Mathematics is the foundation of machine learning algorithms. To understand the shortcomings of existing algorithms and develop more effective methods, it is essential to understand the mathematical concepts underlying these algorithms and their operational principles. This book serves as an introductory resource, outlining the preliminary concepts and offering insights into the mathematical foundations and operational mechanisms of machine learning algorithms. It describes the basic equations and interrelates the questions arising during practical applications of machine learning with the basic mathematical picture of the algorithms used.
Features
Introduces machine learning, highlights the central role of algorithms in machine learning, and explains the core mathematical prerequisites to understanding machine learning algorithms
Systematically examines the sequential steps of classical machine learning algorithms used for classification of data sets into distinct groups; regression, clustering analysis,
Provides an overview of value, policy, and model-based reinforcement learning algorithms.
This book is for academicians, scholars, students, and professionals engaged in the study of machine learning and artificial intelligence.
1. Algorithms in Everyday Life and Computer Science. 1.1 Introduction. 1.2 Human Algorithmic Activities. 1.3 Importance of Algorithms in Our Everyday Activities. 1.4 Algorithms as the Foundation of Computer Science. 1.5 Desirable Features and Properties of an Algorithm. 1.6 Critical Steps in Algorithm Formulation. 1.7 Algorithm and Programming Language. 1.8 Discussion and Conclusions. References and Further Reading. 2. Algorithmic Foundations of Machine and Deep Learning. 2.1 Introduction. 2.2 Artificial Intelligence. 2.3 Machine Learning. 2.4 Machine Learning Algorithms. 2.5 Deep Learning Algorithms. 2.6 Differentiation Between Traditional Computer Algorithms and Machine/Deep Learning Algorithms. 2.7 Types of Machine Learning and Deep Learning Algorithms. 2.8 Modus Operandi of a Typical Machine Learning Algorithm. 2.9 Examples of Machine Learning and Deep Learning Algorithms. 2.10 Types of Artificial Neural Networks. 2.11 Why Are Machine Learning Algorithms Considered as Problem-Solving Strategies and Mathematical Engines of Artificial Intelligence? 2.12 Role of Ethics in AI and ML Development. 2.13 Organizational Plan of the Book. 2.14 Discussion and Conclusions. References and Further Reading. 3. Classification Algorithms: Logistic Regression. 3.1 Introduction. 3.2 Primary Function of a Classification Algorithm. 3.3 Binary, Multi-Class, and Multi-Label Classifiers. 3.4 Performance Evaluation Metrics of Classification Algorithms. 3.5 Logistic Regression Classifier. 3.6 Discussion and Conclusions. References and Further Reading. 4. Decision Trees and Random Forest Classifiers. 4.1 Introduction. 4.2 Decision Tree. 4.3 Random Forest Classification Algorithm. 4.4 Comparison Between Decision Tree and Random Forest Classifiers. 4.5 Discussion and Conclusions. References and Further Reading. 5. Support Vector Machines, K-Nearest Neighbors, and Naïve Bayes' Classifier Algorithms. 5.1 Introduction. 5.2 Support Vector Machine. 5.3 SVM Terminology. 5.4 Main Steps of an SVM Classifier. 5.5 K-Nearest Neighbors Algorithm. 5.6 Naïve Bayes Classifier. 5.7 Comparison between Support Vector Machines, K-Nearest Neighbors, and Naïve Bayes' Classifier Algorithms. 5.8 Discussion and Conclusions. References and Further Reading. 6. Regression Analysis: Linear, Multiple Linear, and Nonlinear Regression. 6.1 Introduction. 6.2 The Regression Algorithm. 6.3 Regression Compared with Classification. 6.4 Linear Regression Algorithms. 6.5 Non-Linear Regression Algorithms. 6.6 Regression Lines and Related Terms. 6.7 Evaluation Metrics of Linear Regression. 6.8 Assumptions of Linear Regression. 6.9 Least Squares Regression. 6.10 Finding the Best Fit Line in Linear Regression by Gradient Descent. 6.11 Comparison between Simple Linear, Multiple Linear, and Polynomial Regression. 6.12 Discussion and Conclusions. References and Further Reading. 7. Lasso, Ridge, and Support Vector Regression. 7.1 Introduction. 7.2 Lasso Regression Algorithm (L1 Regularization). 7.3 Ridge Regression Algorithm (L2 Regularization). 7.4 Elastic Net Regression Algorithm. 7.5 Support Vector Regression (SVR) Algorithm. 7.6 Comparison Between Lasso, Ridge, and Support Vector Regression. 7.7 Discussion and Conclusions. References and Further Reading. 8. Miscellaneous Regression Algorithms: Decision Tree, Random Forest, KNN Regression, and Others. 8.1 Introduction. 8.2 Decision Tree Regression Algorithm. 8.3 Random Forest Regression Algorithm. 8.4 K-Nearest Neighbors (KNN) Regression Algorithm. 8.5 Gradient Boosting Regression Algorithm. 8.6 Gaussian Process Regression (GPR) Algorithm. 8.7 Comparison Between Decision Tree, Random Forest, KNN Regression, Gradient Boosting, and Gaussian Process Regression Algorithms. 8.8 Discussion and Conclusions. References and Further Reading. 9. Clustering Algorithms: Centroid-Based, Density-Based, Distribution-Based, and Hierarchical. 9.1 Introduction. 9. 2 Clustering Analysis. 9.3 Clustering in Comparison to Regression. 9.4 Types of Clustering. 9.5 Centroid-Based Clustering or Partitioning. 9.6 Density-Based Clustering. 