我正在寻找一个函数,它将两个列表作为输入,并返回Pearson相关性,以及相关性的重要性。
当前回答
嗯,很多回复的代码都很长,很难读…
我建议在处理数组时使用numpy及其漂亮的特性:
import numpy as np
def pcc(X, Y):
''' Compute Pearson Correlation Coefficient. '''
# Normalise X and Y
X -= X.mean(0)
Y -= Y.mean(0)
# Standardise X and Y
X /= X.std(0)
Y /= Y.std(0)
# Compute mean product
return np.mean(X*Y)
# Using it on a random example
from random import random
X = np.array([random() for x in xrange(100)])
Y = np.array([random() for x in xrange(100)])
pcc(X, Y)
其他回答
一个替代方法可以是一个来自linreturn的本地scipy函数,它计算:
斜率:回归线的斜率 截距:回归线的截距 R-value:相关系数 p值:零假设为斜率为零的假设检验的双面p值 stderr:估计的标准错误
这里有一个例子:
a = [15, 12, 8, 8, 7, 7, 7, 6, 5, 3]
b = [10, 25, 17, 11, 13, 17, 20, 13, 9, 15]
from scipy.stats import linregress
linregress(a, b)
会回复你:
LinregressResult(slope=0.20833333333333337, intercept=13.375, rvalue=0.14499815458068521, pvalue=0.68940144811669501, stderr=0.50261704627083648)
Pearson相关性可以用numpy的corrcoef来计算。
import numpy
numpy.corrcoef(list1, list2)[0, 1]
如果你不喜欢安装scipy,我使用了这个快速的hack,稍微修改了Programming Collective Intelligence:
def pearsonr(x, y):
# Assume len(x) == len(y)
n = len(x)
sum_x = float(sum(x))
sum_y = float(sum(y))
sum_x_sq = sum(xi*xi for xi in x)
sum_y_sq = sum(yi*yi for yi in y)
psum = sum(xi*yi for xi, yi in zip(x, y))
num = psum - (sum_x * sum_y/n)
den = pow((sum_x_sq - pow(sum_x, 2) / n) * (sum_y_sq - pow(sum_y, 2) / n), 0.5)
if den == 0: return 0
return num / den
def pearson(x,y):
n=len(x)
vals=range(n)
sumx=sum([float(x[i]) for i in vals])
sumy=sum([float(y[i]) for i in vals])
sumxSq=sum([x[i]**2.0 for i in vals])
sumySq=sum([y[i]**2.0 for i in vals])
pSum=sum([x[i]*y[i] for i in vals])
# Calculating Pearson correlation
num=pSum-(sumx*sumy/n)
den=((sumxSq-pow(sumx,2)/n)*(sumySq-pow(sumy,2)/n))**.5
if den==0: return 0
r=num/den
return r
对此,我有一个非常简单易懂的解决方案。对于两个长度相等的数组,Pearson系数可以很容易地计算如下:
def manual_pearson(a,b):
"""
Accepts two arrays of equal length, and computes correlation coefficient.
Numerator is the sum of product of (a - a_avg) and (b - b_avg),
while denominator is the product of a_std and b_std multiplied by
length of array.
"""
a_avg, b_avg = np.average(a), np.average(b)
a_stdev, b_stdev = np.std(a), np.std(b)
n = len(a)
denominator = a_stdev * b_stdev * n
numerator = np.sum(np.multiply(a-a_avg, b-b_avg))
p_coef = numerator/denominator
return p_coef
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