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Biweight midcorrelation
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Biweight midcorrelation : ウィキペディア英語版
Biweight midcorrelation
In statistics, biweight midcorrelation (also called bicor) is a measure of similarity between samples. It is median-based, rather than mean-based, thus is less sensitive to outliers, and can be a robust alternative to other similarity metrics, such as Pearson correlation or mutual information.
==Derivation==
Here we find the biweight midcorrelation of two vectors x and y, with i=1,2, \ldots,m items, representing each item in the vector as x_1, x_2, \ldots, x_m and y_1, y_2, \ldots, y_m. First, we define \operatorname(x) as the median of a vector x and \operatorname(x) as the median absolute deviation (MAD), then define u_i and v_i as,
:
\begin
u_i &= \frac,\\
v_i &= \frac.
\end

Now we define the ''weights'' w_i^ and w_i^ as,
:
\begin
w_i^ &= \left(1-u_i^2\right)^2 I\left(1-|u_i|\right)\\
w_i^ &= \left(1-v_i^2\right)^2 I\left(1-|v_i|\right)
\end

where I is the identity function where,
:
I(x) = \begin1, & \text x >0\\
0, & \text\end

Then we normalize so that the sum of the weights is 1:
:
\begin
\tilde_i &= \frac}(x)) w_j^\right )^2}}\\
\tilde_i &= \frac}(y)) w_j^\right )^2}}.
\end

Finally, we define biweight midcorrelation as,
:
\mathrm\left(x, y\right) = \sum_^m \tilde_i \tilde_i


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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