Artificial neural network note-radial basis function (Radial foundation FUNCTION-RBF)

RBF network originates from the radial basis function method of multivariate interpolation in numerical analysis, which has the best approximation characteristic which is not available in traditional BP network.

The three-layer RBF network has the ability to approximate any function.

It is assumed that the number of nodes in the hidden layer of the input nodes in the network is n,l,m. The function of the hidden layer is to transform the input mode into the high dimensional space in order to facilitate the classification and recognition of the output layer.

The most commonly used radial basis function is the Gaussian kernel function, in the form of K (| | x-xc| |) =exp{-| | x-xc| | ^2/(2*σ) ^2)} XC is the center of the kernel function, and σ is the width parameter of the function, which controls the radial scope of function.

Kernel function Center can get the central vector of clustering by K-means clustering algorithm, and σ is the radius of cluster center. This radius equals the average of the distance between the cluster center vector and the sample that belongs to the class.

When the center vector and radius of each hidden layer are determined, the unknown parameters in the network structure are only the linear weights and thresholds of the output cells.

In the adjustment of linear weights and thresholds, the steepest gradient descent method in BP network can be used.

The above part was originally my draft, because there is a little doubt about the RBF, and then read some related papers, found that is the SOM network and the integrated version of the BP network.

First of all, to get the kernel function, we can use SOM network to get the kernel function center by clustering the samples.

Then the weight adjustment is simple, since it has been said that the BP network can be used to reduce the steepest gradient ... So what's the difference from the BP network? The process has become completely consistent. Of course, I would choose to use PSO particle swarm to accomplish this process.

I see another method in the theory of neural networks that passes through a matrix to a value that can be directly weighted. For the moment, I don't know why.

There are also many papers mentioned in the orthogonal least squares method ... I do not know is my problem or the problem of the paper ... Each paper is not very consistent ... I have no idea what this method is for the time being.

Over

Ps:

I wrote it all to myself. Study the thinking record. ^_^