Page 223 - MATLAB Recipes for Earth Sciences

9.2 Principal Component Analysis 219

we observe that PC (first column) has high negative loads in the fi rst three
1

variables amp, pyr and pla (first to third row), and high positive loads in the
fi fth variable qtz (fifth row). PC (second column) has high negative loads in

2
the vein minerals fl u, sph and gal, and again a positive load in qtz. We create
a number of plots of the PCs, where we also observe significant loads of the

other PCs.
subplot(2,2,1),plot(1:9,pcs(:,1),'o'),axis([1 9 -1 1])
text((1:9)+0.2,pcs(:,1),minerals,'FontSize',8),hold
plot(1:9,zeros(9,1),'r'), title('PC 1')
subplot(2,2,2),plot(1:9,pcs(:,2),'o'),axis([1 9 -1 1])
text((1:9)+0.2,pcs(:,2),minerals,'FontSize',8),hold
plot(1:9,zeros(9,1),'r'),title('PC 2')

subplot(2,2,3),plot(1:9,pcs(:,3),'o'),axis([1 9 -1 1])
text((1:9)+0.2,pcs(:,3),minerals,'FontSize',8),hold
plot(1:9,zeros(9,1),'r'),title('PC 3')
subplot(2,2,4),plot(1:9,pcs(:,4),'o'),axis([1 9 -1 1])
text((1:9)+0.2,pcs(:,4),minerals,'FontSize',8),hold
plot(1:9,zeros(9,1),'r'),title('PC 4')

The loads of the index minerals and their relationship to the PCs can be used
to interpret the relative influence of the source rocks. PC characterized by

1
strong contributions of amp, pyr and pla, and a contribution with opposite
sign of qtz probably describes the amount of magmatic rock clasts in the
sediment. The second principal component PC is clearly dominated by hy-
2
drothermal minerals hence suggesting the detrital input from the vein. PC
3
and PC show a mixed and contradictory pattern of loads and are therefore
4
not easy to interpret. We will see later that this observation is in line with a
rather weak and mixed signal from the sandstone source on the sediments.
An alternative way to plot of the loads is a bivariate plot of two principal
components. We ignore PC and PC at this point and concentrate on PC
3 4 1
and PC .
2
plot(pcs(:,1),pcs(:,2),'o')
text(pcs(:,1)+0.02,pcs(:,2),minerals,'FontSize',14), hold
x=get(gca,'XLim'); y=get(gca,'YLim');
plot(x,zeros(size(x)),'r')
plot(zeros(size(y)),y,'r')
xlabel('First Principal Component Scores')
ylabel('Second Principal Component Scores')

Here we observe the same relationships on a single plot that were previously
shown on several graphs (Fig. 9.3). It is also possible to plot the data set as
functions of the new variables. This needs the second output of princomp