# Graph-Based Taxonomic Semantic Class Labeling
## 3 Graph-Based Taxonomic Semantic Associative Community Labeling
### WordNet Hypernym Labeling
#### 3.3.1 WordNet Hypernym Labeling: Procedure Description  
Starting from the clustered coordination graph Fo\(F[and|or]_{i}^{s}\) of the source lexeme \(s\), a WordNet hypernym label graph \(F[hyper]_{i}^{s}\) is constructed for each of its subgraphs. The procedure for the construction of the hypernym graph consists of the following steps:  
1. For each lexeme node \(c_{j}\) in the clustered coordination community Fo\(F[and|or]_{i}^{s}\) with lexemes \(c_{1},\ldots,c_{n}\), synsets \(t\) are identified on the basis of the WordNet synset relation: \[(\text{lexeme}_{c_{j}})\text{-}[\text{has\_synset}]\rightarrow(\text{ synset}_{t});\]
2. For each of the above synsets \(t\), WordNet hypernyms \(h\) are extracted through the WordNet hypernym relation \[(\text{synset}_{t})\text{-}[\text{has\_hypernym}]\rightarrow(\text{hypernym \_synset}_{h});\]
3. A weighted, first-order (source-friend) directed graph \(F[hyper]_{i}^{s}\) of identified lexical WordNet synset/hypernym collocates of the clustered coordination community Fo\(F[and|or]_{i}^{s}\) is constructed;
4. The most prominent in nodes in the hypernym graph \(F[hyper]_{i}^{s}\) are identified. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Associated Community** & \begin{tabular}{l} _is\_a Labels_ \\ **FoF\({}_{ethics}\)** \\ \end{tabular} & \
\begin{tabular}{l} _is\_a Labels_ \\ **FoF\({}_{ethics}\)** \\ \end{tabular} &
\begin{tabular}{l} _is\_a Labels_ \\ **Mo** \\ \end{tabular} & **WordNet Hypernym Labels** \\ \hline  & aristotle-n, Aristotle-n, plato-n, aquinas-n, & & & \\  & socrates-n, cicero-n, hipprocates-n, descartes-n, & & & \\  & ptolemy-n, augustine-n, galen-n, euclid-n, & & & \\  & pythagoras-n, confucius-n, philosopher-n, & & & \\  & stotics-n & & & \\ \hline
2 & standards-n, values-n, practices-n, guidelines-n, & & & \\  & principles-n, procedures-n, beliefs-n, attitudes-n & & & \\ \hline
3 & ethics-n, conduct-n, theology-n, compliance-n, philosophy-n, ethic-n, psychology-n & & & \\  & elections-n, societies-n, humanities-n, & & & \\  & privilege-n, corporations-n, cultures-n & & & \\ \hline
5 & morals-n, kant-n & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Best-ranked _is_a_ dependency labels and WordNet hypernym labels for associated communities Fo\([and|or]_{i}^{ethics}\) of the source lexeme _ethics-n_ in enTenTen13. More precisely, the hypernym label graph \(F[hyper]_{i}^{s}\) is constructed as follows. Given a clustered coordination community \(\mathrm{FoF}[and|or]_{i}^{s}\) with lexemes \(c_{1},\ldots,c_{n}\) from the coordination lexical graph \(\mathrm{FoF}[and|or]_{s}\), the corresponding synsets \(t\) are extracted from WordNet. Together with the lexemes and the corresponding synsets from the first step, a set of WordNet hypernym synsets is assembled. The hypernym label graph \(F[hyper]_{i}^{s}=G_{H}=(V_{H},E_{H})\) is then defined as the following weighted directed graph. The set of nodes \(V_{H}\) is the set of the community lexeme nodes and the corresponding hypernym lexemes extracted from WordNet:  
\[V_{H} :=\{c_{1},\ldots,c_{n}\}\cup\{h\mid\exists(x,h)\in H\},\qquad \qquad\text{where}\] \[H :=\bigcup_{j=1}^{n}\{\ (c_{j},h)\mid\exists t\ (t\text{ is a synset of }c_{j},h\text{ is a hypernym of }t)\}.\]  
The set \(H\) is a set of directed edges, pointing from the lexeme nodes to their hypernyms, identified through the corresponding synsets \(t\) are extracted from WordNet through its \((\text{lexeme}_{c_{j}})\)-\([\text{has\_synset}]\rightarrow(\text{synset}_{t})\) and \((\text{synset}_{t})\)-\([\text{has\_hypernym}]\rightarrow(\text{hypernym\_synset}_{h})\) relations. This identifies the hypernyms corresponding to the lexemes from the sense community represented with \(\mathrm{FoF}[and|or]_{i}^{s}\), as the in nodes of the edges from \(H\).