Before revision:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together   .
After revision:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together , using the following assumptions: 1) There are m clusters. 2) Each cluster is modeled as a ball in \mathbb{R .