Beyond linear subspace clustering: A comparative study of nonlinear manifold clustering algorithms

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