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Karl Pearson method for fitting multi-planes to data points?

Posted 2 years ago
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Is there a Mathematica routine for the best least squares fit of an m-dimension multiplane to a set of data points in n-dimensional space? The method of Karl Pearson works in such a way that the m-dimensional fit is defined by m+1 points and by dropping the last point we have the best (m-1)-multiplane fit and so on until the first point gives the centroid of the data points.

2 Replies
Posted 2 years ago

Karl Pearson had a lot of methods. Do you mean what is described in

Pearson, K. (1901), On Lines and Planes of Closest Fit to Systems of Points in Space

Thank you for your reply Jim.

Yes, the paper is

Karl Pearson, 'On Lines and Planes of Closest Fit to Systems of Points in Space' [Philosophical Magazine 2:559-572, 1901]

I don't have access to the paper but the situation is this: I'm helping John Browne with his Grassmann Algebra application. He already has an axiom based implementation of the Pearson method. However, whenever I can, I like to make connection to the Mathematica array routines because they provide increased efficiency, especially on numerical problems. But I'm not familiar with all the statistical routines.

The method returns an exterior product in which the first factor is the centroid point (which is the best fit to a point) and then a series of normalized vectors which extend the fit to a line, then a plane, then a 3D multiplane etc., until the full dimension of the space is reached when the fit is trivially perfect. The lesser dimension fits are all subsets of the higher dimension fits.

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