在python sklearn中为一维数组使用高斯混合

Question

我想使用高斯混合模型来返回类似于下图的图像，除了适当的高斯。

我正在尝试使用python sklearn.mixture.GaussianMixture，但失败了。对于任何给定的x值，我都可以将其视为直方图的高度。我的问题是：我是否必须找到一种方法将此图转换为直方图并去除负值，或者是否有办法将GMM直接应用于此数组以产生红色和绿色高斯？

Answer 1

拟合曲线以使用高斯曲线穿过一组点与建模某些数据的概率分布之间存在差异。

使用GMM时，您会做的比较晚，并且将无法使用。

• 如果仅使用Y轴上的变量来应用GMM，则会得到不考虑X变量的Y的高斯分布。
• 如果您使用2个变量应用GMM，您将获得二维高斯曲线，对您的问题没有任何帮助。

现在，如果要拟合高斯曲线。尝试回答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()

有关如何使代码适应多个高斯的更新：

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')