Given a set of training data, this function builds the Linear Discriminant Analysis (LDA) classifier, where the distributions of each class are assumed to be multivariate normal and share a common covariance matrix. When the pooled sample covariance matrix is singular, the linear discriminant function is incalculable. This function replaces the pooled sample covariance matrix with a regularized estimator from Thomaz et al. (2006), where the smallest eigenvalues are replaced with the average eigenvalue. Specifically, small eigenvalues here means that the eigenvalues are less than the average eigenvalue.
Given a set of training data, this function builds the Linear Discriminant Analysis (LDA) classifier, where the distributions of each class are assumed to be multivariate normal and share a common covariance matrix. When the pooled sample covariance matrix is singular, the linear discriminant function is incalculable. This function replaces the pooled sample covariance matrix with a regularized estimator from Thomaz et al. (2006), where the smallest eigenvalues are replaced with the average eigenvalue. Specifically, small eigenvalues here means that the eigenvalues are less than the average eigenvalue.
lda_thomaz(x, ...)# S3 method for default
lda_thomaz(x, y, prior = NULL, ...)
# S3 method for formula
lda_thomaz(formula, data, prior = NULL, ...)
# S3 method for lda_thomaz
predict(object, newdata, ...)
matrix containing the training data. The rows are the sample observations, and the columns are the features.
additional arguments
vector of class labels for each training observation
vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.
A formula of the form groups ~ x1 + x2 + ... That is,
the response is the grouping factor and the right hand side specifies the
(non-factor) discriminators.
data frame from which variables specified in formula are
preferentially to be taken.
trained lda_thomaz object
matrix of observations to predict. Each row corresponds to a new observation.
lda_thomaz object that contains the trained classifier
list predicted class memberships of each row in newdata
The matrix of training observations are given in x. The rows of x
contain the sample observations, and the columns contain the features for each
training observation.
The vector of class labels given in y are coerced to a factor.
The length of y should match the number of rows in x.
An error is thrown if a given class has less than 2 observations because the variance for each feature within a class cannot be estimated with less than 2 observations.
The vector, prior, contains the a priori class membership for
each class. If prior is NULL (default), the class membership
probabilities are estimated as the sample proportion of observations belonging
to each class. Otherwise, prior should be a vector with the same length
as the number of classes in y. The prior probabilities should be
nonnegative and sum to one.
Thomaz, C. E., Kitani, E. C., and Gillies, D. F. (2006). "A maximum uncertainty LDA-based approach for limited sample size problems with application to face recognition," J. Braz. Comp. Soc., 12, 2, 7-18.
Thomaz, C. E., Kitani, E. C., and Gillies, D. F. (2006). "A maximum uncertainty LDA-based approach for limited sample size problems with application to face recognition," J. Braz. Comp. Soc., 12, 2, 7-18.
# NOT RUN {
n <- nrow(iris)
train <- sample(seq_len(n), n / 2)
lda_thomaz_out <- lda_thomaz(Species ~ ., data = iris[train, ])
predicted <- predict(lda_thomaz_out, iris[-train, -5])$class
lda_thomaz_out2 <- lda_thomaz(x = iris[train, -5], y = iris[train, 5])
predicted2 <- predict(lda_thomaz_out2, iris[-train, -5])$class
all.equal(predicted, predicted2)
# }
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