Partial Least Squares and Sparse Partial Least Squares Discriminant Analysis

plsda is used to fit standard PLS models for classification while splsda performs sparse PLS that embeds feature selection and regularization for the same purpose.

plsda(x, ...)

# S3 method for plsda
predict(object, newdata = NULL, ncomp = NULL,
  type = "class", ...)

# S3 method for default
plsda(x, y, ncomp = 2, probMethod = "softmax",
  prior = NULL, ...)

Arguments

x	a matrix or data frame of predictors
...	arguments to pass to plsr or spls. For splsda, this is the method for passing tuning parameters specifications (e.g. K, eta or kappa)
object	an object produced by plsda
newdata	a matrix or data frame of predictors
ncomp	the number of components to include in the model. Predictions can be made for models with values less than ncomp.
type	either "class", "prob" or "raw" to produce the predicted class, class probabilities or the raw model scores, respectively.
y	a factor or indicator matrix for the discrete outcome. If a matrix, the entries must be either 0 or 1 and rows must sum to one
probMethod	either "softmax" or "Bayes" (see Details)
prior	a vector or prior probabilities for the classes (only used for probeMethod = "Bayes")

Value

For plsda, an object of class "plsda" and "mvr". For splsda, an object of class splsda.

The predict methods produce either a vector, matrix or three-dimensional array, depending on the values of type of ncomp. For example, specifying more than one value of ncomp with type = "class" with produce a three dimensional array but the default specification would produce a factor vector.

Details

If a factor is supplied, the appropriate indicator matrix is created.

A multivariate PLS model is fit to the indicator matrix using the plsr or spls function.

Two prediction methods can be used.

The softmax function transforms the model predictions to "probability-like" values (e.g. on [0, 1] and sum to 1). The class with the largest class probability is the predicted class.

Also, Bayes rule can be applied to the model predictions to form posterior probabilities. Here, the model predictions for the training set are used along with the training set outcomes to create conditional distributions for each class. When new samples are predicted, the raw model predictions are run through these conditional distributions to produce a posterior probability for each class (along with the prior). This process is repeated ncomp times for every possible PLS model. The NaiveBayes function is used with usekernel = TRUE for the posterior probability calculations.

See also

plsr, spls

Examples

if (FALSE) {
data(mdrr)
set.seed(1)
inTrain <- sample(seq(along = mdrrClass), 450)

nzv <- nearZeroVar(mdrrDescr)
filteredDescr <- mdrrDescr[, -nzv]

training <- filteredDescr[inTrain,]
test <- filteredDescr[-inTrain,]
trainMDRR <- mdrrClass[inTrain]
testMDRR <- mdrrClass[-inTrain]

preProcValues <- preProcess(training)

trainDescr <- predict(preProcValues, training)
testDescr <- predict(preProcValues, test)

useBayes   <- plsda(trainDescr, trainMDRR, ncomp = 5,
                    probMethod = "Bayes")
useSoftmax <- plsda(trainDescr, trainMDRR, ncomp = 5)

confusionMatrix(predict(useBayes, testDescr),
                testMDRR)

confusionMatrix(predict(useSoftmax, testDescr),
                testMDRR)

histogram(~predict(useBayes, testDescr, type = "prob")[,"Active",]
          | testMDRR, xlab = "Active Prob", xlim = c(-.1,1.1))
histogram(~predict(useSoftmax, testDescr, type = "prob")[,"Active",]
          | testMDRR, xlab = "Active Prob", xlim = c(-.1,1.1))


## different sized objects are returned
length(predict(useBayes, testDescr))
dim(predict(useBayes, testDescr, ncomp = 1:3))
dim(predict(useBayes, testDescr, type = "prob"))
dim(predict(useBayes, testDescr, type = "prob", ncomp = 1:3))

## Using spls:
## (As of 11/09, the spls package now has a similar function with
## the same mane. To avoid conflicts, use caret:::splsda to
## get this version)

splsFit <- caret:::splsda(trainDescr, trainMDRR,
                          K = 5, eta = .9,
                          probMethod = "Bayes")

confusionMatrix(caret:::predict.splsda(splsFit, testDescr),
                testMDRR)
}