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Near-optimal quantum kernel principal component analysis

QUANTUM SCIENCE AND TECHNOLOGY 2025年第1期10卷

作者： Wang, Youle Nanjing Univ Informat Sci & Technol Sch Software Nanjing 210044 Peoples R China

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.

关键词： quantum computing machine learning kernel method kernel principal component analysis

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kernel principal component analysis combining rotation forest method for linearly inseparable data

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COGNITIVE SYSTEMS RESEARCH 2019年 53卷 111-122页

作者： Lu, Huijuan Meng, Yaqiong Yan, Ke Gao, Zhigang China Jiliang Univ Coll Informat Engn Hangzhou 310018 Zhejiang Peoples R China Hangzhou Dianzi Univ Coll Comp Sci Hangzhou 310018 Zhejiang Peoples R China

Rotation forest (RoF) is an ensemble classifier combining linear analysis theories and decision tree algorithms. In recent existing works, RoF was widely applied to various fields with outstanding performance compared to traditional machine learning techniques, given that a reasonable number of base classifiers is provided. However, the conventional RoF algorithm suffers from classifying linearly inseparable datasets. In this study, a hybrid algorithm integrating kernel principal component analysis (KPCA) and the conventional RoF algorithm is proposed to overcome the classification difficulty for linearly inseparable datasets. The radial basis function (RBF) is selected as the kernel for the KPCA method to establish the nonlinear mapping for linearly inseparable data. Moreover, we evaluate various kernel parameters for better performance. Experimental results show that our algorithm improves the performance of RoF with linearly inseparable datasets, and therefore provides higher classification accuracy rates compared with other ensemble machine learning methods. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Rotation forest kernel principal component analysis Linearly inseparable data Decision tree

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kernel principal component analysis-based least squares support vector machine optimized by improved grey wolf optimization algorithm and application in dynamic liquid level forecasting of beam pump

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2020年第6期42卷 1135-1150页

作者： Tian Zhongda Shenyang Univ Technol Coll Informat Sci & Engn Shenyang 110870 Liaoning Peoples R China

Considering the blind parameters selection and the high dimension of input data in least squares support vector machine (LSSVM) modeling process, a kernel principal component analysis (KPCA)-based LSSVM forecasting method optimized by improved grey wolf optimization (GWO) algorithm is proposed. As an excellent forecasting model, the regression forecasting performance of LSSVM is greatly affected by parameters selection of the model. An improved GWO algorithm with better performance is proposed to determine the optimal parameters of LSSVM. This improved GWO algorithm improves the optimization precision and global optimization ability of the standard GWO algorithm. The parameters of LSSVM model are taken as the optimization object that is optimized by improved GWO algorithm. At the same time, the input variables of LSSVM are correlated and redundant. KPCA algorithm can eliminate the correlation and redundancy between input variables. The reduction of input variables reduces the complexity and training time of modeling process, and the coupling between input variables, to improve the prediction accuracy of LSSVM. The dynamic liquid level of beam pump is chosen as the research object. The proposed forecasting method is applied to the prediction of dynamic liquid level. The simulation comparison on actual collected dynamic liquid level data is performed. The simulation results show that the proposed forecasting method has better predictive performance for the dynamic liquid level.

关键词： Least squares support vector machine improved grey wolf optimization algorithm kernel principal component analysis forecasting dynamic liquid level of beam pump

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kernel principal component analysis for texture classification

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IEEE SIGNAL PROCESSING LETTERS 2001年第2期8卷 39-41页

作者： Kim, KI Park, SH Kim, HJ Kyungpook Natl Univ Dept Comp Engn Taegu 702701 South Korea

kernel principal component analysis (PCA) has recently been proposed as a nonlinear extension of PCA. The basic idea Is to first map the input space into a feature space via a nonlinear map and then compute the principal components in that feature space. This letter illustrates the potential of kernel PCA for texture classification. Accordingly, supervised texture classification mas performed using kernel PCA for texture feature extraction. By adopting a polynomial kernel, the principal components were computed within the product space of the input pixels making up the texture patterns, thereby producing a good performance.

关键词： feature extraction kernel principal component analysis machine learning texture analysis

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kernel principal component analysis-based Gaussian process regression modelling for high-dimensional reliability analysis

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COMPUTERS & STRUCTURES 2020年 241卷

作者： Zhou, Tong Peng, Yongbo Tongji Univ State Key Lab Disaster Reduct Civil Engn 1239 Siping Rd Shanghai 200092 Peoples R China Tongji Univ Coll Civil Engn Shanghai 200092 Peoples R China Tongji Univ Shanghai Inst Disaster Prevent & Relief Shanghai 200092 Peoples R China

An efficient reliability method is presented to address the challenge inherent in the high-dimensional reliability analysis. The critical contribution is an elegant implementation of combining the kernel principal component analysis (KPCA)-based nonlinear dimension reduction and the Gaussian process regression (GPR) surrogate model by introducing a nonintrusive, joint-training scheme. This treatment leads to an optimal KPCA-based subspace in which an accurate low-dimensional GPR model, denoted as the KPCA-GPR model, can be readily achieved. Then, the KPCA-GPR model is combined with the active learning (AL) -based sampling strategy and the Monte Carlo simulation (MCS). In this regard, the newly-added sample at each iteration can be employed simultaneously to both update the estimated KPCA-based subspace and refine the GPR model built on that subspace, which alleviates the 'curse of dimensionality' to some extent and improves progressively the failure probability estimation provided by the low-dimensional GPR model. In order to demonstrate the effectiveness of the proposed method, two numerical examples are investigated, involving both the analysis of high-dimensional, nonlinear, explicit performance functions and the static/dynamic reliability analysis of a truss structure with implicit performance functions. Numerical results indicate that the proposed method is of both accuracy and efficiency for high-dimensional reliability problems. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： kernel principal component analysis Gaussian process regression Active learning Monte Carlo simulation Structural reliability Joint-training scheme

