Tag Archives: nonlinear regression

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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.

main figure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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Statistical Method for Prediction of Human Walking Pattern with Gaussian Process Regression

Statistical Method for Prediction of Human Walking Pattern with Gaussian Process Regression

We propose a novel methodology for predicting human gait pattern kinematics based on a statistical and stochastic approach using a method called Gaussian process regression (GPR). We selected 14 body parameters that significantly affect the gait pattern and 14 joint motions that represent gait kinematics. The body parameter and gait kinematics data were recorded from 113 subjects by anthropometric measurements and a motion capture system. We generated a regression model with GPR for gait pattern prediction and built a stochastic function mapping from body parameters to gait kinematics based on the database and GPR, and validated the model with a cross validation method. The function can not only produce trajectories for the joint motions associated with gait kinematics, but can also estimate the associated uncertainties. Our approach results in a novel, low-cost and subject-specific method for predicting gait kinematics with only the subject’s body parameters as the necessary input, and also enables a comprehensive understanding of the correlation and uncertainty between body parameters and gait kinematics.

20130604_DW2013

 

2014

Yun, Youngmok; Kim, Hyun-Chul; Shin, Sung Yul; Lee, Junwon; Deshpande, Ashish D; Kim, Changhwan

Statistical method for prediction of gait kinematics with Gaussian process regression Journal Article

Journal of Biomechanics, 47 (1), pp. 186 - 192, 2014, ISSN: 0021-9290.

Links | BibTeX

2013

Yun, Youngmok; Deshpande, Ashish D

Synthesis of Gait Kinematics Using a Database Conference

Dynamic Walking, 2013.

BibTeX

Yun, Youngmok; Deshpande, Ashish

Statistical Functional Mapping From Body Parameters to Gait Kinematics Conference

American Society of Biomechanics, 2013.

BibTeX