
303(1)
18.3.2.1.3 Third stage merge
303(1)
18.3.2.1.4 Ordered merging (OM) algorithm
304(1)
18.3.2.2 Inference of PFSM using simulated annealing (SA)
305(1)
18.3.2.2.1 Simulated annealing (SA)
306(1)
18.3.2.2.2 Simulated annealing (SA) algorithm
307(1)
18.4 Hierarchical Probabilistic Finite State Machine (HPFSM)
307(7)
18.4.1 Defining an HPFSM
309(1)
18.4.2 MML Assertion Code for the Hypothesis H of HPFSM
310(3)
18.4.3 Encoding the transitions of HPFSM
313(1)
18.5 Experiments
314(9)
18.5.1 Experiments on Artificial datasets
314(1)
18.5.1.1 Example-1
314(3)
18.5.1.2 Example-2
317(2)
18.5.2 Experiments on ADL Datasets
319(4)
18.6 Summary
323(4)
References
324(3)
Solution to Exercises 327(2)
Index 329(6)
About the Author 335
Melbourne Institute of Technology, Australia
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