Distributed Shape Learning of Complex Objects Using Gaussian Kernel

TL;DR

This paper presents a distributed learning method for complex object shape recognition using Gaussian kernels, enabling multiple robots to collaboratively learn and share models efficiently despite the infinite-dimensional nature of Gaussian kernel spaces.

Contribution

It introduces a novel reformulation of distributed kernel-based learning that allows sharing Gaussian kernel functions via finite constraints, overcoming previous limitations with polynomial kernels.

Findings

Effective distributed shape learning demonstrated through simulations

Gaussian kernel-based method outperforms polynomial kernel approaches

Finite constraint formulation enables practical implementation in multi-robot systems

Abstract

This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels assumed in our antecessor, we employ Gaussian kernel as a kernel function for classification. The Gaussian kernel prohibits the robots to share the function through a finite number of equality constraints due to its infinite dimensionality of the function space. We thus reformulate the optimization problem assuming that the target function space is identified with the space spanned by the bases associated with not the data but a finite number of grid points. The above relaxation is shown to allow the robots to share the function by a finite number of equality constraints. We finally demonstrate the present approach through numerical simulations.