gencve (version 0.3)

rdigitsBFOS: BFOS Digit Recognition Problem

Description

BFOS suggested this is data generation model for testing the performance of nonlinear classifiers such as CART. See details and vignette.

Usage

rdigitsBFOS(n, eta = 0.25, alpha = NULL, silent = FALSE)

Arguments

n

Number of 10-tuples to generated.

eta

Bayes optimal missclassification rate.

alpha

Default is Null but if specified it is theprobability line segment is flipped. When alpha is specified corresponding the Bayes rate is determined and shown.

silent

Default is FALSE and in this case the title is displayed otherwise no display.

Value

A dataframe with 10*n rows and 8 columns is produced. Columns 1 to 7 are labeled x1, ..., x7 and correspond to the inputs which are the line segments comprising each digit where 1 indicates on and 0 off. Column 8 is a factor with value the digit, 0, 1, ..., 9. Each successive block of ten rows corresponds to ten successive digits.

Details

Breiman et al. (1984, Section 2.6.1, p.43) mentioned the case alpha=0.1 and stated that the Bayes optimal rule has a 0.26 mis-classification rate. Derivation of this and more details are discussed in the vignette.

References

BFOS (Breiman, Friedman, Olshen, and Stone), 1984 Classification and Regression Trees

See Also

rxor, rmix, ShaoReg

Examples

#debug-rdigitsBFOS.R
#with alpha=0.1, not significantly different from 0.25
require("C50")
n <- 1000
Xy <- rdigitsBFOS(n, alpha=0.1)
attr(Xy, "title")
names(Xy)
ans <- C5.0(digit~., data=Xy)
XyTest <- rdigitsBFOS(n, alpha=0.1)
yHat <- predict(ans, newdata=XyTest[,1:7])
eta <- mean(yHat!=XyTest$digit)
MOE95pc <- 1.96*sqrt(eta*(1-eta)/(10*n))
round(100*unlist(list(misclassifcationRate=eta, "95pcMOE"=MOE95pc)),1)