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

• URL: http://arxiv.org/abs/2103.10656v1
• Date: Fri, 19 Mar 2021 06:34:34 GMT
• Title: Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms
• Authors: Maryam Abdolali, Nicolas Gillis
• Abstract summary: Subspace clustering is an important unsupervised clustering approach. 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 detailed analysis of these approaches unfolds potential research directions and unsolved challenges in this field.
• Score: 22.564682739914424
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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