Geoscience Reference
In-Depth Information
title('IC2')
subplot(3,1,3)
plotyy(1:30,sica(:,1),1:30,s3)
title('IC3')
h e ICA has identii ed the source signals almost perfectly. We notice that the
descending order of the ICs is dif erent from the initial order of
s1
,
s2
and
s3
, which is due to the commutativity of addition. In real-world examples, of
course, the order of the ICs is not relevant. Furthermore, the exact sign and
amplitude does not match the original values and the ICA therefore yields
only semi-quantitative results, as was also the case for the PCA. Finally, we
can actually compute the mixing matrix
a_ica
and the separation matrix
w_
ica
using
a_ica = a_pca*B;
w_ica = B'*w_pca;
h e mixing matrix
a_ica
can be used to estimate the proportions of the
separated variables in our measurements. h e components
a
ij
of the mixing
matrix
a_ica
correspond to the principal component loads, as introduced in
Section 9.2. h e FastICA package is available for MATLAB and can be found
on A. Hyvärinen's webpage:
http://research.ics.aalto.fi/ica/fastica/
9.4 Discriminant Analysis
Discriminant analysis helps to assign objects to established categories or
groups. Examples include the assignment of fossil specimens to established
genera or species, the identii cation of rock types following mineralogical
(or chemical) analysis, and the mapping of vegetation types from satellite
images. Discriminant analysis is dif erent from simple classii cation, which
does not dei ne the number of groups or categories prior to the analysis.
h e classic example of a discriminant analysis in petrography is the QAPF
or Streckeisen diagram (Streckeisen 1974, 1976). h is diagram categorizes
igneous rocks (especially plutonic rocks) by their percentages of quartz (Q),
alkali feldspar (including albite) (A), plagioclase (P), and feldsparthoids (F),
normalized a total of 100%. h e QAPF diagram displays the percentages of
the four minerals in a double ternary plot, with QAP percentages in the upper
half of the graphics and FAP percentages in the lower half. h e QAPF diagram
is commonly used by the International Union of Geological Sciences (IUGS)
to classify plutonic rocks: e.g., a plutonic rock with 50% quartz, 30% alkali
feldspar, 20% plagioclase and 0% feldsparthoids is termed a granite. Whereas
Albert Streckeisen's dei nition of plutonic rocks represents compromises
