Back to Michael E. Cotterell @ UGA CS
This page contains some materials I created for the Advanced Databases class taught by Dr. Miller in Fall 2012.
Classifiers: Naive Bayes, ID3 Decision Tree, and Support Vector Machines (SVM)
$$ X = \textrm{Normal}\left(\mu,\sigma^2\right) $$
$$ \textrm{Pr}\left(X = x\right) = \frac{1}{\sqrt{2 \pi \sigma^2}} \textrm{exp}\left[ - \frac{\left(x - \mu \right)^2}{2 \sigma^2} \right]$$
$$ f\left(x, y, z\right) = \alpha x + \beta y + \gamma z + \delta = 0 $$
$$ \nabla f = \left[ \begin{array}{c} \alpha \\ \beta \\ \gamma \end{array} \right] $$
$$ {\rm sim}(x_1, x_2) = \frac{2 \times \log{P(C_0)}}{\log{P(C_1)} + \log{P(C_2)}} $$
Let f be our alignment matching function.
For our approach, we will simply the alignment function to the following.
$$ f : \mathcal{O} \times \mathcal{O}' \times A \rightarrow \left[ 0, 1 \right]^{n} $$
$$ f \left( O, O', \vec{a} \right) \Rightarrow n = \vert \vec{a} \vert = \vert O \vert \cdot \vert O' \vert $$
where O and O' are the subsets of terms from the source ontologies and a is the initial probability/alignment vector.