A novel sequence space related to [Formula: see text] defined by Orlicz function with application in pattern recognition.

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 [Formula: see text] related to [Formula: see text] using an Orlicz function. Many interesting properties of the sequence space [Formula: see text] 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.

Sequence spaces [Formula: see text] and [Formula: see text] with application in clustering.

Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of [Formula: see text] distance measures, researchers were motivated to use them in almost every clustering process. Beside [Formula: see text] distance measures, there exist several distance measures. Sargent introduced a special type of distance measures [Formula: see text] and [Formula: see text] which is closely related to [Formula: see text]. In this paper, we generalized the Sargent sequence spaces through introduction of [Formula: see text] and [Formula: see text] sequence spaces. Moreover, it is shown that both spaces are BK-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced [Formula: see text]-distance measure (induced by the Sargent sequence space [Formula: see text]) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the [Formula: see text]-distance measure in the k-means algorithm.