numpy corrcoef - 在忽略缺失数据的同时计算相关矩阵

Question

我正在尝试计算多个值的相关矩阵。这些值包括一些 'nan' 值。我正在使用 numpy.corrcoef。对于输出相关矩阵的元素（i，j），我想使用变量 i 和变量 j 存在的所有值计算相关性。

这是我现在拥有的：

In[20]: df_counties = pd.read_sql("SELECT Median_Age, Rpercent_2008, overall_LS, population_density FROM countyVotingSM2", db_eng)
In[21]: np.corrcoef(df_counties, rowvar = False)
Out[21]: 
array([[ 1.        ,         nan,         nan, -0.10998411],
       [        nan,         nan,         nan,         nan],
       [        nan,         nan,         nan,         nan],
       [-0.10998411,         nan,         nan,  1.        ]])

nan 太多了:(

Answer 1

pandas 的主要特点之一是 NaN 友好。要计算相关矩阵，只需调用 df_counties.corr()。下面是一个例子来证明 df.corr() 是 NaN 宽容而 np.corrcoef 不是。

import pandas as pd
import numpy as np

# data
# ==============================
np.random.seed(0)
df = pd.DataFrame(np.random.randn(100,5), columns=list('ABCDE'))
df[df < 0] = np.nan
df

         A       B       C       D       E
0   1.7641  0.4002  0.9787  2.2409  1.8676
1      NaN  0.9501     NaN     NaN  0.4106
2   0.1440  1.4543  0.7610  0.1217  0.4439
3   0.3337  1.4941     NaN  0.3131     NaN
4      NaN  0.6536  0.8644     NaN  2.2698
5      NaN  0.0458     NaN  1.5328  1.4694
6   0.1549  0.3782     NaN     NaN     NaN
7   0.1563  1.2303  1.2024     NaN     NaN
8      NaN     NaN     NaN  1.9508     NaN
9      NaN     NaN  0.7775     NaN     NaN
..     ...     ...     ...     ...     ...
90     NaN  0.8202  0.4631  0.2791  0.3389
91  2.0210     NaN     NaN  0.1993     NaN
92     NaN     NaN     NaN  0.1813     NaN
93  2.4125     NaN     NaN     NaN  0.2515
94     NaN     NaN     NaN     NaN  1.7389
95  0.9944  1.3191     NaN  1.1286  0.4960
96  0.7714  1.0294     NaN     NaN  0.8626
97     NaN  1.5133  0.5531     NaN  0.2205
98     NaN     NaN  1.1003  1.2980  2.6962
99     NaN     NaN     NaN     NaN     NaN

[100 rows x 5 columns]

# calculations
# ================================
df.corr()

        A       B       C       D       E
A  1.0000  0.2718  0.2678  0.2822  0.1016
B  0.2718  1.0000 -0.0692  0.1736 -0.1432
C  0.2678 -0.0692  1.0000 -0.3392  0.0012
D  0.2822  0.1736 -0.3392  1.0000  0.1562
E  0.1016 -0.1432  0.0012  0.1562  1.0000


np.corrcoef(df, rowvar=False)

array([[ nan,  nan,  nan,  nan,  nan],
       [ nan,  nan,  nan,  nan,  nan],
       [ nan,  nan,  nan,  nan,  nan],
       [ nan,  nan,  nan,  nan,  nan],
       [ nan,  nan,  nan,  nan,  nan]])

Answer 2

使用 掩码数组 numpy 模块：

import numpy as np
import numpy.ma as ma

A = [1, 2, 3, 4, 5, np.NaN]
B = [2, 3, 4, 5.25, np.NaN, 100]

print(ma.corrcoef(ma.masked_invalid(A), ma.masked_invalid(B)))

它输出：

[[1.0 0.99838143945703]
 [0.99838143945703 1.0]]

在此处阅读更多内容：https://docs.scipy.org/doc/numpy/reference/maskedarray.generic.html

Answer 3

如果您希望每个数组中的 nan 数量不同，您可以考虑对非 nan 掩码进行逻辑与运算。

import numpy as np
import numpy.ma as ma

a=ma.masked_invalid(A)
b=ma.masked_invalid(B)

msk = (~a.mask & ~b.mask)

print(ma.corrcoef(a[msk],b[msk]))

numpy corrcoef - 在忽略缺失数据的同时计算相关矩阵

numpy corrcoef - compute correlation matrix while ignoring missing data

python

numpy

pandas

correlation