Python 我如何沿着我的图表绘制一条线来显示哪里的数据密度最高

下面的使用测试数据集的示例显示了如何根据密度得出样本权重，然后将这些样本权重提供给曲线拟合算法.

示例数据集是嵌入噪声中的类二次曲线/密度:

我们可以使用skLearning的GaussianMixture对密度进行建模.它 for each 样本提供了一个分数，其中分数越高对应的区域越可能(即密度越大).

使用Scipy的curve_fit()来使用先前计算的采样权重来拟合二次曲线(Scipy将它们解释为误差条，因此使用1/sample_weights):

或者，使用SkLearning的SVR，它直接获取样本权重(尽管结果几乎相同):

叠加各个步骤:

import numpy as np
import matplotlib.pyplot as plt

#Make some test data - a quadratic curve embedded in noise
from sklearn.datasets import make_moons
X1, y1 = make_moons(500, noise=0.7, random_state=0)
X2, y2 = make_moons(500, noise=0.4, random_state=1)
X3, y3 = make_moons(600, noise=0.08, random_state=2)
X = np.concatenate([X1, X2, X3[y3==0]], axis=0)

#View the data
plt.scatter(X[:, 0], X[:, 1], marker='.', s=10)
plt.gca().set(xlabel='x0', ylabel='x1')
plt.gcf().set_size_inches(5, 3)

#Model the density
from sklearn.mixture import GaussianMixture
gmm = GaussianMixture(n_components=20, random_state=0).fit(X)

xx, yy = np.meshgrid(np.linspace(-2, 3), np.linspace(-3, 3))
log_scores = gmm.score_samples(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)
scores = np.exp(log_scores)

plt.contour(xx, yy, scores, levels=8, cmap='plasma_r', alpha=1)

#Get the density score for each datapoint
data_scores = np.exp(gmm.score_samples(X))
# can scale scores to max value = 1
data_scores /= data_scores.max()

#Fit quadratic curve using scipy's curve_fit
# supply 1/data_scores as the sample errors
from scipy.optimize import curve_fit

#Fit a quadratic curve
(A, B, C), _ = curve_fit(lambda x, A, B, C: A*x**2 + B*x + C, X[:, 0], X[:, 1], sigma=1 / data_scores)

x_axis = X[:, 0][np.argsort(X[:, 0])].reshape(-1, 1)

plt.plot(
    x_axis,
    A * x_axis**2 + B * x_axis + C,
    color='tab:brown', lw=10, alpha=0.3, label='curve_fit()'
)
plt.gcf().legend()

#Alternatively, using support vector regressor from sklearn
# Takes data_scores directly as relative sample weights
from sklearn.svm import SVR

#Quadratic curve, as before
svr = SVR(kernel='poly', degree=2).fit(X[:, [0]], X[:, 1], sample_weight=data_scores)
plt.plot(
    x_axis,
    svr.predict(x_axis),
    color='tab:purple', lw=10, alpha=0.35, label='SVR'
)

plt.gcf().legend()