Using Gaussian Mixture for 1D array in python sklearn

Question

I would like to use a Gaussian mixture model to return something like the image below except proper Gaussians.

I'm attempting to use python sklearn.mixture.GaussianMixture but I have failed. I can treat each peak as though it were the height of a histogram for any given x value. My question is: do I have to find a way to transform this graph into a histogram and remove the negative values, or is there a way to apply GMM directly onto this array to produce the red and green gaussians?

Answer 1

There is a difference between fitting a curve to pass through a set of points using a Gaussian curve and modeling a probability distribution of some data using GMM.

When you use GMM you are doing the later, and it won't work.

• If you apply GMM using only the variable on the Y axis you will get a Gaussian distribution of Y that does not take into account the X variable.
• If you apply GMM using 2 variables you will get bi dimensional Gaussians that won't be of any help for your problem.

Now if what you want is to fit a Gaussian curve. Try the answer to this question.

import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# Define some test data which is close to Gaussian
data = numpy.random.normal(size=10000)

hist, bin_edges = numpy.histogram(data, density=True)
bin_centres = (bin_edges[:-1] + bin_edges[1:])/2

# Define model function to be used to fit to the data above:
# Adapt it to as many gaussians you may want
# by copying the function with different A2,mu2,sigma2 parameters
def gauss(x, *p):
    A, mu, sigma = p
    return A*numpy.exp(-(x-mu)**2/(2.*sigma**2))

# p0 is the initial guess for the fitting coefficients (A, mu and sigma above)
p0 = [1., 0., 1.]

coeff, var_matrix = curve_fit(gauss, bin_centres, hist, p0=p0)

# Get the fitted curve
hist_fit = gauss(bin_centres, *coeff)

plt.plot(bin_centres, hist, label='Test data')
plt.plot(bin_centres, hist_fit, label='Fitted data')

# Finally, lets get the fitting parameters, i.e. the mean and standard deviation:
print 'Fitted mean = ', coeff[1]
print 'Fitted standard deviation = ', coeff[2]

plt.show()

Update on how to adapt the code for multiple gaussians:

def gauss2(x, *p):
    A1, mu1, sigma1, A2, mu2, sigma2 = p
    return A1*numpy.exp(-(x-mu1)**2/(2.*sigma1**2)) + A2*numpy.exp(-(x-mu2)**2/(2.*sigma2**2))

# p0 is the initial guess for the fitting coefficients initialize them differently so the optimization algorithm works better
p0 = [1., -1., 1.,1., -1., 1.]

#optimize and in the end you will have 6 coeff (3 for each gaussian)
coeff, var_matrix = curve_fit(gauss, X_data, y_data, p0=p0)

#you can plot each gaussian separately using 
pg1 = coeff[0:3]
pg2 = coeff[3:]

g1 = gauss(X_data, *pg1)
g2 = gauss(X_data, *pg2)

plt.plot(X_data, y_data, label='Data')
plt.plot(X_data, g1, label='Gaussian1')
plt.plot(X_data, g2, label='Gaussian2')