# BELMKN: Bayesian Extreme Learning Machines Kohonen Network
## 2 Methodology
### Partitional Clustering Using the Kohonen Network
Figure 6: Clustering accuracy versus tradeoff parameter \(\lambda\). ### Analysis of Clustering Accuracy Using BELMKN

The proposed BELMKN framework is applied to the 10 datasets from UCI repository. The parameters to the ELM network are set empirically as discussed above, and the outputs of the ELM network with BIC cluster prediction are given to the Kohonen network. Hence, the proposed method is a fully automated clustering approach. This automated approach is observed to perform better than the USELM [28] and the traditional clustering approaches such as k-means, SOM, and EM for most of the datasets. The performance of k-means is observed to be the least for all the datasets. This is because in k-means, the initial centroids are randomly assigned, and cluster centers are iteratively computed. Followed by k-means is SOM, also a linear clustering technique due to the absence of hidden layer. Though k-means and SOM are efficient at grouping linearly separable datasets; SOM overcomes the disadvantage of the k-means approach by using the neighborhood concept, i.e., in SOM the weights of the winning neuron and those neurons within its vicinity (neighborhood threshold) are updated. In Table 3, when we apply k-means and SOM algorithms to Iris dataset, we observe that the class 1 (50 samples), which is linearly separable, is grouped correctly, whereas the grouping of the remaining 100 samples (50 samples of class 2 and 50 samples of class 3) results in more misclassification, as they are nonlinearly separable. Hence, we can observe that k-means and SOM algorithms do not capture the nonlinearity in the dataset. When these algorithms are applied to Glass dataset, it is observed that the overall clustering accuracy is greater but the individual class efficiency is lower, as class 1 and class 2 are dominant in terms of accuracy, with majority of the samples present in these classes (i.e., 70 and 76 samples, respectively), leaving fewer samples to the remaining classes (i.e., class 3, class 4, and class 5 contain 13, 9, and 17 samples, respectively). The overall accuracy for the k-means in Vehicle dataset seems better; this is due to some of the classes data points tend to dominate, and in some case it is sparse; suppose centers are picked in dominated classes; this results slightly better accuracy. Also, the sparse data points are not fully clustered with better accuracy into the respective classes. Overall, it is observed that the accuracy reduces when the sparse data points are overlapped on the dominated data points. From Table 3, we can also observe that the EM algorithm performs better than k-means and SOM. EM clustering is performed probabilistically, unlike k-means and SOM, which use the crisp assignment of the samples to the clusters. When compared to k-means, SOM, and EM algorithms, USELM performs better. In USELM, ELM performs non-linear feature learning, and the extracted features are given to k-means for clustering [28]. In USELM, there is no automatic prediction of the number of clusters [3]; it also suffers from the drawbacks of k-means. In the proposed BELMKN framework, non-linearity is captured well, similarly to USELM network, but the problem of cluster prediction is overcome and the clustering accuracy is improved by using Kohonen Network as the partitional clustering algorithm. Overall, it is observed that the proposed BELMKN framework performs the best among all the clustering techniques used in this study.