Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms

TL;DR

This paper provides a comprehensive comparison of nonlinear manifold clustering algorithms, categorizing them into locality preserving, kernel-based, and neural network-based methods, highlighting their strengths, limitations, and future research directions.

Contribution

It introduces a new taxonomy for nonlinear subspace clustering methods and extensively compares major algorithms on synthetic and real data sets.

Findings

Neural network-based methods outperform others on complex data.

Kernel-based approaches excel in certain synthetic scenarios.

Locality preserving methods show robustness in noisy environments.

Abstract

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the prominent subspace clustering algorithms rely on the representation of the data points as linear combinations of other data points, which is known as a self-expressive representation. To overcome the restrictive linearity assumption, numerous nonlinear approaches were proposed to extend successful subspace clustering approaches to data on a union of nonlinear manifolds. In this comparative study, we provide a comprehensive overview of nonlinear subspace clustering approaches proposed in the last decade. We introduce a new taxonomy to classify the state-of-the-art approaches into three categories, namely locality preserving, kernel based, and neural network based. The major representative algorithms within each category are extensively compared on carefully designed synthetic and real-world data sets. The detailed analysis of these approaches unfolds potential research directions and unsolved challenges in this field.