Abstract:
Computing or approximating the convex hull of a dataset plays a role in a wide range of applications, including economics, statistics, and physics, to name just a few. Ho...Show MoreMetadata
Abstract:
Computing or approximating the convex hull of a dataset plays a role in a wide range of applications, including economics, statistics, and physics, to name just a few. However, convex hull computation and approximation is exponentially complex, in terms of both memory and computation, as the ambient space dimension increases. In this paper, we propose DeepHull, a new convex hull approximation algorithm based on convex deep networks (DNs) with continuous piecewise-affine nonlinearities and nonnegative weights. The idea is that binary classification between true data samples and adversarially generated samples with such a DN naturally induces a polytope decision boundary that approximates the true data convex hull. A range of exploratory experiments demonstrates that DeepHull efficiently produces a meaningful convex hull approximation, even in a high-dimensional ambient space.
Published in: ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Date of Conference: 23-27 May 2022
Date Added to IEEE Xplore: 27 April 2022
ISBN Information: