Abstract
In the field of pattern recognition, clustering groups the data into different clusters on the basis of similarity among them. Many a time, the similarity level between data points is derived through a distance measure; so, a number of clustering techniques reliant on such a measure are developed. Clustering algorithms are modified by employing an appropriate distance measure due to the high versatility of a data set. The distance measure becomes appropriate in clustering algorithm if weights assigned at the components of the distance measure are in concurrence to the problem. In this paper, we propose a new sequence space mathcal{{M}} ( phi,p,mathcal{{F}} ) related to mathcal{L}_{p} using an Orlicz function. Many interesting properties of the sequence space mathcal{{M}} ( phi,p,mathcal{{F}} ) are established by the help of a distance measure, which is also used to modify the k-means clustering algorithm. To show the efficacy of the modified k-means clustering algorithm over the standard k-means clustering algorithm, we have implemented them for two real-world data set, viz. a two-moon data set and a path-based data set (borrowed from the UCI repository). The clustering accuracy obtained by our proposed clustering algoritm outperformes the standard k-means clustering algorithm.
Highlights
Clustering is the process of separating a data set into different groups such that objects in the same cluster should be similar to one another but dissimilar in another cluster [ – ]
The k-means clustering algorithm was introduced by MacQueen [ ], which is based on the minimum distance of the points from the center
4 Conclusions The parameters φ, p, F involved in the sequence space M(φ, p, F ) give additional three degrees of freedom to its induced distance measure
Summary
Clustering is the process of separating a data set into different groups (clusters) such that objects in the same cluster should be similar to one another but dissimilar in another cluster [ – ]. For first time, Khan et al [ ] defined a distance measure of the double sequence of M(φ) and N (φ) to cluster the objects. An Orlicz function and a fuzzy set are used to define other types of double sequence spaces [ , – ]. We define a new double sequence space M(φ, p, F ) related to Lp using the following Orlicz function: M(φ, p, F ). Let be the set of all real-valued double sequences, which is a vector space with coordinatewise addition and scalar multiplication. Let λ be the space of double sequences, converging with respect to some linear convergence rule μ- lim : λ → R.
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