# cv.nfeaturesLDA()

# Cross-validation to find the optimum number of features (variables) in LDA

### Yihui Xie & Lijia Yu / 2017-04-04

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).

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).

```
library(animation)
ani.options(nmax = 10)
par(mar = c(3, 3, 0.2, 0.7), mgp = c(1.5, 0.5, 0))
cv.nfeaturesLDA(pch = 19)
```

```
## Loading required namespace: MASS
```

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