# Optimal Numbers of Bins Calculation Returns the matrix of size $n_{\mathrm{D}} \times d$ containing optimal numbers of bins $v_{1}, \ldots, v_{d}$ for all processed datasets. ```r ## S4 method for signature 'list' optbins(Dataset = list(), Rule = "Knuth equal", ymin = numeric(), ymax = numeric(), kmin = numeric(), kmax = numeric(), ...) ## ... and for other signatures ``` ## Arguments - `Dataset`: a list of length $n_{\mathrm{D}}$ of data frames of size $n \times d$ containing **d**-dimensional datasets. Each of the $d$ columns represents one random variable. Numbers of observations $n$ equal the number of rows in the datasets. - `Rule`: a character giving the histogram binning rule. One of `"Sturges"`, `"Log10"`, `"RootN"`, default `"Knuth equal"` or `"Knuth unequal"`. - `ymin`: a vector of length $d$ containing minimum observations. The default value is `numeric()`. - `ymax`: a vector of length $d$ containing maximum observations. The default value is `numeric()`. - `kmin`: lower limit of the number of bins. The default value is `numeric()`. - `kmax`: upper limit of the number of bins. The default value is `numeric()`. - ``...``: currently not used. ## Methods - **`signature(x = "list")`**: a list of data frames. ## Author(s) Branislav Panic, Marko Nagode ## References K. K. Knuth. Optimal data-based binning for histograms and histogram-based probability density models. Digital Signal Processing, 95:102581, 2019. tools:::Rd_expr_doi("10.1016/j.dsp.2019.102581") . B. Panic, J. Klemenc, M. Nagode. Improved initialization of the EM algorithm for mixture model parameter estimation. Mathematics, 8(3):373, 2020. tools:::Rd_expr_doi("10.3390/math8030373") . ## Examples ```r # Generate multivariate normal datasets. n <- c(750, 1000) Theta <- new("RNGMVNORM.Theta", c = 2, d = 2) a.theta1(Theta, 1) <- c(8, 6) a.theta1(Theta, 2) <- c(6, 8) a.theta2(Theta, 1) <- c(8, 2, 2, 4) a.theta2(Theta, 2) <- c(2, 1, 1, 4) sim2d <- RNGMIX(model = "RNGMVNORM", Dataset.name = paste("sim2d_", 1:5, sep = ""), rseed = -1, n = n, Theta = a.Theta(Theta)) # Calculate optimal numbers of bins. opt.k <- optbins(Dataset = sim2d@Dataset, Rule = "Knuth equal", ymin = sim2d@ymin, ymax = sim2d@ymax, kmin = 2, kmax = 20) opt.k # Create object of class EM.Control. EM <- new("EM.Control", strategy = "exhaustive", variant = "EM", acceleration = "fixed", acceleration.multiplier = 1.0, tolerance = 1.0E-4, maximum.iterations = 1000) # Estimate number of components, component weights and component parameters. sim2dest <- REBMIX(model = "REBMVNORM", Dataset = a.Dataset(sim2d), Preprocessing = "h", cmax = 10, ymin = a.ymin(sim2d), ymax = a.ymax(sim2d), K = opt.k, Criterion = "BIC", EMcontrol = EM) # Plot finite mixture. plot(sim2dest, pos = 3, nrow = 4, what = c("pdf", "marginal pdf", "IC")) # Estimate number of components, component weights and component # parameters for well known Iris dataset. Dataset <- list(iris[, c(1:4)]) # Calculate optimal numbers of bins using non-equal number of bins in each dimension. opt.k <- optbins(Dataset = Dataset, Rule = "Knuth unequal", kmin = 2, kmax = 20) opt.k # Estimate number of components, component weights and component parameters. irisest <- REBMIX(model = "REBMVNORM", Dataset = Dataset, Preprocessing = "h", cmax = 10, K = opt.k, Criterion = "BIC", EMcontrol = EM) irisest ```

optbins function