Tractable Clustering of Data on the Curve Manifold
This addresses the challenge of clustering functional data for machine learning applications, offering a tractable solution that improves performance over naive methods.
The paper tackles the problem of clustering functional data by adapting the Euclidean Low-Rank Representation to the curve manifold, resulting in a method that massively outperforms prior approaches in both speed and accuracy on synthetic and real data.
In machine learning it is common to interpret each data point as a vector in Euclidean space. 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 since the algorithms are ignoring the correlation in the curvature of each function. In this paper we propose a tractable method to cluster functional data or curves by adapting the Euclidean Low-Rank Representation (LRR) to the curve manifold. 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.