Functional data clustering using K-means and random projection with applications to climatological data

Abstract

In this paper, an efficient pattern recognition method for functional data is introduced. The proposed method works based on reproducing kernel Hilbert space (RKHS), random projection and K-means algorithm. First, the infinite dimensional data are projected onto RKHS, then they are projected iteratively onto some spaces with increasing dimension via random projection. K-means algorithm is applied to the projected data, and its solution is used to start K-means on the projected data in the next spaces. We implement the proposed algorithm on some simulated and climatological datasets and compare the obtained results with those achieved by K-means clustering using a single random projection and classical K-means. The proposed algorithm presents better results based on mean square distance (MSD) and Rand index as we have expected. Furthermore, a new kernel based on a wavelet function is used that gives a suitable reconstruction of curves, and the results are satisfactory.