| Summary: | In this work, we consider the problem of determining the number of clusters in the multivariate and functional data, where the data are represented by a mixture model in which each component corresponds to a different cluster without any prior knowledge of the number of clusters. For the multivariate case, we propose a new forward search methodology based on spatial ranks. We also propose a modified algorithm based on the volume of central rank regions. Our numerical examples show that it produces the best results under elliptic symmetry and it outperforms the traditional forward search based on Mahalanobis distances. In addition, a new nonparametric multivariate clustering method based on different weighted spatial ranks (WSR) functions is proposed. The WSR are completely data-driven and easy to compute without any need to parameter estimates of the underlying distributions, which make them robust against distributional assumptions. We have considered parametric and nonparametric weights for comparison. We give some numerical examples based on both simulated and real datasets to illustrate the performance of the proposed method. Moreover, we propose two different clustering methods for functional data. The first method is an extension to the forward search based on functional spatial ranks (FSR) that we proposed for the multivariate case. In the second method, we extend the WSR method to the functional data analysis. The proposed weighted functional spatial ranks (WFSR) method is a filtering method based on FPCA. Comparison between the existing methods has been considered. The results showed that the two proposed methods give a competitive and quite reasonable clustering analysis.
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