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
您可能想知道如何在寻找特定方向的相关性(负相关或正相关)的上下文中解释您的概率。这是我写的一个函数。它甚至可能是正确的!
这是基于我从http://www.vassarstats.net/rsig.html和http://en.wikipedia.org/wiki/Student%27s_t_distribution上收集到的信息,感谢这里发布的其他答案。
# Given (possibly random) variables, X and Y, and a correlation direction,
# returns:
# (r, p),
# where r is the Pearson correlation coefficient, and p is the probability
# that there is no correlation in the given direction.
#
# direction:
# if positive, p is the probability that there is no positive correlation in
# the population sampled by X and Y
# if negative, p is the probability that there is no negative correlation
# if 0, p is the probability that there is no correlation in either direction
def probabilityNotCorrelated(X, Y, direction=0):
x = len(X)
if x != len(Y):
raise ValueError("variables not same len: " + str(x) + ", and " + \
str(len(Y)))
if x < 6:
raise ValueError("must have at least 6 samples, but have " + str(x))
(corr, prb_2_tail) = stats.pearsonr(X, Y)
if not direction:
return (corr, prb_2_tail)
prb_1_tail = prb_2_tail / 2
if corr * direction > 0:
return (corr, prb_1_tail)
return (corr, 1 - prb_1_tail)
其他回答
你可以看看这篇文章。这是一个使用pandas库(适用于Python)根据多个文件的历史外汇货币对数据计算相关性的示例,然后使用seaborn库生成热图图。
http://www.tradinggeeks.net/2015/08/calculating-correlation-in-python/
你可以看看scipy.stats:
from pydoc import help
from scipy.stats.stats import pearsonr
help(pearsonr)
>>>
Help on function pearsonr in module scipy.stats.stats:
pearsonr(x, y)
Calculates a Pearson correlation coefficient and the p-value for testing
non-correlation.
The Pearson correlation coefficient measures the linear relationship
between two datasets. Strictly speaking, Pearson's correlation requires
that each dataset be normally distributed. Like other correlation
coefficients, this one varies between -1 and +1 with 0 implying no
correlation. Correlations of -1 or +1 imply an exact linear
relationship. Positive correlations imply that as x increases, so does
y. Negative correlations imply that as x increases, y decreases.
The p-value roughly indicates the probability of an uncorrelated system
producing datasets that have a Pearson correlation at least as extreme
as the one computed from these datasets. The p-values are not entirely
reliable but are probably reasonable for datasets larger than 500 or so.
Parameters
----------
x : 1D array
y : 1D array the same length as x
Returns
-------
(Pearson's correlation coefficient,
2-tailed p-value)
References
----------
http://www.statsoft.com/textbook/glosp.html#Pearson%20Correlation
您可能想知道如何在寻找特定方向的相关性(负相关或正相关)的上下文中解释您的概率。这是我写的一个函数。它甚至可能是正确的!
这是基于我从http://www.vassarstats.net/rsig.html和http://en.wikipedia.org/wiki/Student%27s_t_distribution上收集到的信息,感谢这里发布的其他答案。
# Given (possibly random) variables, X and Y, and a correlation direction,
# returns:
# (r, p),
# where r is the Pearson correlation coefficient, and p is the probability
# that there is no correlation in the given direction.
#
# direction:
# if positive, p is the probability that there is no positive correlation in
# the population sampled by X and Y
# if negative, p is the probability that there is no negative correlation
# if 0, p is the probability that there is no correlation in either direction
def probabilityNotCorrelated(X, Y, direction=0):
x = len(X)
if x != len(Y):
raise ValueError("variables not same len: " + str(x) + ", and " + \
str(len(Y)))
if x < 6:
raise ValueError("must have at least 6 samples, but have " + str(x))
(corr, prb_2_tail) = stats.pearsonr(X, Y)
if not direction:
return (corr, prb_2_tail)
prb_1_tail = prb_2_tail / 2
if corr * direction > 0:
return (corr, prb_1_tail)
return (corr, 1 - prb_1_tail)
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
本文给出了一种基于稀疏向量的pearson相关的实现方法。这里的向量表示为(index, value)表示的元组列表。两个稀疏向量可以是不同的长度,但总的向量大小必须是相同的。这对于文本挖掘应用程序非常有用,其中向量大小非常大,因为大多数特征都是单词包,因此通常使用稀疏向量执行计算。
def get_pearson_corelation(self, first_feature_vector=[], second_feature_vector=[], length_of_featureset=0):
indexed_feature_dict = {}
if first_feature_vector == [] or second_feature_vector == [] or length_of_featureset == 0:
raise ValueError("Empty feature vectors or zero length of featureset in get_pearson_corelation")
sum_a = sum(value for index, value in first_feature_vector)
sum_b = sum(value for index, value in second_feature_vector)
avg_a = float(sum_a) / length_of_featureset
avg_b = float(sum_b) / length_of_featureset
mean_sq_error_a = sqrt((sum((value - avg_a) ** 2 for index, value in first_feature_vector)) + ((
length_of_featureset - len(first_feature_vector)) * ((0 - avg_a) ** 2)))
mean_sq_error_b = sqrt((sum((value - avg_b) ** 2 for index, value in second_feature_vector)) + ((
length_of_featureset - len(second_feature_vector)) * ((0 - avg_b) ** 2)))
covariance_a_b = 0
#calculate covariance for the sparse vectors
for tuple in first_feature_vector:
if len(tuple) != 2:
raise ValueError("Invalid feature frequency tuple in featureVector: %s") % (tuple,)
indexed_feature_dict[tuple[0]] = tuple[1]
count_of_features = 0
for tuple in second_feature_vector:
count_of_features += 1
if len(tuple) != 2:
raise ValueError("Invalid feature frequency tuple in featureVector: %s") % (tuple,)
if tuple[0] in indexed_feature_dict:
covariance_a_b += ((indexed_feature_dict[tuple[0]] - avg_a) * (tuple[1] - avg_b))
del (indexed_feature_dict[tuple[0]])
else:
covariance_a_b += (0 - avg_a) * (tuple[1] - avg_b)
for index in indexed_feature_dict:
count_of_features += 1
covariance_a_b += (indexed_feature_dict[index] - avg_a) * (0 - avg_b)
#adjust covariance with rest of vector with 0 value
covariance_a_b += (length_of_featureset - count_of_features) * -avg_a * -avg_b
if mean_sq_error_a == 0 or mean_sq_error_b == 0:
return -1
else:
return float(covariance_a_b) / (mean_sq_error_a * mean_sq_error_b)
单元测试:
def test_get_get_pearson_corelation(self):
vector_a = [(1, 1), (2, 2), (3, 3)]
vector_b = [(1, 1), (2, 5), (3, 7)]
self.assertAlmostEquals(self.sim_calculator.get_pearson_corelation(vector_a, vector_b, 3), 0.981980506062, 3, None, None)
vector_a = [(1, 1), (2, 2), (3, 3)]
vector_b = [(1, 1), (2, 5), (3, 7), (4, 14)]
self.assertAlmostEquals(self.sim_calculator.get_pearson_corelation(vector_a, vector_b, 5), -0.0137089240555, 3, None, None)
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