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Identifying the number $K$ of clusters in a dataset is one of the mostdifficult problems in clustering analysis. A choice of $K$ that correctlycharacterizes the features of the data is essential for building meaningfulclusters. In this paper we tackle the problem of estimating the number ofclusters in functional data analysis by introducing a new measure that can beused with different procedures in selecting the optimal $K$. The main idea isto use a combination of two test statistics, which measure the lack ofparallelism and the mean distance between curves, to compute criteria such asthe within and between cluster sum of squares. Simulations in challengingscenarios suggest that procedures using this measure can detect the correctnumber of clusters more frequently than existing methods in the literature. Theapplication of the proposed method is illustrated on several real datasets.

Selection of the Number of Clusters in Functional Data Analysis