diagDA: Diagonal Discriminant Analysis

Description

This function implements a simple Gaussian maximum likelihood discriminant rule, for diagonal class covariance matrices.

In machine learning lingo, this is called “Naive Bayes” (for continuous predictors). Note that naive Bayes is more general, as it models discrete predictors as multinomial, i.e., binary predictor variables as Binomial / Bernoulli.

Usage

dDA(x, cll, pool = TRUE)
# S3 method for dDA
predict(object, newdata, pool = object$pool, …)
# S3 method for dDA
print(x, …)
diagDA(ls, cll, ts, pool = TRUE)

Arguments

x,ls

learning set data matrix, with rows corresponding to cases (e.g., mRNA samples) and columns to predictor variables (e.g., genes).

cll

class labels for learning set, must be consecutive integers.

object

object of class dDA.

ts, newdata

test set (prediction) data matrix, with rows corresponding to cases and columns to predictor variables.

pool

logical flag. If true (by default), the covariance matrices are assumed to be constant across classes and the discriminant rule is linear in the data. Otherwise (pool= FALSE), the covariance matrices may vary across classes and the discriminant rule is quadratic in the data.

…

further arguments passed to and from methods.

Value

dDA() returns an object of class dDA for which there are print and predict methods. The latter returns the same as diagDA():

diagDA() returns an integer vector of class predictions for the test set.

References

S. Dudoit, J. Fridlyand, and T. P. Speed. (2000) Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data. (Statistics, UC Berkeley, June 2000, Tech Report \#576)

Examples

Run this code

# NOT RUN {
## two artificial examples by Andreas Greutert:
d1 <- data.frame(x = c(1, 5, 5, 5, 10, 25, 25, 25, 25, 29),
                 y = c(4, 1, 2, 4,  4,  4,     6:8,     7))
n.plot(d1)
library(cluster)
(cl1P <- pam(d1,k=4)$cluster) # 4 surprising clusters
with(d1, points(x+0.5, y, col = cl1P, pch =cl1P))

i1 <- c(1,3,5,6)
tr1 <- d1[-i1,]
cl1. <- c(1,2,1,2,1,3)
cl1  <- c(2,2,1,1,1,3)
plot(tr1, cex=2, col = cl1, pch = 20+cl1)
(dd.<- diagDA(tr1, cl1., ts = d1[ i1,]))# ok
(dd <- diagDA(tr1, cl1 , ts = d1[ i1,]))# ok, too!
points(d1[ i1,], pch = 10, cex=3, col = dd)

## use new fit + predict instead :
(r1 <- dDA(tr1, cl1))
(r1.<- dDA(tr1, cl1.))
stopifnot(dd == predict(r1,  new = d1[ i1,]),
          dd.== predict(r1., new = d1[ i1,]))

plot(tr1, cex=2, col = cl1, bg = cl1, pch = 20+cl1,
     xlim=c(1,30), ylim= c(0,10))
xy <- cbind(x= runif(500, min=1,max=30), y = runif(500, min=0, max=10))
points(xy, cex= 0.5, col = predict(r1, new = xy))
abline(v=c( mean(c(5,25)), mean(c(25,29))))

## example where one variable xj has  Var(xj) = 0:
x4 <- matrix(c(2:4,7, 6,8,5,6,  7,2,3,1, 7,7,7,7), ncol=4)
y <- c(2,2, 1,1)
m4.1 <- dDA(x4, y, pool = FALSE)
m4.2 <- dDA(x4, y, pool = TRUE)
xx <- matrix(c(3,7,5,7), ncol=4)
predict(m4.1, xx)## gave integer(0) previously
predict(m4.2, xx)
# }

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