python - 如何在Python中使用高斯kde内核设置带宽来平滑线条

Question

我正在尝试使用 python gaussian_kde 平滑以下数据，但是它无法正常工作，看起来 kde 正在对整个数据集的分布进行重新采样，而不是对每个点使用带宽并给出权重平滑

from scipy.stats import gaussian_kde
import matplotlib.pyplot as plt
import numpy as np
y=[ 191.78 ,   191.59,    191.59,    191.41,    191.47,    191.33,    191.25  \
  ,191.33 ,   191.48 ,   191.48,    191.51,    191.43,    191.42,    191.54    \
  ,191.5975,  191.555,   191.52 ,   191.25 ,   191.15  ,  191.01  ]
x = np.linspace(1 ,20,len(y))
kde= gaussian_kde(y)
kde.set_bandwidth(bw_method=kde.factor / 3)

fig, ax = plt.subplots(figsize=(10, 10))
ax.legend(loc='center left', bbox_to_anchor=(1.05, 0.5), frameon=False)
ax.scatter(x, y, color='black', label='data')
ax.plot(x,y,color='red')
ax.plot(x,kde(x))

这是数据图表

Chart of the data without smoothing

您可以注意到图表并未平滑线条

Chart after smoothing

Answer 1

您认为 kde_gaussian 平滑了一条线，但它实际上所做的是平滑数据集的密度分布估计。您的数据不是这样的数据集，而是 x/y 坐标。

以下是平滑线性数据的一些方法示例:

#from scipy.stats import gaussian_kde
import matplotlib.pyplot as plt
import numpy as np

from scipy import interpolate

from scipy import ndimage

y=[ 191.78 ,   191.59,    191.59,    191.41,    191.47,    191.33,    191.25  \
  ,191.33 ,   191.48 ,   191.48,    191.51,    191.43,    191.42,    191.54    \
  ,191.5975,  191.555,   191.52 ,   191.25 ,   191.15  ,  191.01  ]
x = np.linspace(1 ,20,len(y))

# convert both to arrays
x_sm = np.array(x)
y_sm = np.array(y)

# resample to lots more points - needed for the smoothed curves
x_smooth = np.linspace(x_sm.min(), x_sm.max(), 200)

# spline - always goes through all the data points x/y
y_spline = interpolate.spline(x, y, x_smooth)

spl = interpolate.UnivariateSpline(x, y)

sigma = 2
x_g1d = ndimage.gaussian_filter1d(x_sm, sigma)
y_g1d = ndimage.gaussian_filter1d(y_sm, sigma)

fig, ax = plt.subplots(figsize=(10, 10))
ax.legend(loc='center left', bbox_to_anchor=(1.05, 0.5), frameon=False)

plt.plot(x_sm, y_sm, 'green', linewidth=1)
plt.plot(x_smooth, y_spline, 'red', linewidth=1)
plt.plot(x_smooth, spl(x_smooth), 'yellow', linewidth=1)
plt.plot(x_g1d,y_g1d, 'magenta', linewidth=1)

plt.show()

情节如下:

绿色是原始数据，红色是样条线，黄色是 UnivariateSpline，洋红色是 gaussian_1d 滤波后的数据。如果您查找这些函数，可能会发现诸如 sigma 之类的参数，您可以更改这些参数以进一步平滑数据。谷歌一下文档。