# BELMKN: Bayesian Extreme Learning Machines Kohonen Network
## 2 Methodology
### Partitional Clustering Using the Kohonen Network
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sl No.** & **Dataset** & **k-Means** & **SOM** & **EM** & **USELM** & **BELMKN** \\ \hline
1 & Cancer & 85.4\% (5) & 86\% (4) & 91.21\% (2) & 90\% (3) & 92.6\% (1) \\
2 & Dermatology & 26.2\% (5) & 32\% (4) & 67.75\% (3) & 82\% (2) & 90.1\% (1) \\
3 & _E. coli_ & 59.9\% (4) & 61\% (3) & 77.98\% (2) & 82\% (1) & 82\% (1) \\
4 & Glass & 54.2\% (1) & 54\% (2) & 47.66\% (4) & 42\% (5) & 48\% (3) \\
5 & Heart & 59.2\% (4) & 60\% (3) & 53.33\% (5) & 70\% (2) & 75.5\% (1) \\
6 & Horse & 48\% (3) & 48\% (3) & 43.4\% (4) & 65\% (1) & 63.18\% (2) \\
7 & Iris & 80\% (5) & 82\% (4) & 90\% (3) & 96\% (2) & 97\% (1) \\
8 & Thyroid & 86\% (5) & 87\% (4) & 94.27\% (3) & 89\% (3) & 90.5\% (2) \\
9 & Vehicle & 44\% (2) & 44\% (2) & 45.035\% (1) & 42\% (3) & 41\% (4) \\
10 & Wine & 70\% (5) & 75\% (4) & 90.44\% (3) & 94\% (2) & 96.6\% (1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Clustering accuracy percentage and ranking of various techniques on each dataset. In Table 4, the average clustering accuracy for all the clustering techniques with 10 datasets is shown. In this table, we observe that BELMKN has the highest average clustering accuracy, followed by US-ELM. Among traditional clustering methods, EM is better than k-means, and SOM is better than the k-means algorithm. In Table 5, the sum of the ranks for all the datasets taken from Table 3 for each of the clustering techniques is presented. By ranking the sum of ranks, the proposed BELMKN is better than all other clustering methods. This is followed by USELM, whereas EM is better than SOM and k-means, and SOM is better than k-means. ## 5 Conclusions

This paper presents the Bayesian Extreme Learning Machine Kohonen Network (BELMKN) framework, which consists of three levels, to improve the clustering accuracy of the nonlinearly distributed dataset. ELM is used for feature learning, followed by BIC a model selection technique to extract the optimal number of clusters and the Kohonen Network for clustering the dataset. It is also observed that the performance of the BELMKN network depends on the number of parameters such as the tradeoff parameter (\(\lambda\)), the number of nearest neighbours (\(\sigma\)), and the number of hidden neurons (\(\alpha\)), which have to be set empirically for each dataset. These parameters need to be fine-tuned to avoid overfitting or underfitting. The clustering task is successfully accomplished by applying 10 benchmark datasets from the UCI machine learning repository using the process of partitional clustering using the BELMKN. The clustering performance is compared with k-means, Self-Organizing Maps, the EM Algorithm, and USELM. From the results obtained, we can conclude that BELMKN is reliable and involves efficient clustering in terms of accuracy, which can also be used on complex datasets. Although the results are very promising, there is still room for improvement. For example, it is challenging to generate optimal cluster centers with a big dataset with a varying number of dimensions (i.e., some class data points may have fewer samples in comparison with others); this may provide opportunities for further research. In addition, the clustering of the big dataset by implementing the BELMKN as a hierarchical clustering may provide better clustering efficiency. It will be useful to investigate these topics further. [PERSON] conceived and designed the research; [PERSON], [PERSON], [PERSON], and [PERSON] developed and analyzed the data; [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] wrote and edited the paper. The authors declare no conflict of interest. ## References

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