我正在尝试使用拟合高斯总和scikit学习 http://scikit-learn.org/stable/index.html因为 scikit-learn高斯混合 http://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture.fit看起来比使用 curve_fit 更稳健。
Problem：它在拟合单个高斯峰值的截断部分方面效果不佳：
from sklearn import mixture
import matplotlib.pyplot
import matplotlib.mlab
import numpy as np
clf = mixture.GaussianMixture(n_components=1, covariance_type='full')
data = np.random.randn(10000)
data = [[x] for x in data]
clf.fit(data)
data = [item for sublist in data for item in sublist]
rangeMin = int(np.floor(np.min(data)))
rangeMax = int(np.ceil(np.max(data)))
h = matplotlib.pyplot.hist(data, range=(rangeMin, rangeMax), normed=True);
plt.plot(np.linspace(rangeMin, rangeMax),
mlab.normpdf(np.linspace(rangeMin, rangeMax),
clf.means_, np.sqrt(clf.covariances_[0]))[0])
gives
now changing data = [[x] for x in data] to data = [[x] for x in data if x <0] in order to truncate the distribution returns
Any ideas how to get the truncation fitted properly?
Note：分布不一定会在中间被截断，可能会剩下完整分布的 50% 到 100% 之间的内容。
如果有人能给我指出替代方案，我也会很高兴。我只尝试过 curve_fit 但一旦涉及两个以上的峰值就无法让它做任何有用的事情。
有点英国式，但简单的解决方案是将曲线分成两半（data = [[x] for x in data if x < 0]），镜像左侧部分（data.append([-data[d][0]])）然后进行常规高斯拟合。
import numpy as np
from sklearn import mixture
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
np.random.seed(seed=42)
n = 10000
clf = mixture.GaussianMixture(n_components=1, covariance_type='full')
#split the data and mirror it
data = np.random.randn(n)
data = [[x] for x in data if x < 0]
n = len(data)
for d in range(n):
data.append([-data[d][0]])
clf.fit(data)
data = [item for sublist in data for item in sublist]
rangeMin = int(np.floor(np.min(data)))
rangeMax = int(np.ceil(np.max(data)))
h = plt.hist(data[0:n], bins=20, range=(rangeMin, rangeMax), normed=True);
plt.plot(np.linspace(rangeMin, rangeMax),
mlab.normpdf(np.linspace(rangeMin, rangeMax),
clf.means_, np.sqrt(clf.covariances_[0]))[0] * 2)
plt.show()