animation (version 2.0-5)

cv.nfeaturesLDA: Cross-validation to find the optimum number of features (variables) in LDA

Description

This function provids an illustration of the process of finding out the optimum number of variables using k-fold cross-validation in a linear discriminant analysis (LDA).

Usage

cv.nfeaturesLDA(data = matrix(rnorm(600), 60), cl = gl(3, 
    20), k = 5, cex.rg = c(0.5, 3), col.av = c("blue", "red"), 
    ...)

Arguments

data

a data matrix containg the predictors in columns

cl

a factor indicating the classification of the rows of data

k

the number of folds

cex.rg

the range of the magnification to be used to the points in the plot

col.av

the two colors used to respectively denote rates of correct predictions in the i-th fold and the average rates for all k folds

...

arguments passed to points to draw the points which denote the correct rate

Value

• A list containing
• accuracy
  a matrix in which the element in the i-th row and j-th column is the rate of correct predictions based on LDA, i.e. build a LDA model with j variables and predict with data in the i-th fold (the test set)
• optimum
  the optimum number of features based on the cross-validation

Details

For a classification problem, usually we wish to use as less variables as possible because of difficulties brought by the high dimension.

The selection procedure is like this:

• Split the whole data randomly into$k$folds:
  • For the number of features$g = 1, 2, \cdots, g_{max}$, choose$g$features that have the largest discriminatory power (measured by the F-statistic in ANOVA):
    • For the fold$i$($i = 1, 2, \cdots, k$):
      • Train a LDA model without the$i$-th fold data, and predict with the$i$-th fold for a proportion of correct predictions$p_{gi}$;
  • Average the$k$proportions to get the correct rate$p_g$;
• Determine the optimum number of features with the largest$p$.

Note that $g_{max}$ is set by ani.options("nmax") (i.e. the maximum number of features we want to choose).

References

Maindonald J, Braun J (2007). Data Analysis and Graphics Using R - An Example-Based Approach. Cambridge University Press, 2nd edition. pp. 400

http://animation.yihui.name/da:biostat:select_features_via_cv

See Also

kfcv, cv.ani, lda

Examples

oopt = ani.options(nmax = ifelse(interactive(), 10, 
    2))
par(mar = c(3, 3, 0.2, 0.7), mgp = c(1.5, 0.5, 0))
cv.nfeaturesLDA(pch = 19)

## save the animation in HTML pages
saveHTML({
    ani.options(interval = 0.5, nmax = 10)
    par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3, 
        pch = 19, cex = 1.5)
    cv.nfeaturesLDA(pch = 19)
}, img.name = "cv.nfeaturesLDA", htmlfile = "cv.nfeaturesLDA.html", 
    ani.height = 480, ani.width = 600, title = "Cross-validation to find the optimum number of features in LDA", 
    description = c("This", "animation has provided an illustration of the process of finding", 
        "out the optimum number of variables using k-fold cross-validation", 
        "in a linear discriminant analysis (LDA)."))

ani.options(oopt)