One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter.

The main idea is to allocate the jump position of the within-cluster dispersion function using Chebyshev polynomial approximations. The confidence interval for the true number of clusters can be obtained in this way by means of a comparatively small number of the distortion calculations. a significant computational complexity decreasing is proven. Several examples are given to demonstrate the high ability of the proposed methodology.