Metric Learning-Based Subspace Clustering

Yesong Xu, Shuo Chen, Jun Li, Jian Yang

Abstract: The self-expressive strategy has shown excellent capabilities in realizing low-dimensional representations of high-dimensional data for subspace clustering algorithms. The existing designs, however, are formulated on the linearization assumptions of the data, neglecting the precise characterization of linear relationships within samples. Considering that real-world data adheres to diverse distribution forms, it becomes impractical to first treat the samples as existing in a uniform linear space before finding an appropriate manifold space. To handle this challenge, we propose a novel self-expressive-based learning framework termed metric learning-based subspace clustering (MLSC). Particularly, we smoothly incorporate metric learning into the subspace clustering framework by introducing adaptive neighbors learning and defining a linearity-aware distance to discover the linear manifold space of the original data. We simultaneously utilize the generated representation of the linear structure as input for self-expressiveness to pursue an ideal similarity matrix, which establishes an essential connection with the linearization assumption of the self-expressive strategy. Furthermore, we theoretically demonstrate that our measure can accurately describe the level of linear correlation between instances. Finally, our tests demonstrate that the proposed MLSC attains competitive clustering results compared to state-of-the-art approaches on benchmark datasets.