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 . Our suggested algorithm calculates pair-wise projection of the data. We use probabilistic considerations to prove the algorithm correctness. These probabilistic results are of independent interest, as can serve to better understand the geometry of high dimensional objects .