Did you try applying sklearn's PCA to a subsampled dataset? Randomly sampling 1% of your dataset would probably allow you to find the first four principle components in less than 30 minutes.
It would be interesting to see whether these components are significantly different to the ones you got on the whole dataset.
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[ 3.3 ms ] story [ 22.9 ms ] threadhttp://bolt-project.org/ http://thunder-project.org/ http://lightning-viz.org/
and associated work going on at the Freeman lab at HMMI:
https://www.janelia.org/lab/freeman-lab
The Human Connectome Project's neuroimaging approach
http://www.nature.com/neuro/journal/v19/n9/full/nn.4361.html
It would be interesting to see whether these components are significantly different to the ones you got on the whole dataset.