Geoscience Reference
In-Depth Information
between the minerals revealed in the pairwise bivariate scatter plots, again
showing a strong negative correlation between the i rst and second mineral
(
r
=-0.8184), a weak positive correlation between minerals 1 and 3 (
r
=0.3483),
and a moderate negative correlation between minerals 2 and 3 (
r
=-0.5557).
h ese observed dependencies would lead us to expect interesting results
from the application of a PCA.
Various methods exist for scaling the original data before applying a PCA,
such as
mean centering
(using a mean equal to zero) or
standardizing
(using a
mean equal to zero and a standard deviation equal to one). We will, however
use the original data for computing the PCA. h e output of the function
pca
includes the principal component loads
pcs
, the scores
newx
, and the
variances
variances
. h e loads
pcs
are weights (or weighting factors) that
indicate the extent to which the old variables (the minerals) contribute to the
new variables (the principal components, or PCs). h e principal component
scores are the coordinates of the thirty samples in the new coordinate system
dei ned by the three principal components, PC
1
to PC
3
(stored in the three
columns of
pcs
), which we interpret as the three source rocks.
[pcs,newx,variances] = pca(x);
h e loads of the three principal components PC
1
to PC
3
can be shown by
typing
pcs(:,1:3)
ans =
0.6342 -0.5085 0.5825
-0.6215 0.1130 0.7753
0.4600 0.8536 0.2444
We observe that PC
1
(i rst column) has high positive loads in variables 1
and 3 (i rst and third rows), and a high negative load in variable 2 (second
row). PC
2
(second column) has a high negative load in variable 1 and a high
positive load in variable 3, while the load in variable 2 is close to zero. PC
3
(third column) has high loads in variables 1 and 2, with the load in variable 3
being relatively low but also positive. We create a number of plots to visualize
the PCs:
subplot(1,3,1)
plot(1:3,pcs(:,1),'o'), axis([0.5 3.5 -1 1])
text((1:3)+0.2,pcs(:,1),minerals,'FontSize',14), hold
plot(0.5:3.5,zeros(4,1),'r'), title('PC 1')
subplot(1,3,2)
plot(1:3,pcs(:,2),'o'), axis([0.5 3.5 -1 1])
text((1:3)+0.2,pcs(:,2),minerals,'FontSize',14), hold
plot(0.5:3.5,zeros(4,1),'r'), title('PC 2')
