USMLeastSquaresClassifier: Updated Second Moment Least Squares Classifier

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

Updated Second Moment Least Squares Classifier

Description

This methods uses the closed form solution of the supervised least squares problem, except that the second moment matrix (X'X) is exchanged with a second moment matrix that is estimated based on all data. See for instance Shaffer1991, where in this implementation we use all data to estimate E(X'X), instead of just the labeled data. This method seems to work best when the data is first centered x_center=TRUE and the outputs are scaled using y_scale=TRUE.

Usage

USMLeastSquaresClassifier(X, y, X_u, lambda = 0, intercept = TRUE,
  x_center = FALSE, scale = FALSE, y_scale = FALSE, ...,
  use_Xu_for_scaling = TRUE)

Arguments

X	matrix; Design matrix for labeled data
y	factor or integer vector; Label vector
X_u	matrix; Design matrix for unlabeled data
lambda	numeric; L2 regularization parameter
intercept	logical; Whether an intercept should be included
x_center	logical; Should the features be centered?
scale	logical; Should the features be normalized? (default: FALSE)
y_scale	logical; whether the target vector should be centered
...	Not used
use_Xu_for_scaling	logical; whether the unlabeled objects should be used to determine the mean and scaling for the normalization

References

Shaffer, J.P., 1991. The Gauss-Markov Theorem and Random Regressors. The American Statistician, 45(4), pp.269-273.

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, S4VM, SVM, SelfLearning, TSVM, WellSVM, svmlin()

jkrijthe/RSSL documentation built on Jan. 13, 2024, 1:56 a.m.