Editing Pearson correlation coefficient (section)

===Pearson's distance===
A distance metric for two variables ''X'' and ''Y'' known as ''Pearson's distance'' can be defined from their correlation coefficient as<ref>Fulekar (Ed.), M.H. (2009) ''Bioinformatics: Applications in Life and Environmental Sciences'', Springer (pp. 110) {{isbn|1-4020-8879-5}}</ref>
:<math>d_{X,Y}=1-\rho_{X,Y}.</math>
Considering that the Pearson correlation coefficient falls between [−1, +1], the Pearson distance lies in [0, 2]. The Pearson distance has been used in [[cluster analysis]] and data detection for communications and storage with unknown gain and offset.<ref>{{cite journal
 |author1=Immink, K. Schouhamer
 |author2=Weber, J. 
 |title=Minimum Pearson distance detection for multilevel channels with gain and / or offset mismatch 
 |date=October 2010
 |journal=IEEE Transactions on Information Theory 
 |volume=60 |issue=10 |pages=5966–5974
 |doi=10.1109/tit.2014.2342744 |citeseerx=10.1.1.642.9971
 |s2cid=1027502 
 |url=https://www.researchgate.net/publication/265604603
 |access-date=11 February 2018}}</ref>

The Pearson "distance" defined this way assigns distance greater than 1 to negative correlations. In reality, both strong positive correlation and negative correlations are meaningful, so care must be taken when Pearson "distance" is used for nearest neighbor algorithm as such algorithm will only include neighbors with positive correlation and exclude neighbors with negative correlation. Alternatively, an absolute valued distance, <math>d_{X,Y}=1-|\rho_{X,Y}|</math>, can be applied, which will take both positive and negative correlations into consideration. The information on positive and negative association can be extracted separately, later.