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Radial Basis Function Networks

A radial basis function (RBF) is a function that assigns a real value to each input from its domain (it is a real-value function), and the value produced by the RBF is always an absolute value; i.e. it is a measure of distance and cannot be negative.

f(x) = f(||x||)

Euclidean distance, the straight-line distance between two points in Euclidean space, is typically used.

Radial basis functions are used to approximate functions, much as neural networks act as function approximators. The following sum:

RBF network

represents a radial basis function network. The radial basis functions act as activation functions.

The approximant f(x) is differentiable with respect to the weights W, which are learned using iterative updater methods commong among neural networks.

Further Reading

Chris Nicholson

Chris Nicholson is the CEO of Skymind. He previously led communications and recruiting at the Sequoia-backed robo-advisor, FutureAdvisor, which was acquired by BlackRock. In a prior life, Chris spent a decade reporting on tech and finance for The New York Times, Businessweek and Bloomberg, among others.

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