[R] ICA for less common data

[Monica Pisica]

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 behaves 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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