Several methods for dimensionality reduction in the clustering procedures have been proposed. This paper reviews that a method of dimensionality reduction by principal components analysis is formed linear combinations of the features of given patterns. The main object of principal components analysis is to find a lower-dimensional representation that accounts the variance of the features. Moreover, the method of iterative improvement to minimize the sum-of-squared-error criterion for clustering is described. And to show the usefulness of the above mentioned method, the simulation for concrete pattern samples on a computer is excuted, and we can obtain the good agreement with our theoretical results.