# Gaussian Kernel Bandwidth Optimization with Matlab Code

In this article, I write on “Optimization of Gaussian Kernel Bandwidth” with Matlab Code.

First, I will briefly explain a methodology to optimize bandwidth values of Gaussian Kernel for regression problems. In other words, I will explain about “Cross validation Method.”

Then, I will share my Matlab code which optimizes the bandwidths of Gaussian Kernel for Gaussian Kernel Regression. For the theory and source code of the regression, read my previous posts <link for 1D input>, <link for multidimensional input>. This Matlab code can optimize bandwidths for multidimensional inputs. If you know the theory of cross validation, or if you don’t need to know the algorithm of my program, just download the zip file from the below link, then execute demo programs. Probably, you can use the program without big difficulties.

## 1. Bandwidth optimization by a cross validation method

The most common way to optimize a regression parameter is to use a cross validation method. If you want to know about the cross validation deeply, I want to recommend to read this article. Here I will shortly explain about the cross validation method that I am using. This is just a way of cross validation.

1. Randomly sample 75% of the data set, and put into the training data set, and put the remaining part into the test set.

2. Using the training data set, build a regression model. Based on the model, predict the outputs of the test set.

3. Compare between the predicted output, and the actual output. Then, find the best model (best bandwidth) to minimize the gap (e.g, RMSE) between the predicted and actual outputs.

## 2. Matlab code for the algorithm

This program is for multidimensional inputs (of course, 1D is also OK). The most important function is Opt_Hyp_Gauss_Ker_Reg( h0,x,y ) and it requires Matlab optimization toolbox. I am attaching two demo programs and their results. I made these demo programs as much as I can. So, I believe that everybody can understand.

### <Demo 2D>

-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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# Gaussian Kernel Regression for Multidimensional Feature with Matlab code (Gaussian Kernel or RBF Smoother)

I am sharing a Matlab code for Gaussian Kernel Regression algorithm for multidimensional input (feature).

In the previous post (link), I posted a theory of Gaussian Kernel Regression, and shared a Matlab code for one dimensional input. If you want to know about the theory, read the previous post. In the previous post, many visitors asked me for a multidimensional input version. Finally I made a Gaussian Kernel Regression Program for a general dimensional input

I wrote a demo program to show how to use the code as easy as possible.

The below is the demo program, and a demo result plot. In this demo program, the dimension of input is 2 because of visualization, but it is expendable to an arbitrary dimension.

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

I wish this program can save your time and effort for your work.

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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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