Optimal $k$-Discretization Learning

Tong Wang, Zhangyang Wang

Keywords: Clustering

Abstract:

The $k$-discretization problem is known to be NP-hard in general. Existing algorithms exploit various heuristics and obtain at most local minima that are sensitive to initializations. This paper starts by discussing how to leverage polynomial-time optimal solvers for 1-D $k$-discretization which can serve as a powerful and parsimonious regularizer for complex learning tasks.
The algorithm can be accelerated by sampling, with bounded approximation errors proven. The paper then presents an embedding learning approach to handle multi-dimensional $k$-discretization, based on the 1-D solution. Equipped with many novel task-specific modifications, the proposed approach achieves highly promising performance on a vast variety of application tasks, including signal quantization, image clustering, and image smoothening. Our codes are available at \url{https://github.com/VITA-Group/SnC}.

Submission Number: 10