# Tractable Clustering of Data on the Curve Manifold

## TL;DR

This paper introduces a new clustering method for functional data on the curve manifold, adapting low-rank representation techniques to improve speed and accuracy over previous methods.

## Contribution

It presents a novel, tractable approach to cluster functional data by extending Euclidean Low-Rank Representation to the curve manifold.

## Key findings

- Massively outperforms prior methods in accuracy
- Significantly faster clustering process
- Effective on both synthetic and real data

## 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 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.