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A Theoretical Proposal: Utilizing Quantum Walks for Feature Extraction in PSG-Based Sleep Stage Classification

Aron Rodrick Lakra

Published Dec 11, 2024• 0 citations
Publisher

Abstract

This work proposes a novel theoretical framework utilizing quantum walk principles for feature extraction from polysomnographic (PSG) signals, focusing on the classification of sleep stages. By mapping EEG signals to a quantum graph and leveraging the probabilistic and path-dependent properties of quantum walks, this approach offers a potentially transformative methodology for analyzing brain activity. Also discussing the potential solution to class imbalance in sleep datasets using the innate qualities of quantum mechanics like superposition, highlighting the possible use of a hybrid loss function for classification.Outlining the conceptual basis of this framework, discussing its implications, and suggesting potential applications and future research directions.

DOI
10.31224/4214

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This work proposes a novel theoretical framework utilizing quantum walk principles for feature extraction from polysomnographic (PSG) signals, focusing on the classification of sleep stages. By mapping EEG signals to a quantum graph and leveraging the probabilistic and path-dependent properties of quantum walks, this approach offers a potentially transformative methodology for analyzing brain activity. Also discussing the potential solution to class imbalance in sleep datasets using the innate qualities of quantum mechanics like superposition, highlighting the possible use of a hybrid loss function for classification.Outlining the conceptual basis of this framework, discussing its implications, and suggesting potential applications and future research directions.
This paper presents a novel approach to graph traversal and feature extraction leveraging the principles of quantum walks. Classical graph algorithms often suffer from performance limitations when dealing with large, complex graphs, primarily due to their sequential nature and the exponential growth of possible paths. Quantum walks, utilizing superposition and interference, provide a fundamentally different paradigm for graph exploration, offering the potential for significant speedups. We detail the theoretical framework for applying quantum walks to graph traversal, focusing on the efficient extraction of features from nodes and edges. The core concept involves mapping the graph's nodes and edges onto a quantum Hilbert space, allowing the quantum walk to explore the graph's connectivity in a probabilistic manner. We demonstrate how interference effects can be strategically utilized to guide the walk towards regions of interest, thereby enhancing feature extraction. The methodology outlined here provides a robust foundation for developing quantum algorithms for graph analysis across various domains, including social network analysis, knowledge graph reasoning, and anomaly detection. This work establishes a new direction for graph processing, shifting from classical sequential algorithms to quantum probabilistic exploration, ultimately leading to improved efficiency and scalability.
Sleep staging is an important task in the field of medicine and is significant for diagnosing sleep disorders and assessing overall health. Classical machine learning has made significant progress in this field, and with the development of quantum computing, quantum machine learning (QML) provides a new model for solving complex data classification tasks. In this paper, we propose a hybrid quantum-classical neural network (HQCNN) architecture based on electroencephalogram (EEG) single-channel signals for automating the sleep staging task. The classical part uses a convolutional neural network (CNN) and a long short-term memory network (LSTM) to extract features of the EEG signal, while the quantum part utilizes variational quantum circuit (VQC) for feature mapping and classification. We evaluated the model on different datasets. The results show that the model is satisfactory for classification. This indicates that the combination of quantum computing and machine learning has great potential and provides new research directions and technical approaches for developing more efficient computational models and dealing with complex data problems.
This paper explores the application of quantum random walks (QRWs) to feature extraction from high-dimensional data. Classical random walks often struggle with the curse of dimensionality, leading to inefficient exploration of the data space. QRWs, leveraging the inherent randomness of quantum mechanics, offer a potential solution by enabling more efficient exploration and potentially uncovering hidden correlations. This work details the theoretical framework for implementing QRWs on graph-based representations of data, presenting algorithms for both discrete and continuous graphs. We investigate the key differences between classical and quantum random walks, focusing on the role of superposition and entanglement in expanding the search space. The core claim is that QRWs can be utilized to extract meaningful features from high-dimensional data. We provide a mathematical formulation for analyzing the convergence and efficiency of QRWs, demonstrating the potential advantages over traditional methods. The paper concludes with a discussion on the challenges and future directions for this emerging field.
This paper explores the application of quantum walks as a novel approach to optimization within the realm of combinatorial problems. The core argument posits that quantum walks, leveraging the principles of quantum mechanics like superposition and interference, can potentially outperform classical walk-based optimization methods, particularly when dealing with complex problem landscapes. We propose a framework where combinatorial problems are represented as graphs and navigated via quantum walks. The implementation utilizes the inherent probabilistic nature of quantum walks to explore the solution space more efficiently through constructive interference, while suppressing destructive interference that would lead to unproductive exploration. We detail the theoretical underpinnings, focusing on the mathematical formulation of the quantum walk and its interaction with the problem graph. The key objective is to demonstrate a potential speedup in convergence compared to traditional optimization techniques. This work provides a foundational exploration, aiming to lay the groundwork for future research and development in this emerging field.
Applications in behavioural research, human-computer interaction, and mental health depend on the ability to recognize emotions. In order to improve the accuracy of emotion recognition using electroencephalography (EEG) data, this work presents a hybrid quantum deep learning technique. Conventional EEG-based emotion recognition techniques are limited by noise and high-dimensional data complexity, which make feature extraction difficult. To tackle these issues, our method combines traditional deep learning classification with quantum-enhanced feature extraction. To identify important brain wave patterns, Bandpass filtering and Welch method are used as preprocessing techniques on EEG data. Intricate inter-band interactions that are essential for determining emotional states are captured by mapping frequency band power attributes (delta, theta, alpha, and beta) to quantum representations. Entanglement and rotation gates are used in a hybrid quantum circuit to maximize the model's sensitivity to EEG patterns associated with different emotions. Promising results from evaluation on a test dataset indicate the model's potential for accurate emotion recognition. The model will be extended for real-time applications and multi-class categorization in future study, which could improve EEG-based mental health screening instruments. This method offers a promising tool for applications in adaptive human-computer systems and mental health monitoring by showcasing the possibilities of fusing traditional deep learning with quantum processing for reliable, scalable emotion recognition.
Quantum machine learning (QML) is an emerging research field, which is devoted to devising and implementing quantum algorithms that could enable machine learning faster than that of classical computers. In this article, a hierarchic quantum mechanics-based framework is investigated to implement both the feature extraction and classification in the electroencephalogram (EEG) signal. First, the classical EEG signal dataset is prepared as a quantum state while the sign of the data point is preserved. The prepared quantum state is then evolved with the quantum wavelet packet transformation (QWPT) and the wavelet packet energy entropy (WPEE) feature is extracted as the input of the subsequent quantum classifier. We finally propose the improved quantum support vector machine with the arbitrary nonlinear kernel, which is employed to predict the label of the EEG signal. The complexity analysis indicates that the proposed framework provides exponential speedup over the same structured classical counterpart. Besides, the quantitative experimental results verify the feasibility and validity.