我一直在使用Scikit-learn的GMM功能。首先，我已经沿着x=y行创建了一个发行版。
from sklearn import mixture
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
line_model = mixture.GMM(n_components = 99)
#Create evenly distributed points between 0 and 1.
xs = np.linspace(0, 1, 100)
ys = np.linspace(0, 1, 100)
#Create a distribution that's centred along y=x
line_model.fit(zip(xs,ys))
plt.plot(xs, ys)
plt.show()
这将产生预期的分布：
接下来，我将其适合GMM并绘制结果：
#Create the x,y mesh that will be used to make a 3D plot
x_y_grid = []
for x in xs:
for y in ys:
x_y_grid.append([x,y])
#Calculate a probability for each point in the x,y grid.
x_y_z_grid = []
for x,y in x_y_grid:
z = line_model.score([[x,y]])
x_y_z_grid.append([x,y,z])
x_y_z_grid = np.array(x_y_z_grid)
#Plot probabilities on the Z axis.
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(x_y_z_grid[:,0], x_y_z_grid[:,1], 2.72**x_y_z_grid[:,2])
plt.show()
所得的概率分布在
x=0和x=1上具有一些怪异的尾巴，并且在角上还具有额外的概率（x = 1，y = 1和x = 0，y = 0）。使用n_components = 5也会显示此行为：
这是GMM所固有的，还是实现方面存在问题，或者我做错了什么？
编辑：从模型获得分数似乎摆脱了这种行为-这应该是吗？
我正在同一数据集上训练两个模型（x = y从x = 0到x = 1）。通过gmm的
score方法简单地检查概率似乎可以消除这种边界效应。为什么是这样？我已经附上了下面的图和代码。# Creates a line of 'observations' between (x_small_start, x_small_end)
# and (y_small_start, y_small_end). This is the data both gmms are trained on.
x_small_start = 0
x_small_end = 1
y_small_start = 0
y_small_end = 1
# These are the range of values that will be plotted
x_big_start = -1
x_big_end = 2
y_big_start = -1
y_big_end = 2
shorter_eval_range_gmm = mixture.GMM(n_components = 5)
longer_eval_range_gmm = mixture.GMM(n_components = 5)
x_small = np.linspace(x_small_start, x_small_end, 100)
y_small = np.linspace(y_small_start, y_small_end, 100)
x_big = np.linspace(x_big_start, x_big_end, 100)
y_big = np.linspace(y_big_start, y_big_end, 100)
#Train both gmms on a distribution that's centered along y=x
shorter_eval_range_gmm.fit(zip(x_small,y_small))
longer_eval_range_gmm.fit(zip(x_small,y_small))
#Create the x,y meshes that will be used to make a 3D plot
x_y_evals_grid_big = []
for x in x_big:
for y in y_big:
x_y_evals_grid_big.append([x,y])
x_y_evals_grid_small = []
for x in x_small:
for y in y_small:
x_y_evals_grid_small.append([x,y])
#Calculate a probability for each point in the x,y grid.
x_y_z_plot_grid_big = []
for x,y in x_y_evals_grid_big:
z = longer_eval_range_gmm.score([[x, y]])
x_y_z_plot_grid_big.append([x, y, z])
x_y_z_plot_grid_big = np.array(x_y_z_plot_grid_big)
x_y_z_plot_grid_small = []
for x,y in x_y_evals_grid_small:
z = shorter_eval_range_gmm.score([[x, y]])
x_y_z_plot_grid_small.append([x, y, z])
x_y_z_plot_grid_small = np.array(x_y_z_plot_grid_small)
#Plot probabilities on the Z axis.
fig = plt.figure()
fig.suptitle("Probability of different x,y pairs")
ax1 = fig.add_subplot(1, 2, 1, projection='3d')
ax1.plot(x_y_z_plot_grid_big[:,0], x_y_z_plot_grid_big[:,1], np.exp(x_y_z_plot_grid_big[:,2]))
ax1.set_xlabel('X Label')
ax1.set_ylabel('Y Label')
ax1.set_zlabel('Probability')
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
ax2.plot(x_y_z_plot_grid_small[:,0], x_y_z_plot_grid_small[:,1], np.exp(x_y_z_plot_grid_small[:,2]))
ax2.set_xlabel('X Label')
ax2.set_ylabel('Y Label')
ax2.set_zlabel('Probability')
plt.show()
最佳答案
配合没有问题，但您使用的是可视化。提示应该是将（0,1,5）连接到（0,1,0）的直线，它实际上只是两个点的连接的呈现（这是由于读取点的顺序而引起的） 。尽管极值的两个点都在您的数据中，但实际上这条线上没有其他点。
就个人而言，出于上述原因，我认为使用3d图（导线）来表示表面是一个相当糟糕的主意，我建议使用表面图或轮廓图。
尝试这个：
from sklearn import mixture
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
line_model = mixture.GMM(n_components = 99)
#Create evenly distributed points between 0 and 1.
xs = np.atleast_2d(np.linspace(0, 1, 100)).T
ys = np.atleast_2d(np.linspace(0, 1, 100)).T
#Create a distribution that's centred along y=x
line_model.fit(np.concatenate([xs, ys], axis=1))
plt.scatter(xs, ys)
plt.show()
#Create the x,y mesh that will be used to make a 3D plot
X, Y = np.meshgrid(xs, ys)
x_y_grid = np.c_[X.ravel(), Y.ravel()]
#Calculate a probability for each point in the x,y grid.
z = line_model.score(x_y_grid)
z = z.reshape(X.shape)
#Plot probabilities on the Z axis.
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, z)
plt.show()
从学术角度来看，我对使用2D混合模型在2D空间中拟合1D线的目标感到非常不自在。使用GMM进行流形学习至少需要法线方向具有零方差，从而减小了狄拉克分布。在数值和分析上，这是不稳定的，应避免（gmm拟合似乎存在一些稳定技巧，因为模型的法线在直线法线方向上相当大）。
还建议在绘制数据时使用
plt.scatter而不是plt.plot，因为在拟合点的联合分布时没有理由连接点。希望这有助于阐明您的问题。
关于python - 高斯混合模型(GMM)不合适，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/24174349/