Information about 3 principal components analysis

Published on February 17, 2014

Author: dgrapov

Source: slideshare.net

Principal Components Analysis Biology Chemistry Principal Components Analysis Informatics Steps 1. Calculate a PCA model 2. Select optimal model principal component (PC) 3. Overview PCA scores and loadings plots 4. Repeat steps 1-2 using data centering and scaling Visualize: 1. Sample scores annotated by extraction and treatment 2. Leverage and DmodX (distance from model plane) 3. Variable loadings and biplots Exercise: 1. How many PCs are needed to capture 80% variance for raw data and scaled data? 2. Are their any moderate or extreme outliers? 3. What variables contribute most to the variance for raw and scaled data?

Biology Chemistry Informatics PCA Variance Explained (raw data) • Principal Components Analysis • PCs can be selected to explain a minimum %variance in the data (~80%) PCs explaining below 1% variance can be excluded • q2 is the crossvalidated PCA prediction of left out data

PCA Scores (raw data) Biology Chemistry Principal Components Analysis Informatics • Hotelling's T2 ellipse shows 95% CI for bivariate normal distribution • Samples lying outside of the ellipse could be outliers

PCA Loadings (raw data, centered) Biology Chemistry Principal Components Analysis Informatics • Unscaled data PCA loadings are highly correlated with magnitude

PCA Biplot (raw data) Biology Chemistry Sample contains high maleic acid Principal Components Analysis Informatics • Biplots can be used to rapidly overview the correlation between sample scores and variable loadings Sample contains high sucrose (low maleic acid)

Biology Chemistry PCA Leverage and DmodX (raw data) Principal Components Analysis Informatics Leverage is the distance to samples center in the PCA plane (extreme outliers) Distance to model X (DmodX) is the orthogonal distance to the PCA plane (moderate outliers)

Biology Chemistry Principal Components Analysis Informatics PCA Variance Explained (autoscaled)

PCA Scores (autoscaled) Biology Chemistry Principal Components Analysis Informatics • Loadings on PC1 describe differences due to extraction • Loadings on PC2 describe differences due to treatment

Biology Chemistry Principal Components Analysis Informatics PCA Leverage and DmodX (autoscaled) • Samples with both high leverage and DomdX are likely outliers • Evaluate PCA results after their removal

PCA Loadings (autoscaled) Biology Chemistry Principal Components Analysis Informatics • Scaled loadings are independent of variable magnitude and show a rich variance structure of the data

Biology Chemistry Relationship between scores and loadings (autoscaled) Informatics Principal Components Analysis Higher in 100% MeOH Lower in 100% MeOH Extraction

Loadings and Scores Biology Chemistry Informatics Principal Components Analysis Highest negative loading on PC1 Highest positive loading on PC1

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly ...

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Principal Component Analysis 3 Because it is a variable reduction procedure, principal component analysis is similar in many respects to exploratory factor ...

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3 Principal Components Analysis 3.1 Introduction The basic aim of principal components analysis is to describe the variation in a set ofcorrelated ...

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3 Principal Component Analysis 3.1 CONCEPTS Principal componentanalysis(PCA) canbeconsideredas ‘‘the mother ofallmethods in multivariate data analysis

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A tutorial on Principal Components Analysis Lindsay I ... will be required to understand the process of Principal Components Analysis. The ... 3. Set 1: 32 ...

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The Pattern Recognition Class 2012 by Prof. Fred Hamprecht. It took place at the HCI / University of Heidelberg during the summer term of 2012 ...

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A Tutorial on Principal Component Analysis Jonathon Shlens Google Research Mountain View, CA 94043 (Dated: April 7, 2014; Version 3.02) Principal component ...

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PRINCIPAL COMPONENTS ANALYSIS (PCA) Steven M. Ho!and Department of Geology, University of Georgia, Athens, GA 30602-2501 May 2008

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3: 0,83: 10,43: 94,53: 4: 0,18: 2,22: 96,74: 5: 0,11: 1,34: 98,08: 6: 0,08: 0,95: 99,03: 7: ... G. H. Dunteman: Principal Component Analysis. Sage ...

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