# MclustSSC semi-supervised classification Semi-Supervised classification based on Gaussian finite mixture modeling. ```r MclustSSC(data, class, G = NULL, modelNames = NULL, prior = NULL, control = emControl(), 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. Observations with unknown class are encoded as `NA`. - `G`: An integer value specifying the numbers of mixture components or classes. By default is set equal to the number of known classes. See the examples below. - `modelNames`: A vector of character strings indicating the models to be fitted by EM (see the description in `mclustModelNames`). See 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()`. - `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 `'MclustSSC'` providing the optimal (according to BIC) Gaussian mixture model for semi-supervised classification. The details of the output components are as follows: - **call**: The matched call. - **data**: The input data matrix. - **class**: The input class labels (including `NA`s for unknown labels. - **modelName**: A character string specifying the "best" estimated model. - **G**: A numerical value specifying the number of mixture components or classes of the "best" estimated model. - **n**: The total number of observations in the data. - **d**: The dimension of the data. - **BIC**: All BIC values. - **loglik**: Log-likelihood for the selected model. - **df**: Number of estimated parameters. - **bic**: Optimal BIC value. - **parameters**: A list with the following components: - **`pro`**: A vector whose **k**th component is the mixing proportion for the **k**th component of the mixture model. - **`mean`**: The mean for each component. If there is more than one component, this is a matrix whose kth column is the mean of the **k**th component of the mixture model. - **`variance`**: A list of variance parameters for the model. The components of this list depend on the model specification. See the help file for `mclustVariance` for details. - **z**: A matrix whose **[i,k]**th entry is the probability that observation **i** in the test data belongs to the **k**th class. - **classification**: The classification corresponding to `z`, i.e. `map(z)`. - **prior**: The prior used (if any). - **control**: A list of control parameters used in the EM algorithm. ## Details The semi-supervised approach implemented in `MclustSSC()` is a simple Gaussian mixture model for classification where at the first M-step only observations with known class labels are used for parameters estimation. Then, a standard EM algorithm is used for updating the probabiltiy of class membership for unlabelled data while keeping fixed the probabilities for labelled data. ## References 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. ## Author(s) Luca Scrucca ## See Also `summary.MclustSSC`, `plot.MclustSSC`, `predict.MclustSSC` ## Examples ```r # Simulate two overlapping groups n <- 200 pars <- list(pro = c(0.5, 0.5), mean = matrix(c(-1,1), nrow = 2, ncol = 2, byrow = TRUE), variance = mclustVariance("EII", d = 2, G = 2)) pars$variance$sigmasq <- 1 data <- sim("EII", parameters = pars, n = n, seed = 12) class <- data[,1] X <- data[,-1] clPairs(X, class, symbols = c(1,2), main = "Full classified data") # Randomly remove labels cl <- class; cl[sample(1:n, size = 195)] <- NA table(cl, useNA = "ifany") clPairs(X, ifelse(is.na(cl), 0, class), symbols = c(0, 16, 17), colors = c("grey", 4, 2), main = "Partially classified data") # Fit semi-supervised classification model mod_SSC <- MclustSSC(X, cl) summary(mod_SSC, parameters = TRUE) pred_SSC <- predict(mod_SSC) table(Predicted = pred_SSC$classification, Actual = class) ngrid <- 50 xgrid <- seq(-3, 3, length.out = ngrid) ygrid <- seq(-4, 4.5, length.out = ngrid) xygrid <- expand.grid(xgrid, ygrid) pred_SSC <- predict(mod_SSC, newdata = xygrid) col <- mclust.options("classPlotColors")[class] pch <- class pch[!is.na(cl)] = ifelse(cl[!is.na(cl)] == 1, 19, 17) plot(X, pch = pch, col = col) contour(xgrid, ygrid, matrix(pred_SSC$z[,1], ngrid, ngrid), add = TRUE, levels = 0.5, drawlabels = FALSE, lty = 2, lwd = 2) ```

MclustSSC function