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PRINCIPAL COMPONENTS ANALYSIS PCA

PRINCIPAL COMPONENTS A N A LY S I S (P C A )Steven M. HollandDepartment of Geology, University of Georgia, Athens, GA 30602-25013 December 2019 IntroductionSuppose we had measured two variables, length and width, and plotted them as shown below. Both variables have approximately the same variance and they are highly correlated with one another. We could pass a vector through the long axis of the cloud of points and a second vec-tor at right angles to the first, with both vectors passing through the centroid of the we have made these vectors, we could find the coordinates of all of the data points rela-tive to these two perpendicular vectors and re-plot the data, as shown here (both of these figures are from Swan and Sandilands, 1995).In this new reference frame, note that variance is greater along axis 1 than it is on axis 2.

K, Mg, Mn, and Si, stable isotope ratios of carbon and oxygen (d13C and d18O). It also records the stratigraphic position of the samples. As we are most interested in how the geo-Principal Components Analysis 3

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  Analysis, Principal, Component, Carbon, Isotopes, Stable, Principal components analysis pca, Stable isotope, Principal components analysis

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PRINCIPAL COMPONENTS ANALYSIS PCA

strata.uga.edu

One guideline for the number of principal components to use is to accept all principal com-ponents that explain more than one variable’s worth of data. If all the variables contributed the same variance, this cutoff would be 1/p, where p is the number of variables. > abline(h=1/ncol(geochem)*100, col=‘red')

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A SHORT R TUTORIAL - University of Georgia

strata.uga.edu

To download R, macOS users should follow the macOS link from the CRAN page and select the file corresponding to the most recent version of R. This will download a disk image with a file, which you should double-click to install R. R can be run from the apps R and RStudio, and from the command line in Terminal or XQuartz.

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NON METRIC MULTIDIMENSIONAL SCALING MDS

strata.uga.edu

samples, unlike other methods which specify particular measures, such as covariance or corre-lation in PCA or the implied chi-squared measure in detrended correspondence analysis. MDS does suffer from two principal drawbacks, although these are becoming less important as computational power increases.

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Research Statement-Daniel R. Rogers

scholar.harvard.edu

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