sdlda
(Package: sparsediscrim) :
Shrinkage-based Diagonal Linear Discriminant Analysis (SDLDA)
Given a set of training data, this function builds the Shrinkage-based Diagonal Linear Discriminant Analysis (SDLDA) classifier, which is based on the DLDA classifier, often attributed to Dudoit et al. (2002). The DLDA classifier belongs to the family of Naive Bayes classifiers, where the distributions of each class are assumed to be multivariate normal and to share a common covariance matrix. To improve the estimation of the pooled variances, Pang et al. (2009) proposed the SDLDA classifier which uses a shrinkage-based estimators of the pooled covariance matrix.
This function generates a p \times p intraclass covariance matrix with correlation rho. The variance sigma2 is constant for each feature and defaulted to 1.
mdmp
(Package: sparsediscrim) :
The Minimum Distance Rule using Moore-Penrose Inverse (MDMP) classifier
Given a set of training data, this function builds the MDMP classifier from Srivistava and Kubokawa (2007). The MDMP classifier is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Srivastava and Kubokawa (2007) have proposed a modification of the standard maximum likelihood estimator of the pooled covariance matrix, where only the largest 95 their corresponding eigenvectors are kept. The value of 95 and can be changed via the eigen_pct argument.
This function generates a p \times p covariance matrix with autocorrelated blocks. The autocorrelation parameter is rho. There are num_blocks blocks each with size, block_size. The variance, sigma2, is constant for each feature and defaulted to 1.
Given a set of training data, this function builds the HDRDA classifier from Ramey, Stein, and Young (2014). Specially designed for small-sample, high-dimensional data, the HDRDA classifier incorporates dimension reduction and covariance-matrix shrinkage to enable a computationally efficient classifier.
Given a set of training data, this function builds the Diagonal Quadratic Discriminant Analysis (DQDA) classifier, which is often attributed to Dudoit et al. (2002). The DQDA classifier belongs to the family of Naive Bayes classifiers, where the distributions of each class are assumed to be multivariate normal. Note that the DLDA classifier is a special case of the DQDA classifier.
We compute the quadratic form of a vector and the inverse of a matrix in an efficient manner. Let x be a real vector of length p, and let A be a p x p nonsingular matrix. Then, we compute the quadratic form q = x' A^{-1} x.
Given a set of training data, this function builds the Shrinkage-based Diagonal Quadratic Discriminant Analysis (SDQDA) classifier, which is based on the DQDA classifier, often attributed to Dudoit et al. (2002). The DQDA classifier belongs to the family of Naive Bayes classifiers, where the distributions of each class are assumed to be multivariate normal. To improve the estimation of the class variances, Pang et al. (2009) proposed the SDQDA classifier which uses a shrinkage-based estimators of each class covariance matrix.
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