This essential resource bridges the gap between classical data limitations and the future of computing, giving you the scalable, quantum-accelerated PCA strategies needed to conquer today’s massive, high-dimensional datasets.
With the rapid growth of big data in fields such as genomics, internet traffic analysis, and social network data, traditional principal component analysis methods have reached their limits in terms of scalability and computational efficiency. This volume delves into cutting-edge advancements in principal component analysis (PCA), particularly focusing on its applications in handling high-dimensional and large-scale datasets. It also provides practical insights into how PCA can be applied to fields such as machine learning, bioinformatics, and finance. Through real-world case studies, hands-on examples, and guidance on implementing PCA using modern software tools and libraries, the book presents essential principles in quantum information theory and quantum algorithms, establishing the groundwork necessary to comprehend how quantum computing may expedite and improve PCA procedures. This work examines quantum algorithms for matrix decomposition, analyzes the computational benefits of quantum PCA compared to classical approaches, and showcases real applications in quantum machine learning, encryption, and quantum chemistry. Ultimately, this book will serve as a valuable resource for researchers, students, and professionals looking to the future of high-dimensional data analysis and how to apply efficient, scalable methods to PCA in their work.
Table of Contents:
Foreword xix
Preface xxi
1 Integrating Quantum Learning and Principal Component Analysis: From Eigenvectors to Qubits 1
N. Kousika, M. S. C. Sujitha, R. Rajshree and G. Renugadevi
1.1 Introduction 2
1.2 Quantum Computing: A New Paradigm 3
1.3 Performance and Practical Considerations of QPCA 7
1.4 Quantum Machine Learning Horizons and Future Outlook 9
1.5 Conclusion 9
2 Applications in Quantum Cryptography: Harnessing Quantum Principles for Next-Generation Security 13
Manu Y., Tanuja, Niveditha N. M., Rudresh N. C. and Ravikiran H. N.
2.1 Introduction 14
2.2 Basics of Quantum Cryptography 15
2.3 Quantum Key Distribution (QKD) 16
2.4 Applications 19
2.5 Integration with Traditional Classifications 22
2.6 Current Challenges 28
2.7 Future Research Directions 30
2.8 Conclusion 33
3 Quantum PCA in Machine Learning (ML) 37
V. Vanitha, Manoj Kumaran, L. Hari Prasath and R. Narmadha
3.1 Introduction 38
3.2 Fundamentals of PCA 41
3.3 Fundamentals of QC about ML 45
3.4 PCA 47
3.5 Applications of Quantum PCA in ML 50
3.6 Experimental Validation and Benchmarking 54
3.7 Future Directions and Open Problems 55
3.8 Conclusion 57
4 Future Trends and Innovations in Quantum Principal Component Analysis (PCA) 61
Aneesh Pradeep, Raghavendra R., V. Vanitha, Mohamed Uvaze Ahamed and A. Jayanthiladevi
4.1 Introduction 62viii Contents
4.2 Emerging Trends in QPCA 63
4.3 Hardware Innovations Driving QPCA 66
4.4 Application-Driven Innovations 69
4.5 Open Problems and Research Challenges 72
4.6 Future Directions 75
4.7 Conclusion 76
5 Challenges in Scaling Quantum Principal Component Analysis (QPCA) 79
R. Kowsalya, A. Jayanthiladevi, John T. Mesia Dhas and J. Viji Gripsy
5.1 Introduction 80
5.2 A Review of the Literature 81
5.3 Proposed Methodology 82
5.4 Results and Discussion 86Contents ix
5.5 Conclusion 92
5.6 Further Nations 93
6 Open Research Directions in Quantum Principal Component Analysis (QPCA) 97
Aneesh Pradeep, A. Jayanthiladevi, B. N. Shobha, Shashikala S. V. and Naveen K. B.
6.1 Introduction 98
6.2 Mathematical Formulation of QPCA 100
6.3 Open Research Directions in QPCA 102
6.4 Challenges and Future Directions 106
6.5 Case Studies Related to QPCA 110
6.6 Conclusion 111
7 Holomorphic Hierophanies: Quantum PCA (HH-QPCA) as Liturgical Practice in Topological Data Sanctuaries 115
Thamba Meshach W., Soumya T. R., Vineet Kumar Chauhan, Baburao Gaddala and Ananraj I.
7.1 Introduction 116
7.2 Related Works 119
7.3 Model Formulation: Holomorphic Hierophanies Quantum PCA (HH-QPCA) 123
7.4 Experimental Results and Validation 126
7.5 Discussion and Future Directions 128
7.6 Conclusion 130
8 Eigenvalue Ephemera: Non-Abelian PCA Dynamics in Quantum-Holographic Image Reconstruction 135
Manidipa Roy, S. Nancy Lima Christy, P. K. Manoj Kumar, Shoba R. and A. Syed Ismail
8.1 Introduction 136
8.2 Literature Review 139
8.3 Proposed Methodology 141
8.4 Experimental Validation and Results 146
8.5 Discussion and Future Scope 153
8.6 Conclusion 154
9 Principal Component Analysis (PCA) in Machine Learning and Data Science 159
Srinibas Pattanaik, Disha Sharma and Alessandro Vinciarelli
9.1 Introduction 160
9.2 Mathematical Principles of PCA 165
9.3 Approaches for Executing PCA 167
9.4 PCA for Architecture and Selection of Features 167
9.5 PCA Axis Visualization 170
9.6 Modifications and Approaches to PCA 172
9.7 Conclusion 173
10 Price Discovery, Hedging, and Market Efficiency: A Transformer-Based Analysis of Spot and Futures Markets in Indian Base Metal Commodities 177
Bhavani M. and Ilankadhir M.
