## 5 Results and Discussion  
This section presents and discusses the results of applying the three data similarity measures to compute the similarity between PEOs. Tables 3-5 show the similarity of PEOs based on the ED, MD and CS measures, respectively. For the sake of illustration, a heatmap data visualization technique is used to represent the similarity values in different colors. As mentioned above, the ED measures the straight distance between points, hence, theoretically, its values fall in the range between zero and infinity. In Table 3, the ED's values range between 0 (identical pair of PEOs) and 0.43 (the most dissimilar pair of PEOs). As for MD, this measures the distance between the vector space of two points in terms of the number of horizontal and vertical units between them, hence, theoretically, its values fall in the range between zero and infinity. In Table 4, the MD' between the PEOs vector spaces ranges between 0 (identical PEOs) and 1.35 (the most dissimilar pairs of PEO). Finally, the CS measures the cosine of the angle between the vector spaces of two points, hence, theoretically, its values fall in the range between zero and infinity. In Table 5 the CS's values of the PEOs vector space models range between 0.38 (the most dissimilar PEOs) to 1 (identical pair of PEOs). Despite the different mechanisms of measuring similarity and different measurement scales, of the three measures the heatmap visualization of the three measures reflects the degree of consistency between them. Virtually, the three measures show a sort of consistency among them in their evaluation of the similarity between PEOs. However, to quantitatively evaluate the degree of consistency between the three measures, the agreement analysis between them can be employed. Basically, there are two methods for measuring the agreement between similarity measures [18]. The first method applies a simple correlation, such as Pearson's correlation, to measure the correlation between the similarity matrices after flattening them into vectors. The second method is based on generating ranking matrices from the similarity matrices of the measures and then compute \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**PEO** & **LL** & **C** & **L** & **T** & **EC** & **P** & **SC** & **CS** & **TC** & **KC** & **GS** \\ \hline
**LL** & 1 & 10 & 8 & 9 & 11 & 2 & 6 & 4 & 7 & 5 & 3 \\ \hline
**C** & 8 & 1 & 3 & 2 & 9 & 4 & 7 & 5 & 10 & 11 & 6 \\ \hline
**L** & 7 & 6 & 1 & 5 & 4 & 2 & 3 & 8 & 11 & 10 & 9 \\ \hline
**T** & 9 & 5 & 3 & 1 & 6 & 4 & 10 & 2 & 8 & 11 & 7 \\ \hline
**EC** & 7 & 9 & 2 & 4 & 1 & 5 & 3 & 6 & 11 & 8 & 10 \\ \hline
**P** & 2 & 11 & 5 & 8 & 10 & 1 & 3 & 4 & 9 & 7 & 6 \\ \hline
**SC** & 4 & 11 & 3 & 9 & 5 & 2 & 1 & 6 & 10 & 7 & 8 \\ \hline
**CS** & 6 & 11 & 9 & 7 & 10 & 5 & 8 & 1 & 3 & 4 & 2 \\ \hline
**TC** & 5 & 9 & 10 & 7 & 11 & 6 & 8 & 2 & 1 & 2 & 4 \\ \hline
**KC** & 5 & 11 & 9 & 8 & 10 & 6 & 7 & 3 & 2 & 1 & 4 \\ \hline
**GS** & 5 & 10 & 9 & 7 & 11 & 6 & 8 & 2 & 3 & 4 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: PEOs similarity ranking based on ED measure. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**PEO** & **LL** & **C** & **L** & **T** & **EC** & **P** & **SC** & **CS** & **TC** & **KC** & **GS** \\ \hline
**LL** & 1 & 10 & 8 & 9 & 11 & 2 & 6 & 4 & 7 & 5 & 3 \\ \hline
**C** & 9 & 1 & 3 & 2 & 8 & 4 & 7 & 5 & 10 & 11 & 6 \\ \hline
**L** & 7 & 6 & 1 & 5 & 3 & 2 & 4 & 8 & 11 & 10 & 9 \\ \hline
**T** & 10 & 2 & 3 & 1 & 5 & 6 & 9 & 4 & 8 & 11 & 7 \\ \hline
**EC** & 8 & 7 & 2 & 4 & 1 & 5 & 3 & 6 & 11 & 9 & 10 \\ \hline
**P** & 2 & 10 & 4 & 7 & 8 & 1 & 3 & 5 & 11 & 9 & 6 \\ \hline
**SC** & 6 & 9 & 10 & 7 & 11 & 5 & 8 & 1 & 3 & 4 & 2 \\ \hline
**TC** & 5 & 9 & 11 & 7 & 10 & 6 & 8 & 2 & 1 & 4 & 3 \\ \hline
**KC** & 5 & 11 & 10 & 8 & 9 & 6 & 7 & 4 & 3 & 1 & 2 \\ \hline
**GS** & 5 & 9 & 10 & 7 & 11 & 6 & 8 & 2 & 4 & 3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: PEOs similarity ranking based on MD measure.