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pythonnumpygaussiandata-fitting
Alex
Alex

Reputation: 61

Fitting 2D Gaussian to a 2D matrix of values

I'm trying to fit a gaussian to this set of data:

enter image description here

It is a 2D matrix with values (probability distribution). If I plot it in 3D it looks like:

enter image description here

As far as I understood from this other question (https://mathematica.stackexchange.com/questions/27642/fitting-a-two-dimensional-gaussian-to-a-set-of-2d-pixels) I need to compute the mean and the covariance matrix of my data and the Gaussian that I need will be exactly the one defined by that mean and covariance matrix.

However, I can not properly understand the code of that other question (as it is from Mathematica) and I am pretty stuck with statistics.

How would I compute in Python (Numpy, PyTorch...) the mean and the covariance matrix of the Gaussian?

I'm trying to avoid all these optimization frameworks (LSQ, KDE) as I think that the solution is much simpler and the computational cost is something that I have to take into account...

Thanks!

Upvotes: 1

Views: 1102

Answers (1)

Ian
Ian

Reputation: 333

Let's call your data matrix D with shape d x n where d is the data dimension and n is the number of samples. I will assume that in your example, d=5 and n=6, although you will need to determine for yourself which is the data dimension and which is the sample dimension. In that case, we can find the mean and covariance using the following code:

import numpy as np

n = 6
d = 5
D = np.random.random([d, n])

mean = D.mean(axis=1)
covariance = np.cov(D)

Upvotes: 1

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