plsda: Partial Least Squares and Sparse Partial Least Squares Discriminant Analysis

Description

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.

Usage

plsda(x, ...)
## S3 method for class 'default':
plsda(x,  y, ncomp = 2, probMethod = "softmax", prior = NULL, ...)
## S3 method for class 'plsda':
predict(object, newdata = NULL, ncomp = NULL, type = "class", ...)
splsda(x, ...)
## S3 method for class 'default':
splsda(x, y, probMethod = "softmax", prior = NULL, ...)
## S3 method for class 'splsda':
predict(object, newdata = NULL, type = "class", ...)

Arguments

a matrix or data frame of predictors

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

ncomp

the number of components to include in the model. Predictions can be made for models with values less than ncomp.

probMethod

either "softmax" or "Bayes" (see Details)

prior

a vector or prior probabilities for the classes (only used for probeMethod = "Bayes"

...

arguments to pass to plsr or spls. For splsda, this is the method for passing tuning parameters specifications (e.g. K,

object

an object produced by plsda

newdata

a matrix or data frame of predictors

type

either "class", "prob" or "raw" to produce the predicted class, class probabilities or the raw model scores, respectively.

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 prediciton 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.

Examples

Run this code

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

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

confusionMatrix(
                predict(splsFit, testDescr),
                testMDRR)