Focused Principal Component Analysis: Looking at a Correlation Matrix with a Particular Interest in a Given Variable

1999 ◽  
Vol 8 (4) ◽  
pp. 906 ◽  
Author(s):  
Bruno Falissard
Keyword(s):  
Principal Component Analysis ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis

scholarly journals Non-Orthogonal Multiple Access in Multiuser MIMO Configurations via Code Reuse and Principal Component Analysis

Electronics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1330
Author(s):  
Panagiotis K. Gkonis ◽  
Panagiotis T. Trakadas ◽  
Lambros E. Sarakis
Keyword(s):  
Principal Component Analysis ◽  
Interference Cancellation ◽  
Correlation Matrix ◽  
Multiple Access ◽  
Multiple Input Multiple Output ◽  
Principal Component ◽  
Component Analysis ◽  
Inner Product ◽  
Transmission Scheme ◽  
Code Reuse

The goal of the study presented in this paper is to evaluate the performance of a proposed transmission scheme in multiuser multiple-input multiple-output (MIMO) configurations, via code reuse. Hence, non-orthogonal multiple access (NOMA) is performed. To this end, a correlation matrix of the received data is constructed at the transmitter, with feedback as only the primary eigenvector of the equivalent channel matrix, which is derived after principal component analysis (PCA) at the receiver. Afterwards, users experiencing improved channel quality (i.e., diagonal terms of the correlation matrix) along with reduced multiple access interference (i.e., the inner product of transmission vectors) are the potential candidates for their assigned code to be reused. As the results indicate, considering various MIMO configurations, the proposed approach can achieve almost 33% code assignment gain (CAG), when successive interference cancellation (SIC) is employed in mobile receivers. However, even in the absence of SIC, CAG is still maintained with a tolerable average bit error rate (BER) degradation.

A survey of epicuticular waxes among genera of Triticeae. III. Synthesis and conclusion

1982 ◽  
Vol 60 (9) ◽  
pp. 1761-1770 ◽  
Author(s):  
Bernard R. Baum ◽  
A. P. Tulloch
Keyword(s):  
Principal Component Analysis ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Principal Coordinate Analysis ◽  
Epicuticular Waxes ◽  
Whole Plant ◽  
Close Relationship ◽  
Euclidean Distances ◽  
Highly Correlated

Characteristics of ultrastructural morphology and chemical composition of epicuticular waxes on glumes of Triticeae were combined for two series of numerical taxonomic analyses. The first, incorporating within-genus variability, utilized frequencies and information radius. The information radius matrix was subjected to Jardine–Sibson Bk clustering, then transformed to Euclidean distances for distance Wagner and principal-coordinate analyses. The second series employed a table of average character values for each genus which was subjected to four ordinations: (i) principal-component analysis of the correlation matrix, (ii) principal-component analysis of the variance-covariance matrix, (iii) principal-coordinate analysis, and (iv) nonmetric multidimensional scaling. The results are compared and general inferences are drawn. Occurrence of wax filaments on the glumes was highly correlated with presence of appreciable amounts of β-diketones in wax from the whole plant. While some genera, such as Triticum and Aegilops, appeared less closely related than expected from classification based on morphology, this procedure has suggested relationships between other genera, such as Roegneria and Hordeum and Secale and Elymus. The genera Leymus, Elymus, and Aneurolepidium were also closely related to each other and more distantly to Elytrigia, Triticum, and Agropyron. A relatively close relationship was also shown between the seven genera, Crithopsis, Eremopyron, Heteranthelium, Hordelymus, Psathyrostachys, Sitanion, and Taeniatherum, which have waxes which do not contain any β-diketones.

scholarly journals Disjoint and Functional Principal Component Analysis for Infected Cases and Deaths Due to COVID-19 in South American Countries with Sensor-Related Data

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4094
Author(s):  
Carlos Martin-Barreiro ◽  
John A. Ramirez-Figueroa ◽  
Xavier Cabezas ◽  
Víctor Leiva ◽  
M. Purificación Galindo-Villardón
Keyword(s):  
Principal Component Analysis ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
South American ◽  
Related Data ◽  
Johns Hopkins University ◽  
Functional Principal Component ◽  
Functional Components

In this paper, we group South American countries based on the number of infected cases and deaths due to COVID-19. The countries considered are: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Peru, Paraguay, Uruguay, and Venezuela. The data used are collected from a database of Johns Hopkins University, an institution that is dedicated to sensing and monitoring the evolution of the COVID-19 pandemic. A statistical analysis, based on principal components with modern and recent techniques, is conducted. Initially, utilizing the correlation matrix, standard components and varimax rotations are calculated. Then, by using disjoint components and functional components, the countries are grouped. An algorithm that allows us to keep the principal component analysis updated with a sensor in the data warehouse is designed. As reported in the conclusions, this grouping changes depending on the number of components considered, the type of principal component (standard, disjoint or functional) and the variable to be considered (infected cases or deaths). The results obtained are compared to the k-means technique. The COVID-19 cases and their deaths vary in the different countries due to diverse reasons, as reported in the conclusions.

Comparative Analysis of Robust Modification Quality for Principal Component Analysis to Perform Correlated Data Compression

2021 ◽  
pp. 23-45
Author(s):  
V.B. Goryainov ◽  
E.R. Goryainova
Keyword(s):  
Principal Component Analysis ◽  
Data Compression ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Correlated Data ◽  
Quality Of Data ◽  
T Distribution ◽  
Correlated Components

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

Sluice Risk Consequence’s Evaluation Based on Principal Component Analysis Method

2012 ◽  
Vol 166-169 ◽  
pp. 2740-2743
Author(s):  
Hao Yao Zheng ◽  
De Li Zhuang ◽  
Luo Shi Xu ◽  
Zhi Fei Long ◽  
De Wei Yang
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Analysis Method ◽  
Principal Component Analysis Method ◽  
Quantitative Indexes

Many sluices were damaged seriously after several decades’ use. In sluice safety level’s classification standard, there are quantitative indexes and qualitative indexes. Principal component analysis was used to evaluate the sluice. First the data were standardized, correlation matrix was got, and then confirmed principal components and weight, through this step principal components’ value and total value were received, finally sluice risk grades were determined and they could be ordered. The result is objective and reasonable, so we assess sluice easily.

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