Robust functional manifold clustering

In machine learning, it is common to interpret each data sample as a multivariate vector disregarding the correlations among covariates. However, the data may actually be functional, i.e., each data point is a function of some variable, such as time, and the function is discretely sampled. The naive treatment of functional data as traditional multivariate data can lead to poor performance due to the correlations. In this article, we focus on subspace clustering for functional data or curves and propose a new method robust to shift and rotation. The idea is to define a function or curve and all its versions generated by shift and rotation as an equivalent class and then to find the subspace structure among all equivalent classes as the surrogate for all curves. Experimental evaluation on synthetic and real data reveals that this method massively outperforms prior clustering methods in both speed and accuracy when clustering functional data.