[R] - ICA for less common data
Monica Pisica
pisicandru at hotmail.com
Mon Apr 30 14:13:41 CEST 2007
Hi everyone,
I am not sure this is the appropriate list I should put this question to,
but I hope you will re-direct me to the most appropriate one if necessary.
I am doing an independent component analysis on a dataset that represents
different metrics for patchreefs such as depth, area, volume, relative
relief, shape index and rugosity. Doing different multivariate analyses and
correlations among variables we discovered that the average reef depth data
is heavily bi-modal, and rugosity behaves differently in each of the depth
populations. Other reef metrics behave differently with depth as well. Since
not all metrics are really independent we did a PCA analysis followed by
cluster analysis and we tried to compare the results with the results from
the depth analysis. It was not too conclusive I am afraid, and trying to
understand the results I came across independent component analysis (ICA).
So ….. I’ve run it on a combination of principal components and it seems
that certainly we have 2 independent components that keep popping up (if I
can use this expression) when we run the analysis with 2, 3, or 4
components. So I guess these 2 components are the strongest ones …. If I can
say so. My next question is …. How can I relate these 2 components to the
initial data??? I’ve plotted each component and if I add a loess line to
each, visually it seems that one independent component is an unknown
function of rugosity while the other component is an unknown function of
reef geometry and depth. But, of course, I would like something more than a
visual similarity. Also the 2 independent components seem to split the data
in 3 classes, rather than 2, as the analysis of the depth data suggested.
Looking back at the depth histogram it is obvious that there are some data
that actually are not quite modeled by the 2 mixing functions I came up
with. These data correspond to the deepest patch reefs, a category clearly
singled out by ICA classification. The bottom line is that I am trying to
understand what each independent component tells me about the patch reefs
and how I can relate that to the patch reef morphometrics, biology, other
factors that impact some reefs but not others, etc.
If you have any clarifying thoughts or if you know about any other
literature about the subject that can help (except articles that deal with
ICA and image analysis or wave form data) I will really appreciate.
Thank you very much for your consideration,
Monica
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