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Riemannian Measure μ ? #24
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Hi,
Realizing I never responded to this: terribly sorry. I think you are correct in your assessment.
For fixed bandwith kernels I think you are correct. Then the generator is given by
(D_p^{-1} K - I) / e, where p is the row-sum of K. It is easy to see that p is then a left-eigenvector of the generator. For variable-bandwidth kernels we later left-multiply by(1/h(x)^2)whereh(x)is the bandwidth function. Then, to construct the density you would need to take the output of _left_normalize and divide byh(x)^2, I believe. Hope that helps, and sorry again for the delay.
Hello,
Thank you for the wonderful library! I have a question regarding how to obtain the Riemannian Measure / Volume Element μ, also called the leading-left eigenvector of the transition probability matrix μP = μ.
In the original NLSA paper page 3, column 2, paragraph 2 and algorithm page 4, line 40, μ is given explicitly.
Am I correct in thinking that this quantity is calculated as the reciprocal of
row_sumon line 136 ofdiffusion_map.pyduring the_left_normalizefunction, and subsequently discarded?Thank you for any assistance.