# Clustering with Nature-Inspired Algorithm Based on Territorial Behavior of Predatory Animals
## 4 Experimental Results  
During the experimental runs, the proposed algorithm was compared to the standard \(k\)-means approach, which is widely used both in research and technical applications. For the comparison, selected labeled datasets taken from UCI Machine Learning Repository have been used [20]. We have also employed two-dimensional datasets known as s-sets in this experiment [21]. They are characterized by different ratio of clusters overlap. The list of benchmark data used for the experiments can be found in Table 1.  
Both algorithms were executed 100 times. For the newly-introduced \(PAA\) we have used the parameters set provided in Table 2.  
Table 3 provide the results of experiments, with mean of Rand index [28], calculated versus class labels, being used as a performance indicator. The \(\overline{R}_{PAA}\) represents the average value obtained by the proposed algorithm, while \(\overline{R}_{K}\) the average value obtained using \(K\)-Means algorithm. In both cases, the results were taken from 100 repetitions. The last column displays the results of \(t\)-test, with significant performance advantage (at \(\alpha=0.05\) significance level) of \(PAA\) denoted with \(+\), of \(K\)-means with \(-\), and not significant difference with 0. Figure 1: Example behaviour of four individuals randomly initialized in a small dataset during first four steps. It can be observed that while _PAA_-based clustering in terms of performance reaches the level of _k_-means, or it under-performs for simple data division problems (such as s1 or wine) it becomes more competitive for datasets with higher dimensionality. It also offers better performance for clustering instances with overlapping clusters and a more significant number of groups. Figure 2 illustrates the result of clustering obtained for a dataset consisting of 100 randomly generated points. The positions of the points in the set were created randomly with Gaussian distribution around one point and along three line segments. It has an irregular structure of clusters which are overlapping each other and vary in the density of points. In such a case, the use of _PAA_ is again highly recommended, as it can be observed that a classic algorithm (_K_-means) yields poor results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Dimensionality** & \
\begin{tabular}{c} **Number** \\ **of Clusters** \\ \end{tabular} &
\begin{tabular}{c} **Number** \\ **of Instances** \\ \end{tabular} & **Source** \\ \hline wine & 13 & 3 & 178 & [22] \\ glass & 10 & 7 & 214 & [23] \\ anuran calls & 22 & 10 & 7195 & [24] \\ gestures & 33 & 5 & 1000 & [25] \\ libras & 90 & 15 & 360 & [26] \\ yeast & 8 & 10 & 1484 & [27] \\ s1 & 2 & 15 & 5000 & [21] \\ s2 & 2 & 15 & 5000 & [21] \\ s3 & 2 & 15 & 5000 & [21] \\ s4 & 2 & 15 & 5000 & [21] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Datasets used in the experiments. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(t_{search}\) & 0.05 \\ \(t_{correct}\) & 0.05 \\ \(M_{0}\) & 2 \\ \(S\) & 1 \\ \(a\) & 0.8 \\ \(b\) & 0.001 \\ \(T\) & 0.3 \\ \(F(D_{mean},p)\) & \(\frac{D_{mean}}{1.1-p}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of _PAA_ used in the experiments. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\overline{R}_{PA}\) & \(\overline{R}_{K}\) & **Significant Diff.** \\ \hline wine & 0.646324 & 0.658763 & 0 \\ glass & 0.60919 & 0.506494 & 0 \\ anuran calls & 0.682589 & 0.471739 & \(+\) \\ gestures & 0.7235056 & 0.6380335 & \(+\) \\ libras & 0.856796 & 0.8072391 & \(+\) \\ yeast & 0.621127 & 0.627 & 0 \\ s1 & 0.871717 & 0.934503 & \(-\) \\ s2 & 0.869067 & 0.924032 & 0 \\ s3 & 0.840887 & 0.896415 & \(-\) \\ s4 & 0.876354 & 0.874768 & \(+\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of Rand index for _PAA_ and _K_-means and results of the _t_-test. We have also studied the performance of the proposed technique in comparison with the one of the well-know density-based DBSCAN algorithm.