1 research outputs found
K-means algorithms for functional data
Cluster analysis of functional data considers that the objects on which you want to perform a taxonomy
are functions f : X e Rp âŠR and the available information about each object is a sample in a ïŹnite set of points f ÂŒ fĂ°x ; y ĂA X x Rgn . The aim is to infer the meaningful groups by working explicitly with its inïŹnite-dimensional nature.
In this paper the use of K-means algorithms to solve this problem is analysed. A comparative study of three K-means algorithms has been conducted. The K-means algorithm for raw data, a kernel K-means algorithm for raw data and a K-means algorithm using two distances for functional data are tested. These distances, called dVn and dÏ, are based on projections onto Reproducing Kernel Hilbert Spaces (RKHS) and Tikhonov regularization theory. Although it is shown that both distances are equivalent, they lead to two different strategies to reduce the dimensionality of the data. In the case of dVn distance the most suitable strategy is JohnsonâLindenstrauss random projections. The dimensionality reduction for dÏ is based on spectral methods