# BIC for Model-Based Clustering BIC for parameterized Gaussian mixture models fitted by EM algorithm initialized by model-based hierarchical clustering. ```r mclustBIC(data, G = NULL, modelNames = NULL, prior = NULL, control = emControl(), initialization = list(hcPairs = NULL, subset = NULL, noise = NULL), Vinv = NULL, warn = mclust.options("warn"), x = NULL, verbose = interactive(), ...) ``` ## Arguments - `data`: A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. - `G`: An integer vector specifying the numbers of mixture components (clusters) for which the BIC is to be calculated. The default is `G=1:9`, unless the argument `x` is specified, in which case the default is taken from the values associated with `x`. - `modelNames`: A vector of character strings indicating the models to be fitted in the EM phase of clustering. The help file for `mclustModelNames` describes the available models. The default is: - **`c("E", "V")`**: for univariate data - **`mclust.options("emModelNames")`**: for multivariate data (n > d) - **`c("EII", "VII", "EEI", "EVI", "VEI", "VVI")`**: the spherical and diagonal models for multivariate data (n <= d) unless the argument `x` is specified, in which case the default is taken from the values associated with `x`. - `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`. For multivariate data, the default is to compute a hierarchical agglomerative clustering tree by applying function `hc` with model specified by `mclust.options("hcModelName")`, and data transformation set by `mclust.options("hcUse")`. All the input or a subset as indicated by the `subset` argument is used for initial clustering. The hierarchical clustering results are then used to start the EM algorithm from a given partition. For univariate data, the default is to use quantiles to start the EM algorithm. However, hierarchical clustering could also be used by calling `hc` with model specified as `"V"` or `"E"`. - **`subset`**: A logical or numeric vector specifying a subset of the data to be used in the initial hierarchical clustering phase. By default no subset is used unless the number of observations exceeds the value specified by `mclust.options("subset")`. The `subset` argument is ignored if `hcPairs` are provided. Note that to guarantee exact reproducibility of results a seed must be specified (see `set.seed`). - **`noise`**: A logical or numeric vector indicating an initial guess as to which observations are noise in the data. If numeric the entries should correspond to row indexes of the data. If supplied, a noise term will be added to the model in the estimation. - `Vinv`: An estimate of the reciprocal hypervolume of the data region. The default is determined by applying function `hypvol` to the data. Used only if an initial guess as to which observations are noise is supplied. - `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`. - `x`: An object of class `'mclustBIC'`. If supplied, `mclustBIC` will use the settings in `x` to produce another object of class `'mclustBIC'`, but with `G` and `modelNames` as specified in the arguments. Models that have already been computed in `x` are not recomputed. All arguments to `mclustBIC` except `data`, `G` and `modelName` are ignored and their values are set as specified in the attributes of `x`. Defaults for `G` and `modelNames` are taken from `x`. - `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. - ``...``: Catches unused arguments in indirect or list calls via `do.call`. ## Returns Return an object of class `'mclustBIC'` containing the Bayesian Information Criterion for the specified mixture models numbers of clusters. Auxiliary information returned as attributes. The corresponding `print` method shows the matrix of values and the top models according to the BIC criterion. ## See Also `summary.mclustBIC`, `priorControl`, `emControl`, `mclustModel`, `hc`, `me`, `mclustModelNames`, `mclust.options` ## Examples ```r irisBIC <- mclustBIC(iris[,-5]) irisBIC plot(irisBIC) subset <- sample(1:nrow(iris), 100) irisBIC <- mclustBIC(iris[,-5], initialization=list(subset = subset)) irisBIC plot(irisBIC) irisBIC1 <- mclustBIC(iris[,-5], G=seq(from=1,to=9,by=2), modelNames=c("EII", "EEI", "EEE")) irisBIC1 plot(irisBIC1) irisBIC2 <- mclustBIC(iris[,-5], G=seq(from=2,to=8,by=2), modelNames=c("VII", "VVI", "VVV"), x= irisBIC1) irisBIC2 plot(irisBIC2) nNoise <- 450 set.seed(0) poissonNoise <- apply(apply( iris[,-5], 2, range), 2, function(x, n) runif(n, min = x[1]-.1, max = x[2]+.1), n = nNoise) set.seed(0) noiseInit <- sample(c(TRUE,FALSE),size=nrow(iris)+nNoise,replace=TRUE, prob=c(3,1)) irisNdata <- rbind(iris[,-5], poissonNoise) irisNbic <- mclustBIC(data = irisNdata, G = 1:5, initialization = list(noise = noiseInit)) irisNbic plot(irisNbic) ```

mclustBIC function