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This paper introduces regularized functional principal component analysis for multidimensional functional data sets, utilizing Gaussian basis functions. An essential point in a functional approach via... basis expansions is the evaluation of the matrix for the integral of the product of any two bases (cross product matrix). Advantages of the use of the Gaussian type of basis functions in the functional approach are that its cross product matrix can be easily calculated, and it creates a much more flexible instrument for transforming each individual’s observation into a functional form. The proposed method is applied to the analysis of three-dimensional (3D) protein structural data that can be referred to as unbalanced data. It is shown that our method extracts useful information from unbalanced data. Numerical experiments are conducted to investigate the effectiveness of our method via Gaussian basis functions, comparing to the method based on B-splines. On performing regularized functional principal component analysis with B-splines, we also derive the exact form of its cross product matrix. The numerical results show that our methodology is superior to that based on B-splines for unbalanced data.続きを見る
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