Python数据可视化:幂律分布实例详解

#!/usr/bin/env python
# -*-coding:utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model
from scipy.stats import norm

def DataGenerate():
 X = np.arange(10, 1010, 10) # 0-1，每隔着0.02一个数据 0处取对数,会时负无穷 生成100个数据点
 noise=norm.rvs(0, size=100, scale=0.2) # 生成50个正态分布 scale=0.1控制噪声强度
 Y=[]
 for i in range(len(X)):
  Y.append(10.8*pow(X[i],-0.3)+noise[i]) # 得到Y=10.8*x^-0.3+noise

 # plot raw data
 Y=np.array(Y)
 plt.title("Raw data")
 plt.scatter(X, Y, color='black')
 plt.show()

 X=np.log10(X) # 对X，Y取双对数
 Y=np.log10(Y)
 return X,Y

def DataFitAndVisualization(X,Y):
 # 模型数据准备
 X_parameter=[]
 Y_parameter=[]
 for single_square_feet ,single_price_value in zip(X,Y):
  X_parameter.append([float(single_square_feet)])
  Y_parameter.append(float(single_price_value))

 # 模型拟合
 regr = linear_model.LinearRegression()
 regr.fit(X_parameter, Y_parameter)
 # 模型结果与得分
 print('Coefficients: \n', regr.coef_,)
 print("Intercept:\n",regr.intercept_)
 # The mean square error
 print("Residual sum of squares: %.8f"
  % np.mean((regr.predict(X_parameter) - Y_parameter) ** 2)) # 残差平方和

 # 可视化
 plt.title("Log Data")
 plt.scatter(X_parameter, Y_parameter, color='black')
 plt.plot(X_parameter, regr.predict(X_parameter), color='blue',linewidth=3)

 # plt.xticks(())
 # plt.yticks(())
 plt.show()

if __name__=="__main__":
 X,Y=DataGenerate()
 DataFitAndVisualization(X,Y)