In clustering problems, it is difficult to know the optimum number of clusters for a given dataset a priori. Hence, cluster validity indices (CVIs) measuring the fitness of partitions produced by clustering algorithms are important criteria to evaluate the goodness of clustering results. However, many CVIs suffer from asymmetric, arbitrary, noise, and sub-cluster shape of clusters, especially for high-dimensional dataset. Therefore, this paper proposes new CVIs in feature space in which the proposed CVIs transform arbitrary shape of clusters into elliptical or circular clusters by using kernel functions. The experimental results show that the proposed CVIs have a good performance to estimate the optimum number of clusters for asymmetric, noise, and arbitrary shapes of clusters.