## 4 Experimental Results
### The Mushroom Dataset  
The mushroom dataset is retrieved from the UCI machine learning repository ([[http://archive.ics.uci.edu/ml/datasets/Mushroom](http://archive.ics.uci.edu/ml/datasets/Mushroom)]([http://archive.ics.uci.edu/ml/datasets/Mushroom](http://archive.ics.uci.edu/ml/datasets/Mushroom)), accessed on 24 March 2015), which has been applied by various research works. It contains 8124 transactions with two classes, 4208 edible mushrooms and 3916 poisonous mushrooms. Each transaction has 22 categorical attributes with 116 different values in total.  
\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 & 745.6473 & 1698.0084 & 1791.9966 & 2.6 & 2.2697 & 2.4834 & 2.5242 \\
1.2 & 343.3131 & 649.052 & 731.0381 & 2.8 & 0.9636 & 1.2427 & 1.2429 \\
1.4 & 149.1631 & 270.5546 & 300.6443 & 3.0 & 0.4784 & 0.6134 & 0.6141 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of clustering profit values with different repulsion produced by three algorithms on the mushroom dataset.  
Firstly, we compare the profit values of clustering produced by the three algorithms from \(r=1.0\) to \(r=4.0\), as shown in Table 1. According to Equation (4), the profit value becomes smaller as \(r\) grows up. With the same repulsion, the clustering profit value produced by Agg-CLOPE comes to be the best, and CLOPE the worst in most cases. It is proved that the methodology of Agg-CLOPE for grouping transactions into clusters is capable of finding a more proper clustering with much better profit value.  
For the next, we scramble the mushrooms in ten random sequences, and fix \(r=2\) to run the three algorithms. The result shown in Figure 3 proves that the profit values produced by Agg-CLOPE are just the same regardless of the input sequence, while the clustering result of CLOPE and SCLOPE are both unstable.  
Then we make comparison on the executing time of the three algorithms from \(r=1.0\) to \(r=4.0\). The result in Figure 4 shows that CLOPE is fastest with no more than 5 s, while Agg-CLOPE and SCLOPE takes much longer time to produce the clustering results. SCLOPE is the worst as the attributes in each transaction should be sorted during the creation of its FP-Tree structure [8]. The reason that Agg-CLOPE is slow is the time complexity analyzed in Section 3.2.  
Finally, we evaluate the quality of clustering results from \(r=1.0\) to \(r=4.0\). It includes two metrics-purity and cluster number [6]. The purity metric is calculated by summing up the larger one of the number of edible mushrooms and number of poisonous mushrooms. It has a maximum of 8124, the total number of transactions. The number of clusters should be as many as possible, as a clustering with each cluster contains only one transaction would surely achieve the maximum purity.  
As shown in Figure 5 and Figure 6, both CLOPE and Agg-CLOPE reaches the maximum purity of 8124 and maximum cluster number of 23 at \(r=2.8\), while SCLOPE achieves this goal at \(r=3.1\). Besides, Agg-CLOPE is slightly better than CLOPE on both of the two metrics, while SCLOPE appears to be worse.  
Figure 4: Comparison of execution time with different repulsion produced by three algorithms on the mushroom dataset.  
Figure 5: Comparison of purity with different repulsion produced by three algorithms on the mushroom dataset.