This paper presents a clustering algorithm for dot patterns in n-dimensional space. The n-dimensional space often represents a multivariate (nf -dimensional) function in a ns-dimensional space (ns + nf = n). The proposed algorithm decomposes the clustering problem into the two lower dimensional problems. Clustering in nf -dimensional space is performed to detect the sets of dots in n-dimensiona...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...