What are basis functions? Gaussian basis functions

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・Gaussian distribution

■What are basis functions?

A basis function is a function that serves as the basis for expressing an arbitrary function by combining multiple functions. For example, the following function is made up of a combination of cubic, quadratic, and linear functions. At this time, each function is called a basis function.

■Gaussian basis functions

The above is called a polynomial basis function. Others include the Gaussian basis function, which uses a Gaussian distribution as a basis function. It is expressed as follows. The above is called a polynomial basis function. Others include the Gaussian basis function, which uses a Gaussian distribution as a basis function. It is expressed as follows.



In the above, the standard deviation is fixed to an arbitrary value. The coefficients of the Gaussian distribution are included in w.



Below is an example using Gaussian basis functions. By combining various values of w, functions of various shapes can be expressed.

■Uses of basis functions

Used when performing nonlinear regression analysis.

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