Purpose of Procrustes Analysis

[JoshuaHess12]

Hi there,

I am using PHATE on data sets with much success, and I am looking to understand the purpose of the procrustes analysis between the classical MDS embedding and the metric MDS embedding in the embed_mds function. This is not necessarily an issue, but I couldn't find any documentation in the paper "Visualizing structure and transitions in high-dimensional biological data" on the matter.

Thank you!
Josh

[scottgigante]

Hi @JoshuaHess12 ,

This was a recent addition as a result of the switch from using the sklearn SMACOF implementation of MDS to using a stochastic gradient descent implementation which was done after publication. SGD is faster, but it sometimes produces results that are rotated by 90 or 180 degrees, depending on random seed. To produce a more stable output, I rotate the output to match the classic MDS initialisation using Procrustes.

[JoshuaHess12]

Hi @scottgigante ,

Great - that answered my question. Thank you!