Abstract
In this paper, we deal with the relation between functional clustering and functional principal points. The k principal points are defined as the set of k points which minimizes the sum of expected squared distances from every points in the distribution to the nearest point of the set, and are mathematically equivalent to centers of gravity by k-means clustering.[3] The concept of principal points can be extended for functional clustering. We call the extended principal points functional principal points. Random function[5] is defined in a probability space, and functional principal points of a random function have a close relation to functional data analysis. We derive functional principal points of polynomial random functions using orthonormal basis transformation. For functional data following Gaussian random functions, we discuss the relation between the optimum clustering of the functional data and the functional principal points.
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Shimizu, N., Mizuta, M. (2007). Functional Clustering and Functional Principal Points. In: Apolloni, B., Howlett, R.J., Jain, L. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2007. Lecture Notes in Computer Science(), vol 4693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74827-4_63
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DOI: https://doi.org/10.1007/978-3-540-74827-4_63
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