Geoscience Reference
In-Depth Information
subplot(1,3,1), hist(x(:,1))
subplot(1,3,2), hist(x(:,2))
subplot(1,3,3), hist(x(:,3))
We then display the proportions of the minerals in the thirty samples as a
time series, in two separate plots.
plot(x(:,1:3)), grid
legend('Min1','Min2','Min3')
xlabel('Sample ID')
ylabel('Quantity')
We begin with the unmixing of the variables using the PCA. We calculate
the principal components
pcs
, the mixing matrix
a_pca
, and the whitening
matrix
w_pca
using
[pcs,newx,variances] = pca(x);
newx = newx./repmat(std(newx),length(newx),1);
a_pca = pcs*sqrt(diag(variances));
w_pca = inv(sqrt(diag(variances)))*pcs';
h e pre-whitening reduces the unmixing into independent components (
S
)
to a problem of i nding a suitable rotation matrix
B
that can be applied to the
variables
X
PC
:
We need to i nd a rotation matrix
B
such that the variables
S
have a completely
non-Gaussian distribution. h ere are several possibilities for implementing
such a non-Gaussian criterion, such as minimizing or maximizing the excess
kurtosis,
because the excess kurtosis Ęł for normally distributed data is zero. Please
note that the excess kurtosis dif ers from the kurtosis: the excess kurtosis is
the kurtosis minus three, since the kurtosis of Gaussian-distributed data is
three (Section 3.2) but the excess kurtosis of such a distribution is zero. To
i nd a
B
that ensures a minimum or maximum excess kurtosis, a learning
algorithm can be used that i nds the i xed points of the learning rule
