# MclustDA discriminant analysis Discriminant analysis based on Gaussian finite mixture modeling. ```r MclustDA(data, class, G = NULL, modelNames = NULL, modelType = c("MclustDA", "EDDA"), prior = NULL, control = emControl(), initialization = NULL, warn = mclust.options("warn"), verbose = interactive(), ...) ``` ## Arguments - `data`: A data frame or matrix giving the training data. - `class`: A vector giving the known class labels (either a numerical value or a character string) for the observations in the training data. - `G`: An integer vector specifying the numbers of mixture components (clusters) for which the BIC is to be calculated within each class. The default is `G = 1:5`. A different set of mixture components for each class can be specified by providing this argument with a list of integers for each class. See the examples below. - `modelNames`: A vector of character strings indicating the models to be fitted by EM within each class (see the description in `mclustModelNames`). A different set of mixture models for each class can be specified by providing this argument with a list of character strings. See the examples below. - `modelType`: A character string specifying whether the models given in `modelNames` should fit a different number of mixture components and covariance structures for each class (`"MclustDA"`, the default) or should be constrained to have a single component for each class with the same covariance structure among classes (`"EDDA"`). See Details section and the examples below. - `prior`: The default assumes no prior, but this argument allows specification of a conjugate prior on the means and variances through the function `priorControl`. - `control`: A list of control parameters for EM. The defaults are set by the call `emControl()`. - `initialization`: A list containing zero or more of the following components: - **`hcPairs`**: A matrix of merge pairs for hierarchical clustering such as produced by function `hc`. The default is to compute a hierarchical clustering tree by applying function `hc` with `modelName = "E"` to univariate data and `modelName = "VVV"` to multivariate data or a subset as indicated by the `subset` argument. The hierarchical clustering results are used as starting values for EM. - **`subset`**: A logical or numeric vector specifying a subset of the data to be used in the initial hierarchical clustering phase. - `warn`: A logical value indicating whether or not certain warnings (usually related to singularity) should be issued when estimation fails. The default is controlled by `mclust.options`. - `verbose`: A logical controlling if a text progress bar is displayed during the fitting procedure. By default is `TRUE` if the session is interactive, and `FALSE` otherwise. - ``...``: Further arguments passed to or from other methods. ## Returns An object of class `'MclustDA'` providing the optimal (according to BIC) mixture model. The details of the output components are as follows: - **call**: The matched call. - **data**: The input data matrix. - **class**: The input class labels. - **type**: A character string specifying the `modelType` estimated. - **models**: A list of `Mclust` objects containing information on fitted model for each class. - **n**: The total number of observations in the data. - **d**: The dimension of the data. - **bic**: Optimal BIC value. - **loglik**: Log-likelihood for the selected model. - **df**: Number of estimated parameters. ## Details The `"EDDA"` method for discriminant analysis is described in Bensmail and Celeux (1996), while `"MclustDA"` in Fraley and Raftery (2002). ## References Scrucca L., Fraley C., Murphy T. B. and Raftery A. E. (2023) **Model-Based Clustering, Classification, and Density Estimation Using mclust in R**. Chapman & Hall/CRC, ISBN: 978-1032234953, https://mclust-org.github.io/book/ Scrucca L., Fop M., Murphy T. B. and Raftery A. E. (2016) mclust 5: clustering, classification and density estimation using Gaussian finite mixture models, **The R Journal**, 8/1, pp. 289-317. Fraley C. and Raftery A. E. (2002) Model-based clustering, discriminant analysis and density estimation, **Journal of the American Statistical Association**, 97/458, pp. 611-631. Bensmail, H., and Celeux, G. (1996) Regularized Gaussian Discriminant Analysis Through Eigenvalue Decomposition.**Journal of the American Statistical Association**, 91, 1743-1748. ## Author(s) Luca Scrucca ## See Also `summary.MclustDA`, `plot.MclustDA`, `predict.MclustDA`, `classError` ## Examples ```r odd <- seq(from = 1, to = nrow(iris), by = 2) even <- odd + 1 X.train <- iris[odd,-5] Class.train <- iris[odd,5] X.test <- iris[even,-5] Class.test <- iris[even,5] # common EEE covariance structure (which is essentially equivalent to linear discriminant analysis) irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA", modelNames = "EEE") summary(irisMclustDA, parameters = TRUE) summary(irisMclustDA, newdata = X.test, newclass = Class.test) # common covariance structure selected by BIC irisMclustDA <- MclustDA(X.train, Class.train, modelType = "EDDA") summary(irisMclustDA, parameters = TRUE) summary(irisMclustDA, newdata = X.test, newclass = Class.test) # general covariance structure selected by BIC irisMclustDA <- MclustDA(X.train, Class.train) summary(irisMclustDA, parameters = TRUE) summary(irisMclustDA, newdata = X.test, newclass = Class.test) plot(irisMclustDA) plot(irisMclustDA, dimens = 3:4) plot(irisMclustDA, dimens = 4) plot(irisMclustDA, what = "classification") plot(irisMclustDA, what = "classification", newdata = X.test) plot(irisMclustDA, what = "classification", dimens = 3:4) plot(irisMclustDA, what = "classification", newdata = X.test, dimens = 3:4) plot(irisMclustDA, what = "classification", dimens = 4) plot(irisMclustDA, what = "classification", dimens = 4, newdata = X.test) plot(irisMclustDA, what = "train&test", newdata = X.test) plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 3:4) plot(irisMclustDA, what = "train&test", newdata = X.test, dimens = 4) plot(irisMclustDA, what = "error") plot(irisMclustDA, what = "error", dimens = 3:4) plot(irisMclustDA, what = "error", dimens = 4) plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test) plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 3:4) plot(irisMclustDA, what = "error", newdata = X.test, newclass = Class.test, dimens = 4) # simulated 1D data n <- 250 set.seed(1) triModal <- c(rnorm(n,-5), rnorm(n,0), rnorm(n,5)) triClass <- c(rep(1,n), rep(2,n), rep(3,n)) odd <- seq(from = 1, to = length(triModal), by = 2) even <- odd + 1 triMclustDA <- MclustDA(triModal[odd], triClass[odd]) summary(triMclustDA, parameters = TRUE) summary(triMclustDA, newdata = triModal[even], newclass = triClass[even]) plot(triMclustDA, what = "scatterplot") plot(triMclustDA, what = "classification") plot(triMclustDA, what = "classification", newdata = triModal[even]) plot(triMclustDA, what = "train&test", newdata = triModal[even]) plot(triMclustDA, what = "error") plot(triMclustDA, what = "error", newdata = triModal[even], newclass = triClass[even]) # simulated 2D cross data data(cross) odd <- seq(from = 1, to = nrow(cross), by = 2) even <- odd + 1 crossMclustDA <- MclustDA(cross[odd,-1], cross[odd,1]) summary(crossMclustDA, parameters = TRUE) summary(crossMclustDA, newdata = cross[even,-1], newclass = cross[even,1]) plot(crossMclustDA, what = "scatterplot") plot(crossMclustDA, what = "classification") plot(crossMclustDA, what = "classification", newdata = cross[even,-1]) plot(crossMclustDA, what = "train&test", newdata = cross[even,-1]) plot(crossMclustDA, what = "error") plot(crossMclustDA, what = "error", newdata =cross[even,-1], newclass = cross[even,1]) ```

MclustDA function