Low-Rank Representation over the Manifold of Curves

TL;DR

This paper introduces a novel low-rank representation method tailored for functional data on manifolds, effectively capturing the correlation in the curvature of functions, and demonstrates significant performance improvements over traditional methods.

Contribution

It extends low-rank representation techniques to the manifold of curves, addressing the limitations of treating functional data as Euclidean vectors.

Findings

Massively outperforms conventional LRR on synthetic data

Significant improvements on real functional datasets

Effective in capturing curvature correlations

Abstract

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.