metrics.tex (1717B)
1 \begin{frame}{B cube}% 2 \begin{align*} 3 \bcubed \operatorname{precision}(g, c) & = \expectation_{\rndm{X},\rndm{Y}\sim\uniformDistribution(\dataSet_\relationSet)} P\left(g(\rndm{X})=g(\rndm{Y}) \mid c(\rndm{X})=c(\rndm{Y})\right) \\ 4 \bcubed \operatorname{recall}(g, c) & = \expectation_{\rndm{X},\rndm{Y}\sim\uniformDistribution(\dataSet_\relationSet)} P\left(c(\rndm{X})=c(\rndm{Y}) \mid g(\rndm{X})=g(\rndm{Y})\right) \\ 5 \bcubed \fone{}(g, c) & = \frac{2}{\bcubed{} \operatorname{precision}(g, c)^{-1} + \bcubed{} \operatorname{recall}(g, c)^{-1}} \\ 6 \end{align*} 7 \end{frame} 8 9 \begin{frame}{V-measure}% 10 \begin{align*} 11 \operatorname{homogeneity}(g, c) & = 1 - \frac{\entropy\left(c(\rndm{X})\mid g(\rndm{X})\right)}{\entropy\left(c(\rndm{X})\right)} \\ 12 \operatorname{completeness}(g, c) & = 1 - \frac{\entropy\left(g(\rndm{X})\mid c(\rndm{X})\right)}{\entropy\left(g(\rndm{X})\right)} \\ 13 \operatorname{V-measure}(g, c) & = \frac{2}{\operatorname{homogeneity}(g, c)^{-1} + \operatorname{completeness}(g, c)^{-1}} \\ 14 \end{align*} 15 \end{frame} 16 17 \begin{frame}{ARI}% 18 \begin{equation*} 19 \operatorname{\textsc{ri}}(g, c) = \expectation\limits_{\rndm{X},\rndm{Y}} \left[ P\left( 20 c(\rndm{X})=c(\rndm{Y}) \Leftrightarrow g(\rndm{X})=g(\rndm{Y}) 21 \right) \right] 22 \end{equation*} 23 24 \smallskip 25 26 \begin{equation*} 27 \operatorname{\textsc{ari}}(g, c) = 28 \frac{\displaystyle\operatorname{\textsc{ri}}(g, c) - \expectation_{c\sim\uniformDistribution(\relationSet^\dataSet)}[\operatorname{\textsc{ri}}(g, c)]} 29 {\displaystyle\max_{c\in\relationSet^\dataSet} \operatorname{\textsc{ri}}(g, c) - \expectation_{c\sim\uniformDistribution(\relationSet^\dataSet)}[\operatorname{\textsc{ri}}(g, c)]} 30 \end{equation*} 31 \end{frame}