It is crucial to determine optimal number of clusters for the quality of clustering in cluster analysis. From the
standpoint of sample geometry, two concepts of sample clustering distance and sample clustering deviation distance are
defined, and a new clustering validity index is designed. In addition, a method for determining optimal number of clusters
based on affinity propagation clustering algorithm is proposed. Theoretical research and experimental results show that the
proposed index and method can evaluate the clustering results effectively, and be suitable for determining optimal number of
clusters.