An Exact Reformulation of Feature-Vector-based Radial-Basis-Function Networks for Graph-based Observations

01/22/2019
by   Isaac J. Sledge, et al.
14

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squares objective function so that it is purely dependent on entries from the adjacency matrix. From this objective function, we derive a gradient descent update for the network weights. We also derive a gradient update that simulates the repositioning of the radial basis prototypes and changes in the radial basis prototype parameters. An important property of our radial basis function networks is that they are guaranteed to yield the same responses as conventional radial-basis networks trained on a corresponding vector realization of the relationships encoded by the adjacency-matrix. Such a vector realization only needs to provably exist for this property to hold, which occurs whenever the relationships correspond to distances from some arbitrary metric applied to a latent set of vectors. We therefore completely avoid needing to actually construct vectorial realizations via multi-dimensional scaling, which ensures that the underlying relationships are totally preserved.

READ FULL TEXT

page 8

page 9

page 15

research
03/15/2021

Online Learning with Radial Basis Function Networks

We investigate the benefits of feature selection, nonlinear modelling an...
research
04/05/2023

On the universal approximation property of radial basis function neural networks

In this paper we consider a new class of RBF (Radial Basis Function) neu...
research
01/09/2014

Radial basis function process neural network training based on generalized frechet distance and GA-SA hybrid strategy

For learning problem of Radial Basis Function Process Neural Network (RB...
research
03/09/2023

Provable Data Subset Selection For Efficient Neural Network Training

Radial basis function neural networks (RBFNN) are well-known for their c...
research
06/03/2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into ...
research
08/10/2020

Meshless Approximation and Helmholtz-Hodge Decomposition of Vector Fields

The analysis of vector fields is crucial for the understanding of severa...
research
12/12/2019

Towards Expressive Priors for Bayesian Neural Networks: Poisson Process Radial Basis Function Networks

While Bayesian neural networks have many appealing characteristics, curr...

Please sign up or login with your details

Forgot password? Click here to reset