Monday, December 24, 2007

[Math4u] Re: Visualization of n-dimensional space

--- In Math4u@yahoogroups.com, renato ab <renato_eq@...> wrote:
>
> Maybe you can use techniques to reduce the number of input
variables. An example is PCA (principal components analysis).
> If you don't know about this, I suggest you to read some simple
tutorial. I can't find anyone I've read, but you can search for
something on Google. Try that ones without many formulas, just to
know about the technique.
> If you think this can help you, you can use the software Minitab.
If you want some help using the software, you can tell me.
>
>

Hi Renato,

Thanks for your answer. I made a PCA analysis of my data with the
sofware called StatisticXL.

The result is like this. I have reduced the number of variables, in
fact I have 13 Principal Components (PC) and about 80 inputs.

Explained Variance (Eigenvalues)
Value PC 1 PC 2 PC 3
Eigenvalue 29.405 8.662 6.792
% of Var. 34.594 10.191 7.991
Cum. % 34.594 44.785 52.776

Component Loadings
(correlations between initial variables and principal components)

Variable PC 1 PC 2 PC 3
input1 -0.009 0.038 0.029
input2 0.039 0.061 0.608
input3 0.041 0.072 0.620
input4 -0.066 0.017 0.559

Component Score Coefficients (Eigenvectors)
Variable PC 1 PC 2 PC 3
input1 -0.002 0.013 0.011
input2 0.007 0.021 0.233
input3 0.008 0.024 0.238
input4 -0.012 0.006 0.215

Can I use this data to find areas of the total space where the
probability to get "1" as output is maximum or at least big?

Thanks again.


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