Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms
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Abstract (arXiv)
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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References · 32
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20 more
- 2019Neural Collaborative Subspace Clusteringcited by 21
- 2020A Critique of Self-Expressive Deep Subspace Clusteringcited by 18
- 2020Stochastic Sparse Subspace Clusteringcited by 17
- 2013Robust Subspace Clustering via Thresholdingcited by 16
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- 2017Adaptive Low-Rank Kernel Subspace Clusteringcited by 1
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