10.1 Introduction 178
10.2 Literature Review 180
10.3 Methodology 182
10.4 Results and Discussion 193
10.5 Conclusion 199
11 Quantum Computing and Blockchain Security: Threats, Solutions, and Future Directions 203
Navya Mathur, Mokshita Bajpai, Vedika Murarka, Avani Joshi, Ramanathan Lakshmanan and N. Kousika
11.1 Introduction 204
11.2 Fundamentals of Quantum Computing 205
11.3 Structure of Blockchain 207
11.4 Privacy and Security 209Contents xiii
11.5 Quantum Key Sharing Concept (Blockchain-Based QKD Platform) 210
11.6 Quantum-Inspired Algorithms: Quantum-Influenced Quantum Walks (QIQW) 214
11.7 IoT Smart City Infrastructure: Enhancing Blockchain Security through Quantum Computing 217
11.8 The PDI Model with a Special Emphasis on Safety Issues 223
11.9 Advances in Quantum Networks, Secret Codes, and the Way Machines Learn 226
11.10 Where Things Might Go in the Future 228
11.11 Conclusion 230
12 Quantum PCA in Genomics Dimensionality Reduction in Biological Data 235
S. Ranjana Devi, R. C. Suganthee, E. Grace Mary Kanaga, S. Sadesh and S. Gokul
12.1 Introduction 236
12.2 Aim and Objectives 237
12.3 Literature Review 239
12.4 Research Methodology 242
12.5 Tables of Quantum PCA in Genomics Dimensionality Reduction in Biological Data 244
12.6 Further Suggestions for Research 249
12.7 Scope and Limitations 251
12.8 Hypothesis 253
12.9 Acknowledgments 255
12.10 Discussion 256
12.11 Conclusion 259
13 Randomized and Stochastic Algorithms for Large-Scale PCA 263
Barakkath Nisha U., Yasir Abdullah R., Sindhu V. and Sujatha T.
13.1 Introduction 264
13.2 Background and Related Work 266
13.3 Framework of Randomized and Stochastic Algorithms 270
13.4 Applications of Hybrid Swarm Intelligence 276
13.5 Experimental Results and Performance Analysis 278
13.6 Conclusion 282
14 Distributed and Incremental PCA for Real-Time Applications 285
Barakkath Nisha U., Yasir Abdullah R., Palani S., Ramprasath J. and Sivaganesan D.
14.1 Introduction 286
14.2 Background and Related Work 288
14.3 Framework of Randomized and Stochastic Algorithms 294
14.4 Experimental Results and Performance Analysis 298
14.5 Conclusion 304
15 Quantum Palimpsests: Eigenvector Erasure and the Rebirth of Latent Space in Holographic Mnemonic Sanctuaries 307
Shanmugha Priya R. K., Praveena R., B. Saritha, R. Radhika and Prithivirajan P. T.
15.1 Introduction 308
15.2 Related Work 310
15.3 Proposed Work 313
15.4 Experimental Setup and Results 314
15.5 Ablation Study 317
15.6 Conclusion and Future Work 319
References 320
Index 323
About the Author :
Abhishek Kumar, PhD is an Assistant Director and Associate Professor in the Computer Science and?Engineering Department at Chandigarh University, Punjab, India with more than 13 years of experience. He has published more than 50 books and more than 170 publications in reputed, peer-reviewed national and international journals, books, and conferences. His research areas include artificial intelligence, renewable energy, image processing, computer vision, data mining, and machine learning.
J.P. Ananth, PhD is a Professor and Dean in the Internal Quality Assurance Cell at Sri Krishna College of Engineering and Technology, Coimbatore, India. His research work has been documented in many journals, and he serves as a reviewer for several international journals and conferences. His research interests include computer vision, pattern recognition, artificial intelligence, and data analytics.
S. Oswalt Manoj, PhD is an Associate Professor in the Department of Computer Science and Engineering at Sri Krishna College of Engineering and Technology, Tamil Nadu, India. He has more than 100 publications in reputed, peer-reviewed national and international journals, books, and conferences, three published books, and ten patents. His research areas include big data analytics, artificial intelligence, computer vision, machine learning, deep learning, and cloud computing.
Navneet Kaur, PhD is a Professor in the Department of Computer Science and Engineering at Chandigarh University, Mohali, India. She has published many research articles in reputed journals, conferences, and book chapters. Her research interests include wireless sensor networks, wireless body area networks, AI, and cloud computing.
A. Jayanthiladevi, PhD is a Professor of Computer Engineering at Marwadi University. With a strong commitment to groundbreaking research, she has published numerous impactful works in international journals and conferences. Her expertise spans computational life sciences, artificial intelligence, mobile communications, machine learning, quantum computing, and health informatics.
