# Using Conceptual Recurrence and Consistency Metrics for Topic Segmentation in Debate
## 8 Performance Comparison and Evaluation
### Experimental Results  
We conducted experiments based on the description in the sections above. The \(Pk\) and \(WD\) values were derived after unifying the number of topic segmentation points in CSseg and LCseg according to the number of topic segmentation points aggregated from the subjects. First, the method for calculating similarity cohesion is a combined method in which the weights of Plane, Line, and Point are applied in a 1:1:1 ratio. The weights of other-continuity, chain of arguments and counterarguments, and topic guide of moderator are all 2, and the weight of self-continuity is 0.5. Table 1 shows the \(Pk\) and \(WD\) values of CSseg to which all properties of CSseg are applied, and LCseg, the existing topic segmentation model for multi-party discourse. CSseg leads LCseg by about 5-6% on \"basic income\", about 4-5% on \"volunteer military system\", and about 2-3% on \"SAT\". For all three debates, CSseg showed good results. Figure 27 shows the topic segments of CSseg for which Plane, Line, and Point are combined and the debate consistency metrics are applied. The red squares represent topic segments divided by CSseg, and the blue squares represent the topic segments aggregated by seven subjects. Figure 28 shows the topic segments of LCseg. The yellow squares represent topic segments divided by LCseg, and the blue squares represent the topic segments aggregated by seven subjects. Figure 26: Simplified Lexical Chains. The squares at the top indicate sentences. \(R1\)–\(R9\) represent the lexical chains for each word A to I. Next, we derived \(\mathit{Pk}\) and \(\mathit{WD}\) by applying each method and debate consistency metric separately to determine how CSseg's method of calculating similarity cohesion and each debate consistency metric affect the topic segmentation result. Table 2 shows \(\mathit{Pk}\) and \(\mathit{WD}\) for each similarity cohesion calculation method without applying the debate consistency metric. CSseg's Plane was the method that consistently and best derived the values of \(\mathit{Pk}\) and \(\mathit{WD}\) in the three debates. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{\(\mathit{Pk}\)} \\ \cline{2-4}  & **Basic Income** & **Military** & **SAT** \\ \hline CSseg & **0.0474** & **0.1217** & **0.1463** \\ LCseg & 0.1057 & 0.1693 & 0.1714 \\ \hline  & \multicolumn{2}{c}{\(\mathit{WD}\)} \\ \cline{2-4}  & **Basic Income** & **Military** & **SAT** \\ \hline CSseg & **0.0474** & **0.1217** & **0.1463** \\ LCseg & 0.1094 & 0.1746 & 0.1783 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(\mathit{Pk}\) and \(\mathit{WD}\) values of CSseg combined with Plane, Line, and Point and applied with debate consistency metrics, and of the existing model LCseg for multi-party discourse. Figure 28: Topic segments of LCseg. Figure 27: Topic segments of CSseg where Plane, Line, and Point are combined and the debate consistency metrics are applied. Table 3 shows the \(Pk\) and \(WD\) values for CSseg by applying 2 to the weights of other-continuity, chain of arguments and counterarguments, and topic guide of moderator, and 0.5 to the weight of self-continuity, which are the debate consistency metrics. CSseg with Plane + Line and Line + Point were the methods that consistently and best derived the values of \(Pk\) and \(WD\) in the three debates. Table 4 shows CSseg \(Pk\) and \(WD\) values with the weight of other-continuity applied as 2. None of the three debates consistently yielded the best values of \(Pk\) and \(WD\). \begin{table}
\begin{tabular}{c c c c} \hline  & \multicolumn{2}{c}{\(Pk\)} \\ \cline{2-4}  & **Basic Income** & **Military** & **SAT** \\ \hline Plane & **0.0693** & **0.1693** & **0.1371** \\ Line & 0.0802 & 0.1852 & **0.1371** \\ Point & 0.0693 & 0.1852 & **0.1371** \\ Plane + Line & **0.0693** & 0.1852 & 0.1646 \\ Plane + Point & **0.0693** & 0.1693 & 0.1554 \\ Line + Point & 0.0802 & 0.1852 & **0.1371** \\ Plane + Line + Point & **0.0693** & 0.1852 & 0.1646 \\ LCseg & 0.1057 & **0.1693** & 0.1714 \\ \hline \end{tabular}
\end{table}