scholarly journals Quantum data compression by principal component analysis

2019 ◽  
Vol 18 (8) ◽  
Author(s):  
Chao-Hua Yu ◽  
Fei Gao ◽  
Song Lin ◽  
Jingbo Wang
2021 ◽  
Vol 45 (2) ◽  
pp. 235-244
Author(s):  
A.S. Minkin ◽  
O.V. Nikolaeva ◽  
A.A. Russkov

The paper is aimed at developing an algorithm of hyperspectral data compression that combines small losses with high compression rate. The algorithm relies on a principal component analysis and a method of exhaustion. The principal components are singular vectors of an initial signal matrix, which are found by the method of exhaustion. A retrieved signal matrix is formed in parallel. The process continues until a required retrieval error is attained. The algorithm is described in detail and input and output parameters are specified. Testing is performed using AVIRIS data (Airborne Visible-Infrared Imaging Spectrometer). Three images of differently looking sky (clear sky, partly clouded sky, and overcast skies) are analyzed. For each image, testing is performed for all spectral bands and for a set of bands from which high water-vapour absorption bands are excluded. Retrieval errors versus compression rates are presented. The error formulas include the root mean square deviation, the noise-to-signal ratio, the mean structural similarity index, and the mean relative deviation. It is shown that the retrieval errors decrease by more than an order of magnitude if spectral bands with high gas absorption are disregarded. It is shown that the reason is that weak signals in the absorption bands are measured with great errors, leading to a weak dependence between the spectra in different spatial pixels. A mean cosine distance between the spectra in different spatial pixels is suggested to be used to assess the image compressibility.


2014 ◽  
Vol 556-562 ◽  
pp. 4317-4320
Author(s):  
Qiang Zhang ◽  
Li Ping Liu ◽  
Chao Liu

As a zero-emission mode of transportation, an increasing number of Electric Vehicles (EV) have come into use in our daily lives. The EV charging station is an important component of the Smart Grid which is now facing the challenges of big data. This paper presents a data compression and reconstruction method based on the technique of Principal Component Analysis (PCA). The data reconstruction error Normalized Absolute Percent Error (NAPE) is taken into consideration to balance the compression ratio and data reconstruction quality. By using the simulated data, the effectiveness of data compression and reconstruction for EV charging stations are verified.


Author(s):  
V.B. Goryainov ◽  
E.R. Goryainova

Principal component analysis is one of the methods traditionally used to solve the problem of reducing the dimensionality of a multidimensional vector with correlated components. We constructed the principal components using a special representation of the covariance or correlation matrix of the indicators observed. The classical principal component analysis uses Pearson sample correlation coefficients as estimates of the correlation matrix elements. These estimates are extremely sensitive to sample contamination and anomalous observations. To robustify the principal component analysis, we propose to replace the sample estimates of correlation matrices with well-known robust analogues, which include Spearman's rank correlation coefficient, Minimum Covariance Determinant estimates, orthogonalized Gnanadesikan --- Kettenring estimates, and Olive --- Hawkins estimates. The study aims to carry out a comparative numerical analysis of the classical principal component analysis and its robust modifications. For this purpose, we simulated nine-dimensional vectors with known correlation matrix structures and introduced a special metric that allows us to evaluate the quality of data compression. Our extensive numerical experiment has shown that the classical principal component analysis boasts the best compression quality for a Gaussian distribution of observations. When observations are characterised by a Student's t-distribution with three degrees of freedom, as well as when a cluster of outliers, individual anomalous observations, or symmetric contaminations described by the Tukey distribution are present in the data, it is the Gnanadesikan --- Kettenring and Olive --- Hawkins estimates modifying the principal component analysis that show the best compression quality. The quality of the classical principal component analysis and Spearman’s rank modification decreases in these cases


2016 ◽  
Vol 47 (3) ◽  
pp. 297-307 ◽  
Author(s):  
Yejiao Ding ◽  
Ranhong Xie ◽  
Youlong Zou ◽  
Jiangfeng Guo

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