# explained_variance: Calculation of explained variance In mixOmics: Omics Data Integration Project

## Description

This function calculates the variance explained by their own variates (components) based on redundancy.

## Usage

 1 explained_variance(data, variates, ncomp) 

## Arguments

 data numeric matrix of predictors variates variates as obtained from a pls object for instance ncomp number of components. Should be lower than the number of columns of variates

## Details

explained_variance calculates the variance explained by each variate / component and divides by the total variance in data using the definition of 'redundancy'. This applies to any component-based approaches.

Variance explained by component t_h in X for dimension h:

Rd(X, t_h) = \frac{1}{p} ∑_{j = 1}^p \mbox{cor}^2(X^j, t_h)

where X^j is the variable centered and scaled, p is the total number of variables.

## Value

explained_variance returns the explained variance for each variate.

## Author(s)

Florian Rohart, Kim-Anh Lê Cao, Al J Abadi

## References

Tenenhaus, M., La Régression PLS théorie et pratique (1998). Technip, Paris, chap2.

spls, splsda, plotIndiv, plotVar, cim, network.
  1 2 3 4 5 6 7 8 9 10 data(liver.toxicity) X <- liver.toxicity$gene Y <- liver.toxicity$clinic toxicity.spls <- spls(X, Y, ncomp = 2, keepX = c(50, 50), keepY = c(10, 10)) ex = explained_variance(toxicity.spls$X, toxicity.spls$variates$X, ncomp =2) # ex should be the same as toxicity.spls$explained_variance\$X