## 4 Experimental Results
### The Splice-junction Gene Sequences Dataset  
We pick up one of the splice-junction gene sequences datasets from the GenBank website ([[http://www.ncbi.nlm.nih.gov/genbank/](http://www.ncbi.nlm.nih.gov/genbank/)]([http://www.ncbi.nlm.nih.gov/genbank/](http://www.ncbi.nlm.nih.gov/genbank/)), accessed on 04 April 2015). The selected dataset contains 3190 DNA transactions with three classes of boundaries: exon/intron (abbreviated as EI), intron/exon (abbreviated as IE) and neither (abbreviated as N). Each transaction has a sequence with 60 fields filled by one of {A, G, T, C} for each mostly. Combined with the position information, there are totally 287 different categorical attributes.  
The experiments on this dataset are similar to those in the previous subsection. Table 2 shows that Agg-CLOPE has the best profit value and Figure 7 proves Agg-CLOPE to be stable compared to CLOPE and SCLOPE by fixing \(r=3.0\).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(r\) & **CLOPE** & **SCLOPE** & **Agg-CLOPE** & \(r\) & **CLOPE** & **SCLOPE** & **Agg-CLOPE** \\ \hline
1.0 & 398.0057 & 671.4143 & 790.0327 & 2.6 & \(1.9059\times 10^{-3}\) & \(1.9066\times 10^{-3}\) & \(1.9086\times 10^{-3}\) \\
1.2 & 201.1890 & 256.7411 & 263.9993 & 2.8 & \(8.3294\times 10^{-4}\) & \(8.3264\times 10^{-4}\) & \(8.3408\times 10^{-4}\) \\
1.4 & 47.9589 & 81.7548 & 88.2186 & 3.0 & \(3.6453\times 10^{-4}\) & \(3.6395\times 10^{-4}\) & \(3.6459\times 10^{-4}\) \\
1.6 & 16.0532 & 28.5838 & 29.4792 & 3.2 & \(1.5947\times 10^{-4}\) & \(1.5921\times 10^{-4}\) & \(1.5960\times 10^{-4}\) \\
1.8 & 4.9876 & 9.3903 & 9.8508 & 3.4 & \(6.9867\times 10^{-5}\) & \(6.9718\times 10^{-5}\) & \(6.9912\times 10^{-5}\) \\
2.0 & 1.0539 & 0.1744 & 3.2666 & 3.6 & \(3.0626\times 10^{-5}\) & \(3.0527\times 10^{-5}\) & \(3.0643\times 10^{-5}\) \\
2.2 & 0.0100 & \(9.9808\times 10^{-3}\) & 0.0100 & 3.8 & \(1.3428\times 10^{-5}\) & \(1.3379\times 10^{-5}\) & \(1.3443\times 10^{-5}\) \\
2.4 & \(4.3660\times 10^{-3}\) & \(4.3463\times 10^{-3}\) & \(4.3731\times 10^{-3}\) & 4.0 & \(5.8913\times 10^{-4}\) & \(5.8686\times 10^{-4}\) & \(5.8998\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of clustering profit values with different repulsion produced by three algorithms on the splice-junction gene sequence dataset.  
Figure 6: Comparison of cluster number with different repulsion produced by three algorithms on the mushroom dataset.  
However, although the number of transactions in this dataset is smaller than that of mushroom, Agg-CLOPE takes much more time while SCLOPE becomes fastest when \(r\geqslant 2.0\), as illustrated in Figure 8. The reason can be explained in Figure 9, with more than 2700 clusters produced under bigger repulsion values by all three algorithms. Observing the calculation of time complexity in the last paragraph of Section 3.2, the number of clusters \(K\) in each iterative round is a key factor. Let \(\Sigma\) symbolizes the final number of clusters by the corresponding algorithm, and then \(K\) is close to \(\Sigma\) in CLOPE and is always bigger than \(\Sigma\) in Agg-CLOPE. On the other hand, the creation time of FP-Tree in SCLOPE is only affected by \(N\) and \(A\), resulting in faster than CLOPE, Agg-CLOPE and that on the mushroom dataset. Moreover, there are no obvious differences on the purity metric among the three algorithms. As shown in Figure 10, the maximum value of 3190 can be easily achieved on condition of \(r>2.0\), thus the quality of clustering results is almost the same on this dataset.  
Figure 8: Comparison of execution time with different repulsion produced by three algorithms on the splice-junction gene sequence dataset.  
Figure 7: Comparison of stability with different input sequence produced by three algorithms on the splice-junction gene sequence dataset.