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KrishnaswamyLab / PHATE

PHATE (Potential of Heat-diffusion for Affinity-based Transition Embedding) is a tool for visualizing high dimensional data.
http://phate.readthedocs.io
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Purpose of Procrustes Analysis #83

Closed JoshuaHess12 closed 4 years ago

JoshuaHess12 commented 4 years ago

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 commented 4 years ago

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 commented 4 years ago

Hi @scottgigante ,

Great - that answered my question. Thank you!