9.7 Distribution-Based Clustering. 9.8 Hierarchical or Connectivity-Based Clustering. 9.8 Comparison Between Centroid-Based, Density-Based, Distribution-Based, and Hierarchical Clustering Algorithms. 9.9 Discussion and Conclusions. References and Further Reading. 10. Affinity Propagation, Fuzzy Clustering, and OPTICS. 10.1 Introduction. 10.2 Affinity Propagation. 10.3 Fuzzy Clustering. 10.4 OPTICS. 10.5 Comparison Between Affinity Propagation, Fuzzy Clustering, and OPTICS. 10.6 Discussion and Conclusions. References and Further Reading. 11. Feature Selection Algorithms: Filter, Wrapper, and Embedded Methods. 11.1 Introduction. 11.2 Definitions. 11.3 Feature Selection Compared to Clustering. 11.4 Feature Selection Contrasted with Dimensionality Reduction. 11.5 Feature Selection Methods. 11.6 Feature Selection with Filter Methods. 11.7 A Wrapper-Style Algorithm: Recursive Feature Elimination (RFE). 11.8 Feature Selection with Embedded Methods. 11.9 Lasso and Ridge Regression. 11.10 Comparison Between Filter, Wrapper, and Embedded Methods for Feature Selection. 11.11 Discussion and Conclusions. References and Further Reading. 12. Feature Extraction Algorithms: Principal Component Analysis and Linear Discriminant Analysis. 12.1 Introduction. 12.2 Definitions. 12.3 Feature Extraction as Opposed to Feature Selection. 12.4 Feature Extraction in Opposition to Dimensionality Reduction. 12.5 Principal Component Analysis. 12.6 Linear Discriminant Analysis. 12.7 Comparison Between Principal Component Analysis and Linear Discriminant Analysis. 12.8 Discussion and Conclusions. References and Further Reading. 13. Feed Forward Neural Networks and Self-Organizing Maps. 13.1 Introduction. 13.2 Feed Forward Neural Network. 13.3 Self-Organizing Map. 13.4 Comparison Between Feed-Forward Neural Networks and Self-Organizing Maps. 13.5 Discussion and Conclusions. References and Further Reading. 14. Perceptron, Multilayer Perceptron, and Radial Basis Function Networks. 14.1 Introduction. 14.2 Single-Layer Perceptron. 14.3 Multilayer Perceptron. 14.4 Radial Basis Function Network. 14.5 Comparison Between Perceptron, Multilayer Perceptron, and Radial Basis Function Network. 14.6 Discussion and Conclusions. References and Further Reading. 15. Convolution Neural Networks. 15.1 Introduction. 15.2 Salient Characteristics of Convolutional Neural Network. 15.3 Architecture of a CNN and Functions of Different Layers. 15.4 Training a CNN Algorithm. 15.5 Using a Trained CNN Algorithm. 15.6 Applications of CNN. 15.7 Advantages of CNN. 15.8 Disadvantages of CNN. 15.9 Discussion and Conclusions. References and Further Reading. 16. Recurrent, Long Short-Term Memory and Transformer Networks. 16.1 Introduction. 16.2 Recurrent Neural Network. 16.3 Long Short-Term Memory Network. 16.4 Transformer Neural Network. 16.5 Comparison Between Recurrent, Long Short-Term Memory, and Transformer Networks. 16.6 Discussion and Conclusions. References and Further Reading. 17. Restricted Boltzmann Machine, and Deep Belief Network. 17.1 Introduction. 17.2 Elementary Ideas About the Restricted Boltzmann Machine. 17.3 Training a Restricted Boltzmann Machine. 17.4 Using a Trained RBM for Inference. 17.5 Applications of RBM. 17.6 Advantages of RBM. 17.7 Disadvantages of RBM. 17.8 Basic Ideas About the Deep Belief Network. 17.9 Applications of DBN. 17.10 Advantages of DBN. 17.11 Disadvantages of DBN. 17.12 Comparison Between Restricted Boltzmann Machine and Deep Belief Network. 17.13 Discussion and Conclusions. References and Further Reading. 18. Generative Adversarial Networks. 18.1 Introduction. 18.2 Architecture of a Generative Adversarial Network. 18.3 MinMax GAN Loss Function Formula. 18.4 Main Steps of GAN. 18.5 Applications of GANs. 18.6 Advantages of GANs. 18.7 Limitations of GANs. 18.8 Discussion and Conclusions. References and Further Reading. 19. Autoencoders. 19.1 Introduction. 19.2 Architecture of the Autoencoder and the Roles Played by the Layers. 19.3 Training Process of Autoencoder Algorithm. 19.4 Using a Trained Autoencoder Algorithm. 19.5 Applications of Autoencoders. 19.6 Advantages of Autoencoders. 19.7 Disadvantages of Autoencoders. 19.8 Discussion and Conclusions. References and Further Reading. 20. Modular Neural Networks. 20.1 Introduction. 20.2 Mathematical Representation of a Modular Neural Network. 20.3 Main Steps in Designing and Implementing a Modular Neural Network. 20.4 Applications of Modular Neural Networks. 20.5 Advantages of Modular Neural Networks. 20.6 Disadvantages of Modular Neural Networks. 20.7 Comparison of a Modular Neural Network with a Single Large Neural Network. 20.8 Discussion and Conclusions. References and Further Reading. 21 Value-Based, Policy-Based, and Model-Based Reinforcement Learning Algorithms. 21.1 Introduction. 21.2 Value-Based Reinforcement Learning. 21.3 Policy-Based Reinforcement Learning. 21.4 Model-Based Reinforcement Learning. 21.5 Hybrid Reinforcement Learning. 21.6 Comparison Between Value-Based, Policy-Based, and Model-based Reinforcement Learning Algorithms. 21.7 Discussion and Conclusions. References and Further Reading. Glossary-A: Key Terminology of Machine Learning Algorithms. Glossary-B: Brief Rundown of Machine Learning Algorithms and Related Methods. Index.
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