scholarly journals An Algorithm for the Principal Component Analysis of Large Data Sets

2011 ◽  
Vol 33 (5) ◽  
pp. 2580-2594 ◽  
Author(s):  
Nathan Halko ◽  
Per-Gunnar Martinsson ◽  
Yoel Shkolnisky ◽  
Mark Tygert
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Large Data Sets ◽  
Data Sets

scholarly journals Analysis of 46,046 SARS-CoV-2 whole-genomes leveraging principal component analysis (PCA)

2020 ◽  
Author(s):  
Christiane Scherer ◽  
James Grover ◽  
Darby Kammeraad ◽  
Gabe Rudy ◽  
Andreas Scherer
Keyword(s):  
Principal Component Analysis ◽  
Population Genetics ◽  
Phylogenetic Analysis ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Comprehensive Analysis ◽  
Large Data Sets ◽  
Data Sets ◽  
Whole Genomes

AbstractSince the beginning of the global SARS-CoV-2 pandemic, there have been a number of efforts to understand the mutations and clusters of genetic lines of the SARS-CoV-2 virus. Until now, phylogenetic analysis methods have been used for this purpose. Here we show that Principal Component Analysis (PCA), which is widely used in population genetics, can not only help us to understand existing findings about the mutation processes of the virus, but can also provide even deeper insights into these processes while being less sensitive to sequencing gaps. Here we describe a comprehensive analysis of a 46,046 SARS-CoV-2 genome sequence dataset downloaded from the GISAID database in June of this year.SummaryPCA provides deep insights into the analysis of large data sets of SARS-CoV-2 genomes, revealing virus lineages that have thus far been unnoticed.

scholarly journals Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets

1993 ◽  
Vol 13 (1) ◽  
pp. 5-14 ◽  
Author(s):  
K. J. Friston ◽  
C. D. Frith ◽  
P. F. Liddle ◽  
R. S. J. Frackowiak
Keyword(s):  
Principal Component Analysis ◽  
Functional Connectivity ◽  
Verbal Fluency ◽  
Principal Component ◽  
Temporal Correlation ◽  
Large Data ◽  
Component Analysis ◽  
Anterior Cingulate ◽  
Data Sets ◽  
Brain System

The distributed brain systems associated with performance of a verbal fluency task were identified in a nondirected correlational analysis of neurophysiological data obtained with positron tomography. This analysis used a recursive principal-component analysis developed specifically for large data sets. This analysis is interpreted in terms of functional connectivity, defined as the temporal correlation of a neurophysiological index measured in different brain areas. The results suggest that the variance in neurophysiological measurements, introduced experimentally, was accounted for by two independent principal components. The first, and considerably larger, highlighted an intentional brain system seen in previous studies of verbal fluency. The second identified a distributed brain system including the anterior cingulate and Wernicke's area that reflected monotonic time effects. We propose that this system has an attentional bias.

scholarly journals COMPARISON OF FUZZY SUBTRACTIVE CLUSTERING AND FUZZYC-MEANS

Kursor ◽  
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Annisa Eka Haryati ◽  
Sugiyarto Sugiyarto ◽  
Rizki Desi Arindra Putri
Keyword(s):  
Principal Component Analysis ◽  
Fuzzy Clustering ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Subtractive Clustering ◽  
Validity Index ◽  
Fuzzy Clustering Method ◽  
Dependent Variables ◽  
Better Than

Multivariate statistics have related problems with large data dimensions. One method that can be used is principal component analysis (PCA). Principal component analysis (PCA) is a technique used to reduce data dimensions consisting of several dependent variables while maintaining variance in the data. PCA can be used to stabilize measurements in statistical analysis, one of which is cluster analysis. Fuzzy clustering is a method of grouping based on membership values ​​that includes fuzzy sets as a weighting basis for grouping. In this study, the fuzzy clustering method used is Fuzzy Subtractive Clustering (FSC) and Fuzzy C-Means (FCM) with a combination of the Minkowski Chebysev distance. The purpose of this study was to compare the cluster results obtained from the FSC and FCM using the DBI validity index. The results obtained indicate that the results of clustering using FCM are better than the FSC.

