Back to the Future: Radial Basis Function Network Revisited.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Computational Science

Background:

• Radial Basis Function (RBF) networks are established supervised learning algorithms.
• Current training often uses kernel methods with Reproducing Kernel Hilbert Space (RKHS) regularization.
• Older RBF training approaches warrant modern re-evaluation.

Purpose of the Study:

• To analyze older Radial Basis Function (RBF) network training methods from a contemporary viewpoint.
• To demonstrate that common regularization techniques can be viewed as data-dependent kernels.
• To compare these methods against standard kernel approaches.

Main Methods:

• Analysis of RBF network training using coefficient norm regularization.
• Investigation of RBF network training with k-means clustering for centers.
• Recasting these regularization procedures as data-dependent kernels.
• Theoretical analysis and experimental validation.

Main Results:

• Both analyzed RBF methods are shown to be equivalent to specific data-dependent kernels.
• Experimental results demonstrate competitive performance against standard kernel methods.
• Identified advantages in flexibility, including unlabeled data incorporation, and reduced computational complexity.

Conclusions:

• Older RBF network training methods, when re-examined, function as flexible and computationally efficient data-dependent kernels.
• These findings provide theoretical grounding for recent successes in image recognition using soft k-means features.
• The revisited methods offer a valuable alternative to traditional kernel-based RBF network training.