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How is the correlation coefficient calculated?

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How is the correlation coefficient calculated?

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The similarity metrix used is based on Pearson correlation which measures the strength and direction of a linear relationship between the X and Y variables. The measure represents both negative and positive correlations (ranging from -1 to 1), both of which are of biological interest. According to the formula below, it indicates that the Pearson correlation coefficient effectively normalizes the magnitude of the expression vector. That is, for genes which have a relatively moderate expression pattern, even if the expression levels are dramatically different, they will be identified as having a similar expression response (the Pearson correlation coefficient is close to one).

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