Publication

Local linear correlation analysis with the SOM

Alain Germond
1998
Journal Articles

Abstract

The purpose of this paper is to illustrate a method which can be used to select relevant input variables for non-linear regression. The proposed method is an extension to the concept of SOM such that the linear correlation coefficient is computed over a whole data manifold in neighbour subspaces. Using the topographic properties of the usual SOM a localised correlation coefficient may be obtained by modified Kohonen learning. The graphical ordered plot of the obtained local correlation allows to study the non-linear dependencies of variables

Official source

https://infoscience.epfl.ch/entities/publication/263cbec6-f1c1-4c9f-be40-264a8b609378

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Alain Germond
1998
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/263cbec6-f1c1-4c9f-be40-264a8b609378

About this result

Related concepts (32)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Correlation coefficient

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.

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Local linear correlation analysis with the SOM

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