Analysis and Extension of Arc-Cosine Kernels for Large Margin Classification

Understand

We investigate a recently proposed family of positive-definite kernels that mimic the computation in large neural networks.

• We examine the properties of these kernels using tools from differential geometry; specifically, we analyze the geometry of surfaces in Hilbert space that are induced by these kernels.
• When this geometry is described by a Riemannian manifold, we derive results for the metric, curvature, and volume element.
• Interestingly, though, we find that the simplest kernel in this family does not admit such an interpretation.