CSCI 8370 Advanced Databases

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.

Review Lectures

Classifiers: Naive Bayes, ID3 Decision Tree, and Support Vector Machines (SVM)

Other

Normal Distribution

$$ X = \textrm{Normal}\left(\mu,\sigma^2\right) $$

$$ \textrm{Pr}\left(X = x\right) = \frac{1}{\sqrt{2 \pi \sigma^2}} \textrm{exp}\left[ - \frac{\left(x - \mu \right)^2}{2 \sigma^2} \right]$$

Hyperplanes

$$ f\left(x, y, z\right) = \alpha x + \beta y + \gamma z + \delta = 0 $$

$$ \nabla f = \left[ \begin{array}{c} \alpha \\ \beta \\ \gamma \end{array} \right] $$

Information-Theoretic Similarity

$$ {\rm sim}(x_1, x_2) = \frac{2 \times \log{P(C_0)}}{\log{P(C_1)} + \log{P(C_2)}} $$

Markov Models for Ontology Alignment

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.

  1. Create a Pairwise Connectivity Graph (PCG) using O and O'.
  2. Add weights to the graph such