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kernel principal component analysis fault diagnosis method based on improving Golden Jackal optimization algorithm

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2024年第5期238卷 874-887页

作者： Zhang, Ruicheng Sun, Weiliang Liang, Weizheng North China Univ Sci & Technol Coll Elect Engn Tangshan Peoples R China North China Univ Sci & Technol Coll Elect Engn Tangshan 063210 Hebei Peoples R China

Aiming at the shortcomings of the Golden Jackal optimization algorithm, such as low convergence accuracy and easy falling into the optimal local solution, an improved Golden Jackal optimization algorithm was proposed. First, sine and piecewise linear (SPM) chaotic mapping was introduced to increase the population number to achieve the purpose of initial population diversity. The self-adaptive weight and sine-cosine algorithm improved the position update formula of the Golden Jackal optimization algorithm, so the global search ability of the golden jackal algorithm is improved, and avoid the algorithm that fell into local optimality. Second, simulation experiments with eight standard test functions are performed to prove that the algorithm has excellent optimization ability. The improved Golden Jackal optimization algorithm was applied to optimize the kernel parameters of hybrid kernel principal component analysis. A fault diagnosis model is proposed to improve the golden jackal algorithm to optimize the kernel principal component analysis. Finally, the proposed method is used to fault diagnosis in the hot strip mill process. According to the study of simulation results, the faulty data can be identified effectively by this method, the accuracy is up to 100%, and the fault false alarm rate is greatly reduced.

关键词： Golden Jackal optimization algorithm kernel principal component analysis adaptive weight fault diagnosis hot strip mill process

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kernel principal component analysis for stochastic input model generation

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JOURNAL OF COMPUTATIONAL PHYSICS 2011年第19期230卷 7311-7331页

作者： Ma, Xiang Zabaras, Nicholas Cornell Univ Sibley Sch Mech & Aerosp Engn Mat Proc Design & Control Lab Ithaca NY 14853 USA

Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen-Loeve (K-L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen-Loeve (K-L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Stochastic partial differential equations Data-driven models kernel principal component analysis Non-linear model reduction Flow in random porous media

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kernel principal component analysis FOR THE CONSTRUCTION OF THE EXTENDED MORPHOLOGICAL PROFILE

KERNEL PRINCIPAL COMPONENT ANALYSIS FOR THE CONSTRUCTION OF ...

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IEEE International Geoscience and Remote Sensing Symposium

作者： Fauvel, M. Chanussot, J. Benediktsson, J. A. INRIA Rhones Alpes MISTIS Grenoble France

ISBN: (纸本)9781424433940

kernel principal component, analysis (KPCA) is investigated for feature extraction from hyperspectral remote-sensing data. Features extracted using KPCA are used to construct. the Extended Morphological Profile (EM P) Classification results, in terms of accuracy, are improved in comparison to original approach which used conventional principal component analysis for constructing the EMP Experimental results presented in this paper confirm the usefulness of the KPCA for the analysis of hyperspectral data The overall classification accuracy increases from 79% to 96% with the proposed approach.

关键词： Morphological Profile hyperspectral data kernel principal component analysis SVM

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kernel principal component analysis OF THE EAR MORPHOLOGY

KERNEL PRINCIPAL COMPONENT ANALYSIS OF THE EAR MORPHOLOGY

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Zolfaghari, Reza Epain, Nicolas Jin, Craig T. Glaunes, Joan Tew, Anthony Univ Sydney CARLab Sch Elect & Informat Engn Sydney NSW Australia IRT B Com 1219 Ave Champs Blancs F-35510 Cesson Sevigne France Univ York Dept Elect York N Yorkshire England Univ Paris 05 Sorbonne Paris Cites MAP5 F-75006 Paris France

ISBN: (纸本)9781509041176

This paper describes features in the ear shape that change across a population of ears and explores the corresponding changes in ear acoustics. The statistical analysis conducted over the space of ear shapes uses a kernel principal component analysis (KPCA). Further, it utilizes the framework of large deformation diffeomorphic metric mapping and the vector space that is constructed over the space of initial momentums, which describes the diffeomorphic transformations from the reference template ear shape. The population of ear shapes examined by the KPCA are 124 left and right ear shapes from the SYMARE database that were rigidly aligned to the template (population average) ear. In the work presented here we show the morphological variations captured by the first two kernel principal components, and also show the acoustic transfer functions of the ears which are computed using fast multipole boundary element method simulations.

关键词： Morphoacoustics LDDMM kernel principal component analysis Ear shape analysis FM-BEM

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kernel principal component analysis: Applications, Implementation and Comparison

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2nd International Conference on Network analysis

作者： Olsson, Daniel Georgiev, Pando Pardalos, Panos M. Royal Inst Technol KTH Stockholm Sweden Univ Florida Ctr Appl Optimizat Gainesville FL 32611 USA

ISBN: (纸本)9781461485872;9781461485889

kernel principal component analysis (KPCA) is a dimension reduction method that is closely related to principal component analysis (PCA). This report gives an overview of kernel PCA and presents an implementation of the method in MATLAB. The implemented method is tested in a transductive setting on two data bases. Two methods for labeling data points are considered, the nearest neighbor method and kernel regression, together with some possible improvements of the methods.

关键词： Reproducing kernel Hilbert space kernel principal component analysis Dimension reduction Nearest neighbor kernel regression

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