EMLeastSquaresClassifier: An Expectation Maximization like approach to Semi-Supervised...

In RSSL: Implementations of Semi-Supervised Learning Approaches for Classification

An Expectation Maximization like approach to Semi-Supervised Least Squares Classification

Description

As studied in Krijthe & Loog (2016), minimizes the total loss of the labeled and unlabeled objects by finding the weight vector and labels that minimize the total loss. The algorithm proceeds similar to EM, by subsequently applying a weight update and a soft labeling of the unlabeled objects. This is repeated until convergence.

Usage

EMLeastSquaresClassifier(X, y, X_u, x_center = FALSE, scale = FALSE,
  verbose = FALSE, intercept = TRUE, lambda = 0, eps = 1e-09,
  y_scale = FALSE, alpha = 1, beta = 1, init = "supervised",
  method = "block", objective = "label", save_all = FALSE,
  max_iter = 1000)

Arguments

X	matrix; Design matrix for labeled data
y	factor or integer vector; Label vector
X_u	matrix; Design matrix for unlabeled data
x_center	logical; Should the features be centered?
scale	Should the features be normalized? (default: FALSE)
verbose	logical; Controls the verbosity of the output
intercept	logical; Whether an intercept should be included
lambda	numeric; L2 regularization parameter
eps	Stopping criterion for the minimization
y_scale	logical; whether the target vector should be centered
alpha	numeric; the mixture of the new responsibilities and the old in each iteration of the algorithm (default: 1)
beta	numeric; value between 0 and 1 that determines how much to move to the new solution from the old solution at each step of the block gradient descent
init	objective character; "random" for random initialization of labels, "supervised" to use supervised solution as initialization or a numeric vector with a coefficient vector to use to calculate the initialization
method	character; one of "block", for block gradient descent or "simple" for LBFGS optimization (default="block")
objective	character; "responsibility" for hard label self-learning or "label" for soft-label self-learning
save_all	logical; saves all classifiers trained during block gradient descent
max_iter	integer; maximum number of iterations

Details

By default (method="block") the weights of the classifier are updated, after which the unknown labels are updated. method="simple" uses LBFGS to do this update simultaneously. Objective="responsibility" corresponds to the responsibility based, instead of the label based, objective function in Krijthe & Loog (2016), which is equivalent to hard-label self-learning.

References

Krijthe, J.H. & Loog, M., 2016. Optimistic Semi-supervised Least Squares Classification. In International Conference on Pattern Recognition (To Appear).

See Also

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

Examples

library(dplyr)
library(ggplot2)

set.seed(1)

df <- generate2ClassGaussian(200,d=2,var=0.2) %>% 
 add_missinglabels_mar(Class~.,prob = 0.96)

# Soft-label vs. hard-label self-learning
classifiers <- list(
 "Supervised"=LeastSquaresClassifier(Class~.,df),
 "EM-Soft"=EMLeastSquaresClassifier(Class~.,df,objective="label"),
 "EM-Hard"=EMLeastSquaresClassifier(Class~.,df,objective="responsibility")
)

df %>% 
 ggplot(aes(x=X1,y=X2,color=Class)) +
 geom_point() +
 coord_equal() +
 scale_y_continuous(limits=c(-2,2)) +
 stat_classifier(aes(linetype=..classifier..),
                 classifiers=classifiers)
                 

RSSL documentation built on May 29, 2024, 2:38 a.m.