Quantum locally linear embedding for nonlinear dimensionality reduction

He, Xi; Sun, Li; Lyu, Chufan; Wang, Xiaoting

doi:10.1007/s11128-020-02818-y

Cited by 16 publications

(7 citation statements)

References 27 publications

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“…A structured method for reducing dimensionality while preserving discriminative information is provided by the qDR proposed by Yu et al (2023) using linear discriminant analysis (LDA) [35]. A novel method for reducing nonlinear dimensionality in quantum datasets was presented by He et al (2020) with the introduction of Quantum Locally Linear Embedding [36]. Through nonlinear DR, Yang et al (2021) proposed a method to detect quantum phase transitions and represent quantum phases.…”

Section: Literature Reviewmentioning

confidence: 99%

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Sihare

2024

Preprint

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This research explores the potential of quantum computing in data analysis, focusing on the efficient analysis of high-dimensional quantum datasets using dimensionality reduction techniques. The study aims to fill the knowledge gap by developing robust quantum dimensionality reduction techniques that can mitigate noise and errors. The research methodology involved a comprehensive review and analysis of existing quantum dimensionality reduction techniques, such as quantum principal component analysis, quantum linear discriminant analysis and quantum generative models. The study also explored the limitations imposed by NISQ devices and proposed strategies to adapt these techniques to work efficiently within these constraints. The key results demonstrate the potential of quantum dimensionality reduction techniques to effectively reduce the dimensionality of high-dimensional quantum datasets while preserving critical quantum information. The evaluation of quantum principal component analysis, quantum linear discriminant analysis and quantum generative models showed their effectiveness in improving quantum data analysis, particularly in improving simulation speed and predicting properties. Despite the challenges posed by noise and errors, robust quantum dimensionality reduction methods showed promise in mitigating these effects and preserving quantum information. Finally, this research contributes to the advancement of quantum data analysis by presenting a comprehensive analysis of quantum dimensionality reduction techniques and their applications. It highlights the importance of developing robust quantum feature learning methods that can operate efficiently in noisy quantum environments, especially in the NISQ era.

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Section: Literature Reviewmentioning

confidence: 99%

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Sihare

2024

Preprint

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“…At the feature selection level, dimensionality reduction algorithms in machine learning are the primary strategy to consider because of the huge impact of redundant features on signal quality. Principal component analysis [15], linear discriminant analysis (LDA), isometric mapping [16], locally linear embedding [17,18] and Laplacian eigenmaps [19], multi-dimensional scaling [20], t-distributed stochastic neighbor embedding [21,22] are classical dimensionality reduction algorithms, and these can extract the essential features of the signals. But on the issue of signal classification, it is necessary to pay attention not only to the essential characteristics of signals, but also to the common characteristics of the same class of signals and the individual characteristics among different classes of signals, and this guidance is reflected in the need to design feature selection algorithms based on known class labels.…”

Section: Related Workmentioning

confidence: 99%

A novel multi-featured decision system for multi-classification tasks

Xu¹

2023

Meas. Sci. Technol.

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Feature engineering is a difficult task, and for real signal data, it is difficult to find a certain feature that can easily distinguish all classes. Multiple features can provide more information, which means the fusion of multi-feature learning strategies has potential significant advantages. Based on this premise, this paper proposes a multi-class framework based on the multi-featured decision to distinguish all the different classes, and takes Automatic Dependent Surveillance-Broadcast (ADS-B) signal data as an example, first extracts the phase features and wavelet decomposition features of the signal data, then selects the features with high discrimination between classes, then proposes a one-dimensional residual neural network based on 16 convolutional layers to learn the unique features of different features and classes separately, and finally proposes a novel multi-featured decision method based on voting method and a priori probability. Results show that the proposed one-dimensional residual neural network has better performance metrics on the test set compared to some machine learning-based and neural network-based algorithms, with classification accuracies of 86.1%, 84.6% and 83.6% on wavelet decomposition features, raw features and phase features, respectively, on ADS-B preamble signals. The proposed feature decision framework based on the voting method and a priori probability has a recall, precision and F1 value of 80.24%, 89.89% and 84.79% on ADS-B preamble signals, respectively.

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“…Since the covariance matrix Σ is semi-positive definite, we can implement it by Hamiltonian simulation [18]. Assuming that Σ N j 1 λ j |μ j 〉〈μ j | [19]. Prepare a quantum black box given access to Hermitian matrix Σ, any time t, and errors ϵ, operate with approximate unitary precision ϵ through a quantum circuit U 2 .…”

Section: Calculating the Mahalanobis Distancementioning

confidence: 99%

Quantum K-nearest neighbors classification algorithm based on Mahalanobis distance

Gao

Guo

et al. 2022

Front. Phys.

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Mahalanobis distance is a distance measure that takes into account the relationship between features. In this paper, we proposed a quantum KNN classification algorithm based on the Mahalanobis distance, which combines the classical KNN algorithm with quantum computing to solve supervised classification problem in machine learning. Firstly, a quantum sub-algorithm for searching the minimum of disordered data set is utilized to find out K nearest neighbors of the testing sample. Finally, its category can be obtained by counting the categories of K nearest neighbors. Moreover, it is shown that the proposed quantum algorithm has the effect of squared acceleration compared with the classical counterpart.

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Quantum locally linear embedding for nonlinear dimensionality reduction

Cited by 16 publications

References 27 publications

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

A novel multi-featured decision system for multi-classification tasks

Quantum K-nearest neighbors classification algorithm based on Mahalanobis distance

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