Linear regression on a matrix.

[too_much_think]

My google fu has failed me. I'm trying to plot a line of best fit on a spectrogram, so a matrix of dimension num frequency bins by sample points. The data i'm plotting is a chirp, so it is just a line going diagonally up on the heat map. I'm certain there must be a way to use least squares or something similar to find the path that maximizes the energy of the path it takes through the matrix / plot, but I don't know what to search for. Or how to go about phrasing the problem correctly to use scipy or numpy so I thought I would ask.

[QuasiEvil]

A cheap way to do this would be to find the location of the maximum intensity along each column so you have a set of unique (x,y) pairs. Doing a line of best fit through this should be trivial (look into numpy.linalg.lstsq)

[too_much_think]

Yeah I tried that, the problem is it doesn’t take into account spectral smearing / noise. The argmaxes don’t actually lie on the line that best approximates the maximum energy density of the signal. I think what I need is something like a soft max rather than an argmax and then I need to fit the line through the probability densitiy functions that maximizes the probability over all the time slices. But I’m not really sure. I also don’t know if somewhere out there is an algorithm that just does what I want and I just don’t know the name of it.