Table 2 Distance measures between two expression profiles. Two expression profiles x = (x₁, ..., x_n, y = (y₁, ..., y_n) have medians m(x), m(y) and the means $\overline{x}$, $\overline{y}$. The arithmetic relationship between the measures is as following: $E(\sout{x},\sout{y})=\sqrt{2(n-1)(1-r_{x,y})}$, $E(\tilde{x},\tilde{y})=\sqrt{2n(1-r_{x,y}^{\cos })}$ and E(x', y') = d(x, y) where ${\sout{x}}_i=(x_i-\overline{x})/\sqrt{{\displaystyle \sum {(x_i-\overline{x})}^2}/(n-1)}$, ${\tilde{x}}_i=x_i/\sqrt{{\displaystyle \sum x_i^2}/n}$, and ${x^{\prime }}_i$ = log₂ (x/m(x)) and ${\sout{y}}_i$, ${\tilde{y}}_i$, ${y^{\prime }}_i$ defined similarly.

Correlation

$r_{x,y}={\displaystyle \sum _1^n(x_i-\overline{x})(y_i-\overline{y})}/\sqrt{{\displaystyle \sum _1^n{(x_i-\overline{x})}^2}{\displaystyle \sum _1^n{(y_i-\overline{y})}^2}}$

Cosine correlation

$r_{x,y}^{\cos }={\displaystyle \sum _1^n{x}_i{y}_i}/\sqrt{{\displaystyle \sum _1^n{x}_i^2}{\displaystyle \sum _1^n{y}_i^2}}$

Euclidian distance

$E(x,y)=\sqrt{{\displaystyle \sum _1^n{(x_i-y_i)}^2}}$

New distance measure

$d(x,y)=\sqrt{{\displaystyle \sum _{i=1}^n{\left\{{\log }_2(x_i/m(x))-{\log }_2(y_i/m(y))\right\}}^2}}$