This paper proposes a new method called depth difference (DeD), for estimating the optimal number of clusters (k) in a dataset based on data depth. The DeD method estimates the k parameter before actual clustering is constructed. We define the depth within clusters, depth between clusters, and depth difference to finalize the optimal value of k, which is an input value for the clustering algorithm. The experimental comparison with the leading state-of-the-art alternatives demonstrates that the proposed DeD method outperforms.

Clustering is a key method in unsupervised learning with various applications in data mining, pattern recognition and intelligent information processing. However, the number of groups to be formed, usually notated as [Formula: see text] is a vital parameter for most of the existing clustering algorithms as their clustering results depend heavily on this parameter. The problem of finding the optimal [Formula: see text] value is very challenging. This paper proposes a novel idea for finding the correct number of groups in a dataset based on data depth. The idea is to avoid the traditional process of running the clustering algorithm over a dataset for [Formula: see text] times and further, finding the [Formula: see text] value for a dataset without setting any specific search range for [Formula: see text] parameter. We experiment with different indices, namely CH, KL, Silhouette, Gap, CSP and the proposed method on different real and synthetic datasets to estimate the correct number of groups in a dataset. The experimental results on real and synthetic datasets indicate good performance of the proposed method.

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Boosting is a generally known technique to convert a group of weak learners into a powerful ensemble. To reach this desired objective successfully, the modules are trained with distinct data samples and the hypotheses are combined in order to achieve an optimal prediction. To make use of boosting technique in online condition is a new approach. It motivates to meet the requirements due to its success in offline conditions. This work presents new online boosting method. We make use of mean error rate of individual base learners to achieve effective weight distribution of the instances to closely match the behavior of OzaBoost. Experimental results show that, in most of the situations, the proposed method achieves better accuracies, outperforming the other state-of-art methods.

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The purpose of this paper is to design an algorithm for star partitions of the graph. We shall now bring out a useful connection between the domination number of a graph and what we shall choose to call the 'star partition number' of the graph which is an invariant of the graph defined by a certain type of partition of its vertex set. We consider finite undirected graphs without loops or multiple edges