# BELMKN: Bayesian Extreme Learning Machines Kohonen Network
## 1 Introduction  
Clustering is an unsupervised way of exploring the data and its distribution by grouping data points into a number of clusters [1; 2]. The aim of clustering is to find the internal structure of the data and is therefore exploratory in nature. Clustering is used in many engineering applications, for example, in a search for data clustering in Google Scholar [3], which reveals thousands of entries year-wise [4]; in social networking sites to identify the cohesive group of friends; and in online shopping sites to group customers with similar behavior based on their past purchase records. It is further used in satellite image processing to identify land use land cover [5; 6] and to locate the sensitive regions during an earthquake [7]. It is also used in biomedical applications [8] and software effort estimation [9]. In the literature, most of the unsupervised learning methods in particular clustering can be categorized into a crisp or probabilistic-based approach to cluster the data [10; 11; 12]. These clustering algorithms are found to work extensively well on linearly separable datasets, but the clustering accuracy drastically decreases with a multi-modal, multi-class overlap dataset with higher dimensionality and a large number of samples, because they fail to explore the underlying structureof the data [13]. Among different clustering algorithms, k-means is a widely used crisp-based approach for clustering the dataset [14]. The k-means algorithm requires apriori information of the number of clusters. The clustering is performed iteratively by random initialization of cluster centers, and groups the samples using some similarity measures (distance criteria) [14; 15]. The Kohonen Network (KN) [16] is a crisp-based neural network clustering algorithm. The KN uses a competitive learning mechanism to extract knowledge in the form of weights (cluster centers), iteratively [17]. The Expectation Maximization (EM) algorithm is a widely used, probabilistic-based approach, in which likelihood estimation of the data points to the cluster is performed [18]. EM uses a Gaussian Mixture Model (GMM) to cluster the datasets. The GMM algorithm is a useful model selection tool with which to estimate the likelihood of data distribution by fitting the finite mixture model [19]. The common problems in most of the aforementioned algorithms are in estimating the number of clusters prior to, and that converge to, local optima [20; 21]. This results in low clustering efficiency for nonlinearly separable datasets in which the samples of different classes overlap. To overcome the problems involved with these conventional clustering approaches, there is a need for an efficient clustering algorithm that takes care of feature learning [22] and cluster prediction [23]. The automatic prediction of the number of clusters can be statistically determined using the model selection approach [24]. To perform efficient clustering, it is crucial to choose the right feature learning technique. Therefore, the useful data representations are first extracted using the Extreme Learning Machine (ELM)-based feature learning technique [25; 26]. ELM is a non-iterative feature learning technique that uses a single hidden layer [27]. ELM has many advantages over iterative feature learning algorithms such as gradient-based methods. The problem with gradient-based methods is that they are mostly iterative in nature, do not guarantee convergence to global minima, and are computationally expensive. ELM computes the weights between the hidden and output layer in one step with better generalization [25]. ELM was initially used for classification and regression [26]; recently, [PERSON] et al., 2014 [28] proposed the Unsupervised ELM (US-ELM) to solve the clustering problem. In their study, the number of clusters is assigned apriori and feature extracted data is clustered using k-means algorithm [28]. In this paper, we propose the Bayesian Extreme Learning Machine Kohonen Network (BELMKN) framework for clustering the datasets.