# K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony
## 4 Numerical Experiments
### CAABC-K-means Performance Analysis  
The CAABC clustering algorithm on four standard evaluation indices are tested and compared with other well-known algorithms to evaluate the clustering performance of the proposed algorithm. To prove the clustering performance of the improved algorithm, in addition to the comparison algorithm mentioned above, experimental comparison with PA [35] and GPAM [37] clustering algorithm are also added. The general parameter setting is shown in Table 2. In addition, the maximum number of iterations \(max\)_cycle_ is set to 100. The eleven datasets are Iris (7 January 1988), Balance-scale (22 April 1994), Wine (7 January 1991), E.coli (1 September 1996), Glass (9 January 1987), Abalone (12 January 1995), Musk (9 December 1994), Pendigits (7 January 1998), Skin Seg (17 July 2012), CMC (7 July 1997), and Cancer datasets (3 March 2017)([[http://archive.ics.uci.edu/ml/](http://archive.ics.uci.edu/ml/)]([http://archive.ics.uci.edu/ml/](http://archive.ics.uci.edu/ml/))). They have been considered to study and evaluate the performance of algorithms by many authors. The details of Iris, Balance-scale, Wine, E.coli, Glass, Abalone, Musk, Pendigits, Skin Seg, CMC, and Cancer datasets are summarized in Table 5. The optimal result is shown in bold in Tables 6-9. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Datasets** & **K-Means** & \begin{tabular}{c} **ABC+K-** \\ **Means** \\ \end{tabular} & \begin{tabular}{c} **PSO+K-** \\ **Means** \\ \end{tabular} & \
\begin{tabular}{c} **CAABC-** \\ **K-Means** \\ \end{tabular} & **PAM** & **GPAM** \\ \hline Iris & 70.22 & 71.32 & 73.32 & **79.08** & 77.39 & 79.06 \\ \hline
\begin{tabular}{c} Balance- \\ scale \\ \end{tabular} & 52.33 & 53.21 & 56.33 & **59.03** & 53.49 & 57.83 \\ \hline Glass & 39.44 & 40.32 & 40.36 & **49.32** & 48.23 & 49.03 \\ \hline Wine & 38.09 & 40.30 & 53.20 & **57.20** & 56.32 & 57.04 \\ \hline ECOLI & 57.00 & 57.30 & 57.40 & **60.32** & 56.03 & 58.33 \\ \hline Abalone & 49.00 & 47.30 & 49.50 & **68.09** & 48.22 & 57.34 \\ \hline Musk & 50.02 & 53.40 & 59.32 & **59.98** & 47.56 & 54.99 \\ \hline Pendigits & 40.05 & 40.78 & 49.03 & **58.93** & 40.00 & 56.09 \\ \hline Skin Seg. & 78.00 & 79.03 & 83.01 & **88.7** & 63.04 & 80.37 \\ \hline CMC & 68.04 & 79.03 & 83.07 & **89.00** & 69.34 & 74.95 \\ \hline Cancer & 53.99 & 58.34 & 56.83 & **59.99** & 57.09 & 59.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The Normalized Mutual Information for classifying the eleven training datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datasets** & **K-Means** & \begin{tabular}{c} **ABC+K-** \\ **Means** \\ \end{tabular} & \begin{tabular}{c} **PSO+K-** \\ **Means** \\ \end{tabular} & \
\begin{tabular}{c} **CAABC-** \\ **K-Means** \\ \end{tabular} & **PAM** & **GPAM** \\ \hline Iris & 50.28 & 54.32 & 53.02 & **59.06** & 58.99 & 59.00 \\ \hline
\begin{tabular}{c} Balance- \\ scale \\ \end{tabular} & 50.33 & 52.29 & 51.03 & **60.01** & 54.04 & 58.32 \\ \hline Glass & 60.44 & 59.32 & 58.96 & **69.32** & 68.33 & 69.08 \\ \hline Wine & 89.10 & 89.19 & 90.43 & **93.11** & 92.84 & 92.94 \\ \hline ECOLI & 83.76 & 84.30 & 85.29 & **89.04** & 86.00 & 87.04 \\ \hline Abalone & 70.99 & 72.02 & 74.91 & **84.11** & 84.01 & 84.05 \\ \hline Musk & 60.73 & 69.93 & 68.34 & **70.00** & 68.35 & 69.68 \\ \hline Pendigits & 50.82 & 50.01 & 59.11 & **63.47** & 53.06 & 62.44 \\ \hline Skin Seg. & 70.93 & 72.38 & 80.93 & **81.02** & 60.99 & 75.64 \\ \hline CMC & 59.02 & 59.24 & 59.15 & **62.03** & 58.37 & 60.75 \\ \hline Cancer & 49.03 & 53.04 & 53.75 & **59.23** & 57.98 & 59.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The Accuracy for classifying the eleven training datasets. We use standard evaluation index, Normalized Mutual Information (\(NMI\)), Accuracy (\(ACC\)), and F-score [38] to evaluate the clustering performance of CAABC-K-means algorithm and other algorithms. The corresponding results and the running time of the algorithm are analyzed in Tables 6-9.