Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds.

Segmentation, the task of delineating and isolating distinct objects, is a fundamental problem in computer vision. Much of the current approaches are supervised, relying on expensive manual annotations.

Multi-task learning is a promising paradigm for handling several tasks simultaneously using a unified architecture.

We study the proportional clustering problem of Chen et al. (ICML '19) and relate