2019-01-04[Stay Sharp] RBF netwo

作者: 三千雨点 | 来源:发表于2019-01-04 22:00 被阅读4次

RBF Network

RBF stands for Radial Basis Function, and RBF network is an artificial neural network. Its output is linear combination of radial basis functions of the inputs and neuron parameters.

From WikiPedia

RBF network (usually has one hidden layer) can be written by following:

$\varphi ( \boldsymbol { x } ) = \sum _ { i = 1 } ^ { N } w _ { i } \rho \left( \boldsymbol { x } , \boldsymbol { c } _ { i } \right)$

$\rho \left( \boldsymbol { x } , \boldsymbol { c } _ { i } \right) = e ^ { - \beta _ { i } \left\| \boldsymbol { x } - \boldsymbol { c } _ { i } \right\| ^ { 2 } }$
In above equations, $N$ is the number of neurons in the hidden layer, $\boldsymbol {c}_{i}$ is the center vector for neuron $i$ and $w_{i}$ is the weight of neuron $i$ for the output neuron. So the function only depends on the distance from center vector, i.e. the function is radially symmetric about the vector, that's why the function is called radial basis function.