多机器人协同学习复杂物体形状，用高斯核提升分类精度。
Distributed Shape Learning of Complex Objects Using Gaussian Kernel
- 用高斯核替代多项式核，突破原有方法限制
- 通过网格点基函数近似无限维空间，实现有限约束共享
- 适合分布式机器人系统中的形状学习任务
本文针对多个网络化机器人在分布式环境下对复杂物体的形状学习问题，结合分布式优化与基于核的支持向量机方法。为克服先前工作依赖多项式核带来的根本局限，采用高斯核进行分类。由于高斯核对应函数空间无限维，无法通过有限个等式约束直接共享函数，因此将目标函数空间重构为由有限网格点对应的基函数张成的空间。该近似使机器人可通过有限个等式约束实现函数共享。最后通过数值仿真验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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