Correlation


The correlation between two points, a and b, with k dimensions is calculated as:

hc_correlation_eq_1.png

where

hc_correlation_eq_2.png

hc_correlation_eq_3.png

hc_correlation_eq_4.png

This correlation is called Pearson Product Momentum Correlation, simply referred to as Pearson's correlation or Pearson's r. It ranges from +1 to -1 where +1 is the highest correlation. Complete opposite points have correlation -1.

hc_correlation_+1_fig.png

a and b are identical, which means they have maximum correlation.

hc_correlation_-1_fig.png

a and b are perfectly mirrored, which means they have the maximum negative correlation.

See also:

Distance Measures Overview