解释(和比较)numpy.correlate的输出 [英] Interpreting (and comparing) output from numpy.correlate

问题描述

我查看了这个问题，但是它并没有真正给我任何答案.

I have looked at this question but it hasn't really given me any answers.

本质上，如何使用 np.correlate 确定是否存在强相关性?我希望我能理解的输出与从Matlab的 xcorr 和带有 coeff 选项的输出相同(1是滞后 l 的强相关性，滞后 l 时0是不相关的)，但是即使输入矢量已在0到1之间进行归一化， np.correlate 也会产生大于1的值.

Essentially, how can I determine if a strong correlation exists or not using np.correlate? I expect the same output as I get from matlab's xcorr with the coeff option which I can understand (1 is a strong correlation at lag l and 0 is no correlation at lag l), but np.correlate produces values greater than 1, even when the input vectors have been normalised between 0 and 1.

示例输入

import numpy as np
x = np.random.rand(10)
y = np.random.rand(10)

np.correlate(x, y, 'full')

这将提供以下输出:

array([ 0.15711279,  0.24562736,  0.48078652,  0.69477838,  1.07376669,
    1.28020871,  1.39717118,  1.78545567,  1.85084435,  1.89776181,
    1.92940874,  2.05102884,  1.35671247,  1.54329503,  0.8892999 ,
    0.67574802,  0.90464743,  0.20475408,  0.33001517])

如果我不知道最大可能的相关值是多少，如何分辨强相关性是什么?

How can I tell what is a strong correlation and what is weak if I don't know the maximum possible correlation value is?

另一个例子:

In [10]: x = [0,1,2,1,0,0]

In [11]: y = [0,0,1,2,1,0]

In [12]: np.correlate(x, y, 'full')
Out[12]: array([0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0])

编辑:这是一个很难回答的问题，但带标记的答案确实可以回答所提出的问题.我认为重要的是要注意我在该区域进行挖掘时发现的内容，您无法比较互相关的输出.换句话说，使用互相关的输出来说信号 x 与信号 y 的相关性比信号 z .互相关不提供此类信息

This was a badly asked question, but the marked answer does answer what was asked. I think it is important to note what I have found whilst digging around in this area, you cannot compare outputs from cross-correlation. In other words, it would not be valid to use the outputs from cross-correlation to say signal x is better correlated to signal y than signal z. Cross-correlation does not provide this kind of information

推荐答案

numpy.correlate 位于 之下.我认为我们可以理解.让我们从示例案例开始:

numpy.correlate is under-documented. I think that we can make sense of it, though. Let's start with your sample case:

>>> import numpy as np
>>> x = [0,1,2,1,0,0]
>>> y = [0,0,1,2,1,0]
>>> np.correlate(x, y, 'full')
array([0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0])

这些数字是每个滞后的互相关.为了更清楚地说明这一点，让我们将延迟数字放在相关性之上:

Those numbers are the cross-correlations for each of the possible lags. To make that more clear, let's put the lag numbers above the correlations:

>>> np.concatenate((np.arange(-5, 6)[None,...], np.correlate(x, y, 'full')[None,...]), axis=0)
array([[-5, -4, -3, -2, -1,  0,  1,  2,  3,  4,  5],
       [ 0,  0,  1,  4,  6,  4,  1,  0,  0,  0,  0]])

在这里，我们可以看到互相关以-1的滞后达到其峰值.如果您看一下上面的 x 和 y ，那是有道理的:将 y 左移一位，它与完全是.

Here, we can see that the cross-correlation reaches its peak at a lag of -1. If you look at x and y above, that makes sense: it one shifts y to the left by one place, it matches x exactly.

要验证这一点，让我们再试一次，这次将 y 进一步移动:

To verify this, let's try again, this time shifting y further:

>>> y = [0, 0, 0, 0, 1, 2]
>>> np.concatenate((np.arange(-5, 6)[None,...], np.correlate(x, y, 'full')[None,...]), axis=0)
array([[-5, -4, -3, -2, -1,  0,  1,  2,  3,  4,  5],
       [ 0,  2,  5,  4,  1,  0,  0,  0,  0,  0,  0]])

现在，相关性以-3的滞后性达到峰值，这意味着当 y 移动时， x 和 y 之间的最佳匹配向左3个地方.

Now, the correlation peaks at a lag of -3, meaning that the best match between x and y occurs when y is shifted to the left by 3 places.

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