LAUSR

Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of lp$l_{p}$ distance measures, researchers were motivated to use them in almost every clustering process. Beside lp$l_{p}$ distance measures, there exist several distance measures. Sargent introduced a special type of distance measures m(ϕ)$m(\phi)$ and n(ϕ)$n(\phi)$ which is closely related to lp$l_{p}$. In this paper, we generalized the Sargent sequence spaces through introduction of M(ϕ)$M(\phi)$ and N(ϕ)$N(\phi)$ 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 M(ϕ)$M(\phi)$-distance measure (induced by the Sargent sequence space M(ϕ)$M(\phi)$) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the M(ϕ)$M(\phi)$-distance measure in the k-means algorithm.