22 mar. 2015

Mahalanobis in PC space (removing redundat)

In a previous post, we used "prospectr", with the duplex function to select a training set (30 samples), in order to spend less money in lab analysis. This way, we remove redundants spectra, and the selected spectra are well dispersing all around the PC space. Redundant were discarded according to its Neighborhood Mahalanobis distance.
In this plot, we can see the selected samples (red ones), and a Mahalanobis ellipse, considering all the samples with the "drawMahal" function from the package "chemometrics".

If we consider just the red samples (the 30 samples for the training set), the center of the population will be different that with all the samples (156), so we have to calculate the PCs again (their orientation will change), and we can draw a new Mahalanobis  ellipse (97.5 quantile).

As we can see in the plots,  removing the redundantswill give more weigth to the extreme samples, to be retained, and not be consider as outliers.

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