RSSL (version 0.9.3)

KernelLeastSquaresClassifier: Kernelized Least Squares Classifier

Description

Use least squares regression as a classification technique using a numeric encoding of classes as targets. Note this method minimizes quadratic loss, not the truncated quadratic loss.

Usage

KernelLeastSquaresClassifier(X, y, lambda = 0, kernel = vanilladot(),
  x_center = TRUE, scale = TRUE, y_scale = TRUE)

Arguments

X

Design matrix, intercept term is added within the function

y

Vector or factor with class assignments

lambda

Regularization parameter of the l2 penalty in regularized least squares

kernel

kernlab kernel function

x_center

TRUE, whether the dependent variables (features) should be centered

scale

If TRUE, apply a z-transform to the design matrix X before running the regression

y_scale

TRUE center the target vector

Value

S4 object of class LeastSquaresClassifier with the following slots:

theta

weight vector

classnames

the names of the classes

modelform

formula object of the model used in regression

scaling

a scaling object containing the parameters of the z-transforms applied to the data

See Also

Other RSSL classifiers: EMLeastSquaresClassifier, EMLinearDiscriminantClassifier, GRFClassifier, ICLeastSquaresClassifier, ICLinearDiscriminantClassifier, LaplacianKernelLeastSquaresClassifier(), LaplacianSVM, LeastSquaresClassifier, LinearDiscriminantClassifier, LinearSVM, LinearTSVM(), LogisticLossClassifier, LogisticRegression, MCLinearDiscriminantClassifier, MCNearestMeanClassifier, MCPLDA, MajorityClassClassifier, NearestMeanClassifier, QuadraticDiscriminantClassifier, S4VM, SVM, SelfLearning, TSVM, USMLeastSquaresClassifier, WellSVM, svmlin()

Examples

# NOT RUN {
library(RSSL)
library(ggplot2)
library(dplyr)

# Two class problem
df <- generateCrescentMoon(200)

class_lin <- KernelLeastSquaresClassifier(Class~.,df,
                                          kernel=kernlab::vanilladot(), lambda=1)
class_rbf1 <- KernelLeastSquaresClassifier(Class~.,df,
                                          kernel=kernlab::rbfdot(), lambda=1)
class_rbf5 <- KernelLeastSquaresClassifier(Class~.,df,
                                          kernel=kernlab::rbfdot(5), lambda=1)
class_rbf10 <- KernelLeastSquaresClassifier(Class~.,df,
                                           kernel=kernlab::rbfdot(10), lambda=1)

df %>% 
  ggplot(aes(x=X1,y=X2,color=Class,shape=Class)) +
  geom_point() +
  coord_equal() +
  stat_classifier(aes(linetype=..classifier..),
                  classifiers = list("Linear"=class_lin,
                                     "RBF sigma=1"=class_rbf1,
                                     "RBF sigma=5"=class_rbf5,
                                     "RBF sigma=10"=class_rbf10),
                  color="black")

# Second Example
dmat<-model.matrix(Species~.-1,iris[51:150,])
tvec<-droplevels(iris$Species[51:150])
testdata <- data.frame(tvec,dmat[,1:2])
colnames(testdata)<-c("Class","X1","X2")

precision<-100
xgrid<-seq(min(dmat[,1]),max(dmat[,1]),length.out=precision)
ygrid<-seq(min(dmat[,2]),max(dmat[,2]),length.out=precision)
gridmat <- expand.grid(xgrid,ygrid)

g_kernel<-KernelLeastSquaresClassifier(dmat[,1:2],tvec,
                                       kernel=kernlab::rbfdot(0.01),
                                       lambda=0.000001,scale = TRUE)
plotframe <- cbind(gridmat, decisionvalues(g_kernel,gridmat))
colnames(plotframe)<- c("x","y","Output")
ggplot(plotframe, aes(x=x,y=y)) +
  geom_tile(aes(fill = Output)) +
  scale_fill_gradient(low="yellow", high="red",limits=c(0,1)) +
  geom_point(aes(x=X1,y=X2,shape=Class),data=testdata,size=3) +
  stat_classifier(classifiers=list(g_kernel))

# Multiclass problem
dmat<-model.matrix(Species~.-1,iris)
tvec<-iris$Species
testdata <- data.frame(tvec,dmat[,1:2])
colnames(testdata)<-c("Class","X1","X2")

precision<-100
xgrid<-seq(min(dmat[,1]),max(dmat[,1]),length.out=precision)
ygrid<-seq(min(dmat[,2]),max(dmat[,2]),length.out=precision)
gridmat <- expand.grid(xgrid,ygrid)

g_kernel<-KernelLeastSquaresClassifier(dmat[,1:2],tvec,
                      kernel=kernlab::rbfdot(0.1),lambda=0.00001,
                      scale = TRUE,x_center=TRUE)

plotframe <- cbind(gridmat, 
                   maxind=apply(decisionvalues(g_kernel,gridmat),1,which.max))
ggplot(plotframe, aes(x=Var1,y=Var2)) +
  geom_tile(aes(fill = factor(maxind,labels=levels(tvec)))) +
  geom_point(aes(x=X1,y=X2,shape=Class),data=testdata,size=4,alpha=0.5)
# }