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).
cv.nfeaturesLDA(
data = matrix(rnorm(600), 60),
cl = gl(3, 20),
k = 5,
cex.rg = c(0.5, 3),
col.av = c("blue", "red"),
...
)a data matrix containg the predictors in columns
a factor indicating the classification of the rows of data
the number of folds
the range of the magnification to be used to the points in the plot
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
A list containing
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)
the optimum number of features based on the cross-validation
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).
Examples at https://yihui.org/animation/example/cv-nfeatureslda/
Maindonald J, Braun J (2007). Data Analysis and Graphics Using R - An Example-Based Approach. Cambridge University Press, 2nd edition. pp. 400