Low-Rank Representation over the Manifold of Curves
This work addresses the challenge of improving subspace analysis for functional data in machine learning, which is an incremental advancement over existing LRR methods.
The paper tackles the problem of analyzing functional data, where each data point is a function, by proposing a method using Low-Rank Representation (LRR) to account for curvature correlations, and it reports that this method massively outperforms conventional LRR 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 method to analyse subspace structure of the functional data by using the state of the art Low-Rank Representation (LRR). Experimental evaluation on synthetic and real data reveals that this method massively outperforms conventional LRR in tasks concerning functional data.