Tag Archives: rbf kernel

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Gaussian kernel regression with Matlab code (Gaussian Kernel or RBF Smoother)

Gaussian kernel regression with Matlab code

In this article, I will explain Gaussian Kernel Regression (or Gaussian Kernel Smoother, or Gaussian Kernel-based linear regression, RBF kernel regression)  algorithm. Plus I will share my Matlab code for this algorithm. 

If you already know the theory. Just download  from here.  <Download>

You can see how to use this function from the below. It is super easy.

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From here, I will explain the theory.

Basically, this algorithm is a kernel based linear smoother algorithm and just the kernel is the Gaussian kernel. With this smoothing method, we can find a nonlinear regression function.

The linear smoother is expressed with the below equation

y^* = \frac{\sum^N_{i=1}K(x^*,x_i)y_i}{\sum^N_{i=1}K(x^*,x_i)}

here x_i is the i_th training data input, y_i is the i_th training data output, K is a kernel function. x^* is a query point, y^* is the predicted output.

In this algorithm, we use the Gaussian Kernel which is expressed with the below equation. Another name of this functions is Radial Basis Function (RBF) because it is not exactly same with the Gaussian function.

K(x^*,x_i)=\exp\left(-\frac{ (x^*-x_i)^2}{2b^2}\right)

With these equation, we can smooth the training data outputs, thus we can find a regression function.

This program <Download> was made for one-dimensional inputs. If you need multi-dimension, please leave a reply, see this article. I recently made a new version for multidimensional input.

For the optimization of kernel bandwidth, see my other article <Link>.

 

Then good luck.

 

-Mok-

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I am Youngmok Yun, and writing about robotics theories and my research.

My main site is http://youngmok.com, and Korean ver. is  http://yunyoungmok.tistory.com.

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