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This paper introduces functional cluster analysis (FCA) for multidimensional functional data sets, utilizing orthonormal Gaussian basis functions. An essential point in FCA is the use of orthonormal b...ases that yield the identity matrix for the integral of the product of any two bases (identity cross product matrix). We construct orthonormal Gaussian basis functions using Cholesky decomposition and derive its property concerning the Gram-Schmidt orthonormalization. Advantages of the functional clustering approach are that it can be applied to the data observed at possibly different time points for each subject, and the functional structure behind the data can be captured by removing the measurement errors. The proposed method is applied to three-dimensional (3D) protein structural data that determine the 3D arrangement of amino acids in individual protein. In addition, numerical experiments are conducted to investigate the effectiveness of our method with the orthonormal Gaussian bases, comparing to conventional cluster analysis. The numerical results show that our methodology is superior to the conventional method for noisy data sets with outliers.続きを見る
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