CODEWITHSUNDEEP
pythonmachine-learningdimensionality-reduction
Cortexelus
Cortexelus

Reputation: 341

Circular Dimensionality Reduction?

I want dimensionality reduction such that dimensions it returns are circular.

ex) If I reduce 12d data to 2d, normalized between 0 and 1, then I want (0,0) to be as equally close to (.1,.1) as (.9,.9).

What is my algorithm? (bonus points for python implementation)

PCA gives me 2d plane of data, whereas I want spherical surface of data.

Make sense? Simple? Inherent problems? Thanks.

Upvotes: 6

Views: 555

Answers (1)

embert
embert

Reputation: 7592

I think what you ask is all about transformation.

Circular

I want (0,0) to be as equally close to (.1,.1) as (.9,.9).

PCA

Taking your approach of normalization what you could do is to map the values in the interval from [0.5, 1] to [0.5, 0]

MDS

If you want to use a distance metric, you could first compute the distances and then do the same. For instance taking the correlation, you could do 1-abs(corr). Since the correlation is between [-1, 1] positive and negative correlations will give values close to zero, while non correlated data will give values close to one. Then, having computed the distances you use MDS to get your projection.

Space

PCA gives me 2d plane of data, whereas I want spherical surface of data.

Since you want a spherical surface you can directly transform the 2-d plane to a sphere as I think. A spherical coordinate system with a constant Z would do that, wouldn't it?

Another question is then: Is all this a reasonable thing to do?

Upvotes: 0

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