Classical and Quantum Principal Component Analysis in Data Engineering

Abhishek Kumar, PhD is an Assistant Director and Professor in the Computer Science and Engineering Department at Chandigarh University. He has more than 250 publications in reputed, peer-reviewed national and international journals, authored seven books, and edited more than 110 books. His research interests 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.

• Foreword xixPreface xxi1 Integrating Quantum Learning and Principal Component Analysis: From Eigenvectors to Qubits 1N. Kousika, M. S. C. Sujitha, R. Rajshree and G. Renugadevi1.1 Introduction 21.2 Quantum Computing: A New Paradigm 31.3 Performance and Practical Considerations of QPCA 71.4 Quantum Machine Learning Horizons and Future Outlook 91.5 Conclusion 92 Applications in Quantum Cryptography: Harnessing Quantum Principles for Next-Generation Security 13Manu Y., Tanuja, Niveditha N. M., Rudresh N. C. and Ravikiran H. N.2.1 Introduction 142.2 Basics of Quantum Cryptography 152.3 Quantum Key Distribution (QKD) 162.4 Applications 192.5 Integration with Traditional Classifications 222.6 Current Challenges 282.7 Future Research Directions 302.8 Conclusion 333 Quantum PCA in Machine Learning (ML) 37V. Vanitha, Manoj Kumaran, L. Hari Prasath and R. Narmadha3.1 Introduction 383.2 Fundamentals of PCA 413.3 Fundamentals of QC about ML 453.4 PCA 473.5 Applications of Quantum PCA in ML 503.6 Experimental Validation and Benchmarking 543.7 Future Directions and Open Problems 553.8 Conclusion 574 Future Trends and Innovations in Quantum Principal Component Analysis (PCA) 61Aneesh Pradeep, Raghavendra R., V. Vanitha, Mohamed Uvaze Ahamed and A. Jayanthiladevi4.1 Introduction 62viii Contents4.2 Emerging Trends in QPCA 634.3 Hardware Innovations Driving QPCA 664.4 Application-Driven Innovations 694.5 Open Problems and Research Challenges 724.6 Future Directions 754.7 Conclusion 765 Challenges in Scaling Quantum Principal Component Analysis (QPCA) 79R. Kowsalya, A. Jayanthiladevi, John T. Mesia Dhas and J. Viji Gripsy5.1 Introduction 805.2 A Review of the Literature 815.3 Proposed Methodology 825.4 Results and Discussion 86Contents ix5.5 Conclusion 925.6 Further Nations 936 Open Research Directions in Quantum Principal Component Analysis (QPCA) 97Aneesh Pradeep, A. Jayanthiladevi, B. N. Shobha, Shashikala S. V. and Naveen K. B.6.1 Introduction 986.2 Mathematical Formulation of QPCA 1006.3 Open Research Directions in QPCA 1026.4 Challenges and Future Directions 1066.5 Case Studies Related to QPCA 1106.6 Conclusion 1117 Holomorphic Hierophanies: Quantum PCA (HH-QPCA) as Liturgical Practice in Topological Data Sanctuaries 115Thamba Meshach W., Soumya T. R., Vineet Kumar Chauhan, Baburao Gaddala and Ananraj I.7.1 Introduction 1167.2 Related Works 1197.3 Model Formulation: Holomorphic Hierophanies Quantum PCA (HH-QPCA) 1237.4 Experimental Results and Validation 1267.5 Discussion and Future Directions 1287.6 Conclusion 1308 Eigenvalue Ephemera: Non-Abelian PCA Dynamics in Quantum-Holographic Image Reconstruction 135Manidipa Roy, S. Nancy Lima Christy, P. K. Manoj Kumar, Shoba R. and A. Syed Ismail8.1 Introduction 1368.2 Literature Review 1398.3 Proposed Methodology 1418.4 Experimental Validation and Results 1468.5 Discussion and Future Scope 1538.6 Conclusion 1549 Principal Component Analysis (PCA) in Machine Learning and Data Science 159Srinibas Pattanaik, Disha Sharma and Alessandro Vinciarelli9.1 Introduction 1609.2 Mathematical Principles of PCA 1659.3 Approaches for Executing PCA 1679.4 PCA for Architecture and Selection of Features 1679.5 PCA Axis Visualization 1709.6 Modifications and Approaches to PCA 1729.7 Conclusion 17310 Price Discovery, Hedging, and Market Efficiency: A Transformer-Based Analysis of Spot and Futures Markets in Indian Base Metal Commodities 177Bhavani M. and Ilankadhir M.10.1 Introduction 17810.2 Literature Review 18010.3 Methodology 18210.4 Results and Discussion 19310.5 Conclusion 19911 Quantum Computing and Blockchain Security: Threats, Solutions, and Future Directions 203Navya Mathur, Mokshita Bajpai, Vedika Murarka, Avani Joshi, Ramanathan Lakshmanan and N. Kousika11.1 Introduction 20411.2 Fundamentals of Quantum Computing 20511.3 Structure of Blockchain 20711.4 Privacy and Security 209Contents xiii11.5 Quantum Key Sharing Concept (Blockchain-Based QKD Platform) 21011.6 Quantum-Inspired Algorithms: Quantum-Influenced Quantum Walks (QIQW) 21411.7 IoT Smart City Infrastructure: Enhancing Blockchain Security through Quantum Computing 21711.8 The PDI Model with a Special Emphasis on Safety Issues 22311.9 Advances in Quantum Networks, Secret Codes, and the Way Machines Learn 22611.10 Where Things Might Go in the Future 22811.11 Conclusion 23012 Quantum PCA in Genomics Dimensionality Reduction in Biological Data 235S. Ranjana Devi, R. C. Suganthee, E. Grace Mary Kanaga, S. Sadesh and S. Gokul12.1 Introduction 23612.2 Aim and Objectives 23712.3 Literature Review 23912.4 Research Methodology 24212.5 Tables of Quantum PCA in Genomics Dimensionality Reduction in Biological Data 24412.6 Further Suggestions for Research 24912.7 Scope and Limitations 25112.8 Hypothesis 25312.9 Acknowledgments 25512.10 Discussion 25612.11 Conclusion 25913 Randomized and Stochastic Algorithms for Large-Scale PCA 263Barakkath Nisha U., Yasir Abdullah R., Sindhu V. and Sujatha T.13.1 Introduction 26413.2 Background and Related Work 26613.3 Framework of Randomized and Stochastic Algorithms 27013.4 Applications of Hybrid Swarm Intelligence 27613.5 Experimental Results and Performance Analysis 27813.6 Conclusion 28214 Distributed and Incremental PCA for Real-Time Applications 285Barakkath Nisha U., Yasir Abdullah R., Palani S., Ramprasath J. and Sivaganesan D.14.1 Introduction 28614.2 Background and Related Work 28814.3 Framework of Randomized and Stochastic Algorithms 29414.4 Experimental Results and Performance Analysis 29814.5 Conclusion 30415 Quantum Palimpsests: Eigenvector Erasure and the Rebirth of Latent Space in Holographic Mnemonic Sanctuaries 307Shanmugha Priya R. K., Praveena R., B. Saritha, R. Radhika and Prithivirajan P. T.15.1 Introduction 30815.2 Related Work 31015.3 Proposed Work 31315.4 Experimental Setup and Results 31415.5 Ablation Study 31715.6 Conclusion and Future Work 319References 320Index 323