Create exact Principal Geodesic Analysis on the hyberbolic plane #1969
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## main #1969 +/- ##
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+ Coverage 91.53% 91.64% +0.12%
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Files 151 150 -1
Lines 13843 13834 -9
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Thanks @alebrigant! Looking forward for your comments on the questions I've raised.
geomstats/learning/pca.py
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| 8000 | costs = self.space_ext.metric.dist(mn_ext, projections) ** 2 | |
| return gs.sum(costs) | ||
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| costs = [ |
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we can probably vectorize here. (I can help you out)
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Can't vectorize actually. I think this is the best implementation.
geomstats/learning/pca.py
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| angles_half_space = gs.linspace(0.0, 2 * gs.pi, self.n_vec) | ||
| angles_half_space = gs.expand_dims(angles_half_space, axis=1) | ||
| vectors_half_space = gs.hstack( | ||
| (gs.cos(angles_half_space), gs.sin(angles_half_space)) | ||
| ) | ||
| norms = self.half_space.metric.norm(vectors_half_space, mean_half_space) | ||
| vectors_half_space = gs.einsum("ij,i->ij", vectors_half_space, 1 / norms) | ||
| vectors_ext = self.space.half_space_to_extrinsic_tangent( | ||
| vectors_half_space, mean_half_space | ||
| ) |
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What would be the difference if we get only the last tangent vector from vectors_half_space, transform it to extrinsic, get the geodesic function directly from extrinsic, and then sample it uniformly between 0 and 1 with n_vec?
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The difference is that you need to sample from tangent vectors in the extrinsic tangent space and I wanted to go fast so I didn't write down the formula (no need to look for one in the half-space). But it should certainly be changed at some point.
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@alebrigant, a couple of very small changes due to naming and ready to go from my side.
geomstats/learning/pca.py
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| costs = self.space_ext.metric.dist(mn_ext, projections) ** 2 | ||
| return gs.sum(costs) | ||
|
|
||
| costs = [ |
There was a problem hiding this comment.
Can't vectorize actually. I think this is the best implementation.
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This PR:
TODO: