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IEEE International Symposium on Circuits and Systems proceedings

Eigen-Component Analysis: A Quantum Theory-Inspired Linear Model

R.M.M. Chen, Yaping Zhao, Hanghang Liu, Haohan Xu, Shaohua Ma, Edmund Y. M. Lam

Published May 25, 2025• 0 citations
Publisher

Abstract

In modern machine learning circuits and systems, the need for centralized, standardized data poses significant challenges, especially in privacy-sensitive, resource-constrained, real-time, or asynchronous environments. We introduce Eigen-Component Analysis (ECA), a quantum-inspired linear model that circumvents these requirements by leveraging intrinsic data structures. ECA uses an orthogonal transformation to extract meaningful features from decentralized, non-standardized data, ensuring high classification accuracy without extensive preprocessing. Unlike traditional linear models, ECA adapts to complex data distributions and shows superior performance in feature extraction and classification across various datasets. Experiments indicate that ECA achieves robust accuracy with fewer parameters, highlighting its potential where data centralization and standardization are impractical. Our work extends the feasibility of linear models in diverse scenarios, enhancing interpretability and efficiency in challenging data environments.

DOI
10.1109/iscas56072.2025.11044249

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In modern machine learning circuits and systems, the need for centralized, standardized data poses significant challenges, especially in privacy-sensitive, resource-constrained, real-time, or asynchronous environments. We introduce Eigen-Component Analysis (ECA), a quantum-inspired linear model that circumvents these requirements by leveraging intrinsic data structures. ECA uses an orthogonal transformation to extract meaningful features from decentralized, non-standardized data, ensuring high classification accuracy without extensive preprocessing. Unlike traditional linear models, ECA adapts to complex data distributions and shows superior performance in feature extraction and classification across various datasets. Experiments indicate that ECA achieves robust accuracy with fewer parameters, highlighting its potential where data centralization and standardization are impractical. Our work extends the feasibility of linear models in diverse scenarios, enhancing interpretability and efficiency in challenging data environments.
For a linear system, the response to a stimulus is often superposed by its responses to other decomposed stimuli. In quantum mechanics, a state is the superposition of multiple eigenstates. Here, by taking advantage of the phase difference, a common feature as we identified in data sets, we propose eigen component analysis (ECA), an interpretable linear learning model that incorporates the principle of quantum mechanics into the design of algorithm design for feature extraction, classification, dictionary and deep learning, and adversarial generation, etc. The simulation of ECA, possessing a measurable class-labelclass\text{-}labelclass-label H\mathcal{H}H, on a classical computer outperforms the existing classical linear models. Eigen component analysis network (ECAN), a network of concatenated ECA models, enhances ECA and gains the potential to be not only integrated with nonlinear models, but also an interface for deep neural networks to implement on a quantum computer, by analogizing a data set as recordings of quantum states. Therefore, ECA and ECAN promise to expand the feasibility of linear learning models, by adopting the strategy of quantum machine learning to replace heavy nonlinear models with succinct linear operations in tackling complexity.
Quantum Machine Learning (QML) offers a paradigm shift in data analysis, potentially surpassing the limitations of classical machine learning algorithms with its capacity for enhanced pattern recognition and data representation. This paper explores the application of quantum algorithms to address the challenges posed by inherently non-standard datasets, such as sensor data and time-series data characterized by complex correlations and high dimensionality. We propose a novel framework centered on quantum principal component analysis (QPCA) and Grover's algorithm to extract key insights from these datasets, demonstrating potential improvements in data understanding and feature extraction. This work aims to establish a foundation for QML applications in diverse fields, including anomaly detection, predictive modeling, and signal processing, where traditional methods often fall short. The core mechanism involves leveraging quantum properties to overcome challenges inherent in these data types.
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This paper investigates the potential of leveraging quantum algorithms for feature extraction in machine learning. Traditional feature extraction methods often struggle with high-dimensional data and computational complexity, leading to performance bottlenecks in downstream machine learning tasks. We explore the application of quantum algorithms, specifically Quantum Principal Component Analysis (QPCA) and Quantum Support Vector Machines (QSVM), to extract more efficient and potentially more informative features from datasets. The core claim of this research is that utilizing quantum algorithms can significantly enhance the performance of machine learning models. The mechanism involves applying quantum algorithms to reduce the dimensionality of data while preserving crucial information, which is then fed into classical machine learning models. This work provides a foundational exploration into this emerging field, demonstrating the potential for increased efficiency and accuracy in machine learning applications. ---
Abstract Kernel principal component analysis (kernel PCA) is a nonlinear dimensionality reduction technique that employs kernel functions to map data into a high-dimensional feature space, thereby extending the applicability of linear PCA to nonlinear data and facilitating the extraction of informative principal components. However, kernel PCA necessitates the manipulation of large-scale matrices, leading to high computational complexity and posing challenges for efficient implementation in big data environments. Quantum computing has recently been integrated with kernel methods in machine learning, enabling effective analysis of input data within intractable feature spaces. Although existing quantum kernel PCA proposals promise exponential speedups, they impose stringent requirements on quantum hardware that are challenging to fulfill. In this work, we propose a quantum algorithm for kernel PCA by establishing a connection between quantum kernel methods and block encoding, thereby diagonalizing the centralized kernel matrix on a quantum computer. The query complexity is logarithmic with respect to the size of the data vector, D , and linear with respect to the size of the dataset. An exponential speedup could be achieved when the dataset consists of a few high-dimensional vectors, wherein the dataset size is polynomial in log ⁡ ( D ) , with D being significantly large. In contrast to existing work, our algorithm enhances the efficiency of quantum kernel PCA and reduces the requirements for quantum hardware. Furthermore, we have also demonstrated that the algorithm based on block encoding matches the lower bound of query complexity, indicating that our algorithm is nearly optimal. Our research has laid down new pathways for developing quantum machine learning algorithms aimed at addressing tangible real-world problems and demonstrating quantum advantages within machine learning.
Quantum Machine Learning (QML) offers a paradigm shift in computational modeling, potentially surpassing the limitations of classical algorithms. This paper investigates the application of QML techniques to enhance feature extraction and modeling, focusing on efficient data processing and improved model performance, particularly in scenarios involving high-dimensional data and complex datasets. We explore the core mechanism of leveraging quantum properties to accelerate feature extraction, refine model representations, and ultimately boost the effectiveness of machine learning models. The research details a novel approach to feature representation using quantum algorithms, demonstrating significant improvements across various datasets. This work presents a framework for intelligently extracting key features from data, enabling the development of more robust and accurate models. The core claim is that QML can significantly enhance machine learning performance, particularly with complex datasets and high dimensionality.