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