RSSL (version 0.9.3)

S4VM: Safe Semi-supervised Support Vector Machine (S4VM)

Description

R port of the MATLAB implementation of Li & Zhou (2011) of the Safe Semi-supervised Support Vector Machine.

Usage

S4VM(X, y, X_u = NULL, C1 = 100, C2 = 0.1, sample_time = 100,
  gamma = 0, x_center = FALSE, scale = FALSE, lambda_tradeoff = 3)

Arguments

X

matrix; Design matrix for labeled data

y

factor or integer vector; Label vector

X_u

matrix; Design matrix for unlabeled data

C1

double; Regularization parameter for labeled data

C2

double; Regularization parameter for unlabeled data

sample_time

integer; Number of low-density separators that are generated

gamma

double; Width of RBF kernel

x_center

logical; Should the features be centered?

scale

logical; Should the features be normalized? (default: FALSE)

lambda_tradeoff

numeric; Parameter that determines the amount of "risk" in obtaining a worse solution than the supervised solution, see Li & Zhou (2011)

Value

S4VM object with slots:

predictions

Predictions on the unlabeled objects

labelings

Labelings for the different clusters

Details

The method randomly generates multiple low-density separators (controlled by the sample_time parameter) and merges their predictions by solving a linear programming problem meant to penalize the cost of decreasing the performance of the classifier, compared to the supervised SVM. S4VM is a bit of a misnomer, since it is a transductive method that only returns predicted labels for the unlabeled objects. The main difference in this implementation compared to the original implementation is the clustering of the low-density separators: in our implementation empty clusters are not dropped during the k-means procedure. In the paper by Li (2011) the features are first normalized to [0,1], which is not automatically done by this function. Note that the solution may not correspond to a linear classifier even if the linear kernel is used.

References

Yu-Feng Li and Zhi-Hua Zhou. Towards Making Unlabeled Data Never Hurt. In: Proceedings of the 28th International Conference on Machine Learning (ICML'11), Bellevue, Washington, 2011.

See Also

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

Examples

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

set.seed(1)
df_orig <- generateSlicedCookie(100,expected=TRUE)
df <- df_orig %>% add_missinglabels_mar(Class~.,0.95)
g_s <- SVM(Class~.,df,C=1,scale=TRUE,x_center=TRUE)
g_s4 <- S4VM(Class~.,df,C1=1,C2=0.1,lambda_tradeoff = 3,scale=TRUE,x_center=TRUE)

labs <- g_s4@labelings[-c(1:5),]
colnames(labs) <- paste("Class",seq_len(ncol(g_s4@labelings)),sep="-")

# Show the labelings that the algorithm is considering
df %>%
  filter(is.na(Class)) %>% 
  bind_cols(data.frame(labs,check.names = FALSE)) %>% 
  select(-Class) %>% 
  gather(Classifier,Label,-X1,-X2) %>% 
  ggplot(aes(x=X1,y=X2,color=Label)) +
  geom_point() +
  facet_wrap(~Classifier,ncol=5)

# Plot the final labeling that was selected
# Note that this may not correspond to a linear classifier
# even if the linear kernel is used.
# The solution does not seem to make a lot of sense,
# but this is what the current implementation returns
df %>% 
  filter(is.na(Class)) %>% 
  mutate(prediction=g_s4@predictions) %>% 
  ggplot(aes(x=X1,y=X2,color=prediction)) +
  geom_point() +
  stat_classifier(color="black", classifiers=list(g_s))
# }