Multiple factor analysis: principal component analysis for multitable and multiblock data sets

2013 ◽  
Vol 5 (2) ◽  
pp. 149-179 ◽  
Author(s):  
Hervé Abdi ◽  
Lynne J. Williams ◽  
Domininique Valentin
2017 ◽  
Vol 12 (3) ◽  
pp. 179-186
Author(s):  
László Sipos ◽  
Sándor Kovács ◽  
László Nagygyörgy ◽  
János Lázár ◽  
Attila László Gere ◽  
...  

A nemzetközi kutatási eredmények azt mutatják, hogy a műszeres analitikai eredmények és az emberi érzékelés paraméterei között nagyfokú korreláció adódik a termékek különböző összetevőire vetítve. Munkánkban célul tűztük ki 6 magánfőzött és 4 kereskedelmi forgalomban kapható vilmoskörte párlat gázkromatográfiás (GC-MS) és érzékszervi profilanalitikus vizsgálatát. A gázkromatográfiás vizsgálatokat a Wessling Hungary Kft. végezte, míg az érzékszervi profilanalitikus vizsgálatokat (ISO 13299:2016) a Szent István Egyetem Érzékszervi Minősítő Laboratóriumában (ISO 8589:2007) szakértői bírálócsoport segítségével (ISO 8586:2012) végeztük. Az egyváltozós elemzésekkel illó komponensenként és érzékszervi tulajdonságonként értékeltük az egyes párlatokat, az érzékszervi bírálói teljesítmény megfelelőségének szoftveres értékelése után (PanelCheck, ISO 11132:2012). Munkánkban sokdimenziós térredukciós módszerek matematikai módszereket alkalmazunk (principal component analysis, PCA; multiple factor analysis, MFA). Eredményeinkben bemutatjuk az érzékszervi és analitikai dimenziók közötti összefüggéseket, melyek során többek között alátámasztottuk, hogy a vilmoskörte vezéraromák (metil-2-transz-4-cisz-dekadienoát, etil-2- transz-4-ciszdekadienoát) szoros kapcsolatban vannak a körte íz érzékszervi dimenziójával. 


2016 ◽  
Vol 2 (4) ◽  
pp. 211
Author(s):  
Girdhari Lal Chaurasia ◽  
Mahesh Kumar Gupta ◽  
Praveen Kumar Tandon

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. 


Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková

In this chapter we compare two methods applied to reduce the dimensionality of data sets. The first method is Principal component analysis, and second method is Factor analysis. We present these methods on data from Atanassov’s intuitionistic fuzzy sets [6]. Earlier we construct an example of applying these methods. The calculations are performed in program R.


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