如何创建适合高斯分布的 3D 数据集

Question

我正在尝试创建适合高斯分布的数据集。 x 和 y 值将相同，并且在 z 轴上，这些值将符合高斯分布。将此站点作为自己的资源：https://towardsdatascience.com/a-python-tutorial-on-generating-and-plotting-a-3d-guassian-distribution-8c6ec6c41d03 I wrote the following code. But unfortunately, the output I got was not like the one in the link I gave. I think there is an error with the mathematical formulas. I would be very happy if you could help me fix it. While I was waiting for a graph like this I got that kind of graph.

提前致谢。

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

def np_bivariate_normal_pdf(domain, mean, variance):
  X = np.arange(-domain+mean, domain+mean, variance)
  Y = np.arange(-domain+mean, domain+mean, variance)
  X, Y = np.meshgrid(X, Y)
  R = np.sqrt(X**2 + Y**2)
  Z = ((1. / np.sqrt(2 * np.pi)) * np.exp(-.5*R**2))

  return X, Y, Z

    
def plt_plot_bivariate_normal_pdf(x, y, z):
  fig = plt.figure(figsize=(10, 10))
  ax = fig.gca(projection='3d')
  ax.plot_surface(x, y, z, 
                  cmap=cm.coolwarm,
                  linewidth=0, 
                  antialiased=True)
  ax.set_xlabel('x')
  ax.set_ylabel('y')
  ax.set_zlabel('z');
  ax.set_xlim(-5, +20)
  ax.set_ylim(-5, +20)
  plt.show()
  
a = np_bivariate_normal_pdf(0.75, 5, 0.01)
b = np_bivariate_normal_pdf(1.875, 3, 0.025)
c = np_bivariate_normal_pdf(1.5, 7.5, 0.02)
d = np_bivariate_normal_pdf(2.25, 12, 0.03)

plt_plot_bivariate_normal_pdf(*a)
plt_plot_bivariate_normal_pdf(*b)
plt_plot_bivariate_normal_pdf(*c)
plt_plot_bivariate_normal_pdf(*d)

Answer 1

函数 np_bivariate_normal_pdf() 使用一维正态分布的公式，而您打算计算已实现多元正态分布的 multivariate normal distribution. The multivariate distribution depends on a mean which is a vector (this determines where the peak of the graph is located), and a covariance matrix (which controls how steep the graph is as you approach the peak from different sides). In your function both mean and variance are numbers, and the formula you are using actually does not involve these parameters at all. You can change your code to fix it, or you can use one of several Python libraries (e.g. scipy.stats)。

如何创建适合高斯分布的 3D 数据集

How to create 3D data set suitable for Gaussian Distribution

python

numpy

matplotlib

dataset

gaussian