Principal Component Analysis of Hydrological Data

2010 ◽  
pp. 364-388
Author(s):  
Petr Praus
Keyword(s):  
Water Quality ◽  
Principal Component Analysis ◽  
Drinking Water ◽  
Ground Water ◽  
Principal Component ◽  
Component Analysis ◽  
Data Sets ◽  
Hydrological Data ◽  
First Case

In this chapter the principals and applications of principal component analysis (PCA) applied on hydrological data are presented. Four case studies showed the possibility of PCA to obtain information about wastewater treatment process, drinking water quality in a city network and to find similarities in the data sets of ground water quality results and water-related images. In the first case study, the composition of raw and cleaned wastewater was characterised and its temporal changes were displayed. In the second case study, drinking water samples were divided into clusters in consistency with their sampling localities. In the case study III, the similar samples of ground water were recognised by the calculation of cosine similarity, the Euclidean and Manhattan distances. In the case study IV, 32 water-related images were transformed into a large image matrix whose dimensionality was reduced by PCA. The images were clustered using the PCA scatter plots.

EVALUATION AND MODELLING OF GROUND WATER QUALITY DATA OF ALLAHABAD CITY BY ENVIRONMETRIC METHODS

2016 ◽  
Vol 2 (4) ◽  
pp. 211
Author(s):  
Girdhari Lal Chaurasia ◽  
Mahesh Kumar Gupta ◽  
Praveen Kumar Tandon
Keyword(s):  
Water Quality ◽  
Principal Component Analysis ◽  
Cluster Analysis ◽  
Factor Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Sampling Location ◽  
Data Sets ◽  
Multivariate Statistical ◽  
Positive Loading

Water is an essential resource for all the organisms, plants and animals including the human beings. It is the backbone for agricultural and industrial sectors and all the small business units. Increase in human population and economic activities have tremendously increased the demand for large-scale suppliers of fresh water for various competing end users.The quality evaluation of water is represented in terms of physical, chemical and Biological parameters. A particular problem in the case of water quality monitoring is the complexity associated with analyzing the large number of measured variables. The data sets contain rich information about the behavior of the water resources. Multivariate statistical approaches allow deriving hidden information from the data sets about the possible influences of the environment on water quality. Classification, modeling and interpretation of monitored data are the most important steps in the assessment of water quality. The application of different multivariate statistical techniques, such as cluster analysis (CA), principal component analysis (PCA) and factor analysis (FA) help to identify important components or factors accounting for most of the variances of a system. In the present study water samples were analyzed for various physicochemical analyses by different methods following the standards of APHA, BIS and WHO and were subjected to further statistical analysis viz. the cluster analysis to understand the similarity and differences among the various sampling stations.  Three clusters were found. Cluster 1 was marked with 3 sampling locations 1, 3 & 5; Cluster-2 was marked with sampling location-2 and cluster-3 was marked with sampling location-4. Principal component analysis/factor analysis is a pattern reorganization technique which is used to assess the correlation between the observations in terms of different factors which are not observable. Observations correlated either positively or negatively, are likely to be affected by the same factors while the observations which are not correlated are influenced by different factors. In our study three factors explained 99.827% of variances. F1 marked  51.619% of total variances, high positive strong loading with TSS, TS, Temp, TDS, phosphate and moderate with electrical conductivity with loading values of 0.986, 0.970, 0.792, 0.744, 0.695,  0.701, respectively. Factor 2 marked 27.236% of the total variance with moderate positive loading with total alkalinity & temp. with loading values 0.723 & 0.606 respectively. It also explained the moderate negative loading with conductivity, TDS, and chloride with loading values -0.698, -0.690, -0.582. Factor F 3 marked 20.972 % of the variances with positive loading with PH, chloride, and phosphate with strong loading of pH 0.872 and moderate positive loading with chloride and phosphate with loading values 0.721, and 0.569 respectively. 

Identification of Excitation Source Number Using Principal Component Analysis

2011 ◽  
Vol 199-200 ◽  
pp. 850-857
Author(s):  
Jian Chao Dong ◽  
Tie Jun Yang ◽  
Xin Hui Li ◽  
Zhi Jun Shuai ◽  
You Hong Xiao
Keyword(s):  
Principal Component Analysis ◽  
Signal To Noise Ratio ◽  
Multiple Input Multiple Output ◽  
Principal Component ◽  
Relevant Information ◽  
Component Analysis ◽  
Data Sets ◽  
Blind Signal ◽  
Input Multiple Output ◽  
Source Number

Principal component analysis (PCA), serving as one of the basic blind signal processing techniques, is extensively employed in all forms of analysis for extracting relevant information from confusing data sets. The principle of PCA is explained in this paper firstly, then the simulation and experiment are carried out to a simply supported beam rig, and PCA is used in frequency domain to identify sources number of several cases. Meanwhile principal components (PCs) contribution coefficient and signal to noise ratio between neighboring PCs (neighboring SNR) are introduced to cutoff minor components quantificationally. The results show that when observation number is equal to or larger than source number and additive noise is feebleness, accurate prediction of the number of uncorrelated excitation sources in a multiple input multiple output system could be obtained by principal component analysis.

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