Geoscience Reference
In-Depth Information
subplot(1,3,3)
plot(1:3,pcs(:,3),'o'), axis([0.5 3.5 -1 1])
text((1:3)+0.2,pcs(:,3),minerals,'FontSize',14), hold
plot(0.5:3.5,zeros(4,1),'r'), title('PC 3')
h e loads of the minerals and their relationships to the PCs can be used to
interpret the relative (not absolute) inl uences of the dif erent source rocks.
PC
1
is characterized by strong positive contributions of minerals 1 and 3,
rel ecting a relatively strong inl uence of the i rst rock type as a source of the
sediments. An opposite sign for the contribution of mineral 2 to the sediment
rel ects either dif erent mobilization processes for this mineral within
the catchment area, or a dilution ef ect. h e second principal component
PC
2
is also dominated by minerals 1 and 3, but with opposite signs, while
mineral 2 has relatively little inl uence. h e third principal component PC
3
is inl uenced by all three minerals, with the same sign. An alternative way to
plot of the loads is as a bivariate plot of two principal components. We ignore
PC
3
at this point and concentrate on PC
1
and PC
2
. Remember to either close
the i gure window before plotting the loads or clear the i gure window using
clf
, in order to avoid integrating the new plot as a fourth subplot in the
previous i gure window.
plot(pcs(:,1),pcs(:,2),'o'), hold on
text(pcs(:,1)+0.02,pcs(:,2),minerals,'FontSize',14)
plot([-1 1],[0 0],'r')
plot([0 0],[-1 1],'r')
xlabel('First Principal Component Loads')
ylabel('Second Principal Component Loads')
hold off
We can now observe in a single plot the same relationships that have
previously been shown in several graphics (Fig. 9.3). It is also possible to plot
the data set as functions of the new variables (the source rocks). h is requires
the second output of
pca
, containing the principal component scores.
plot(newx(:,1),newx(:,2),'+'), hold on
text(newx(:,1)+2,newx(:,2),samples,'FontSize',14)
plot([-400 400],[0 0],'r')
plot([0 0],[-150 300],'r')
xlabel('First Principal Component Scores')
ylabel('Second Principal Component Scores')
hold off
h is plot clearly dei nes groups of samples with similar inl uences, e.g.,
samples 19, 20 and 26, and possibly also sample 18. We next use the third
output from the function
pca
to compute the variances of the PCs.
percent_explained = 100*variances/sum(variances)
