REBMIX-class {rebmix}

Class "REBMIX"

Description

Object of class REBMIX.

Objects from the Class

Objects can be created by calls of the form new("REBMIX", ...). Accessor methods for the slots are a.Dataset(x = NULL, pos = 0), a.Preprocessing(x = NULL), a.cmax(x = NULL), a.cmin(x = NULL), a.Criterion(x = NULL), a.Variables(x = NULL), a.pdf(x = NULL), a.theta1(x = NULL), a.theta2(x = NULL), a.theta3(x = NULL), a.K(x = NULL), a.ymin(x = NULL), a.ymax(x = NULL), a.ar(x = NULL), a.Restraints(x = NULL), a.Mode(x = NULL), a.w(x = NULL, pos = 0), a.Theta(x = NULL, pos = 0), a.summary(x = NULL, col.name = character(), pos = 0), a.summary.EM(x = NULL, col.name = character(), pos = 0), a.pos(x = NULL), a.opt.c(x = NULL), a.opt.IC(x = NULL), a.opt.logL(x = NULL), a.opt.Dmin(x = NULL), a.opt.D(x = NULL), a.all.K(x = NULL), a.all.IC(x = NULL), a.theta1.all(x = NULL, pos = 1), a.theta2.all(x = NULL, pos = 1) and a.theta3.all(x = NULL, pos = 1), where x, pos and col.name stand for an object of class REBMIX, a desired slot item and a desired column name, respectively.

Slots

Dataset:

a list of length n_{\mathrm{D}} of data frames or objects of class Histogram. Data frames should have 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.

Preprocessing:

a character vector giving the preprocessing types. One of "histogram",
"kernel density estimation" or "k-nearest neighbour".

cmax:

maximum number of components c_{\mathrm{max}} > 0. The default value is 15.

cmin:

minimum number of components c_{\mathrm{min}} > 0. The default value is 1.

Criterion:

a character giving the information criterion type. One of default Akaike "AIC", "AIC3", "AIC4" or "AICc", Bayesian "BIC", consistent Akaike "CAIC", Hannan-Quinn "HQC", minimum description length "MDL2" or "MDL5", approximate weight of evidence "AWE", classification likelihood "CLC", integrated classification likelihood "ICL" or "ICL-BIC", partition coefficient "PC", total of positive relative deviations "D" or sum of squares error "SSE".

Variables:

a character vector of length d containing types of variables. One of "continuous" or "discrete".

pdf:

a character vector of length d containing continuous or discrete parametric family types. One of "normal", "lognormal", "Weibull", "gamma", "Gumbel", "binomial", "Poisson", "Dirac", "uniform" or "vonMises".

theta1:

a vector of length d containing initial component parameters. One of n_{il} = \textrm{number of categories} - 1 for "binomial" distribution.

theta2:

a vector of length d containing initial component parameters. Currently not used.

theta3:

a vector of length d containing initial component parameters. One of \xi_{il} \in \{-1, \textrm{NA}, 1\} for "Gumbel" distribution.

K:

a character or a vector or a list of vectors containing numbers of bins v for the histogram and the kernel density estimation or numbers of nearest neighbours k for the k-nearest neighbour. There is no genuine rule to identify v or k. Consequently, the REBMIX algorithm identifies them from the set K of input values by minimizing the information criterion. The Sturges rule v = 1 + \mathrm{log_{2}}(n), \mathrm{Log}_{10} rule v = 10 \mathrm{log_{10}}(n) or RootN rule v = 2 \sqrt{n} can be applied to estimate the limiting numbers of bins or the rule of thumb k = \sqrt{n} to guess the intermediate number of nearest neighbours. If, e.g., K = c(10, 20, 40, 60) and minimum IC coincides, e.g., 40, brackets are set to 20 and 60 and the golden section is applied to refine the minimum search. See also kseq for sequence of bins or nearest neighbours generation. The default value is "auto".

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().

ar:

acceleration rate 0 < a_{\mathrm{r}} \leq 1. The default value is 0.1 and in most cases does not have to be altered.

Restraints:

a character giving the restraints type. One of "rigid" or default "loose". The rigid restraints are obsolete and applicable for well separated components only.

Mode:

a character giving the mode type. One of "all", "outliers" or default "outliersplus".The modes are determined in decreasing order of magnitude from all observations if Mode = "all". If Mode = "outliers", the modes are determined in decreasing order of magnitude from outliers only. In the meantime, some outliers are reclassified as inliers. Finally, when all observations are inliers, the procedure is completed. If Mode = "outliersplus", the modes are determined in decreasing magnitude from the outliers only. In the meantime, some outliers are reclassified as inliers. Finally, if all observations are inliers, they are converted to outliers and the mode determination procedure is continued.

w:

a list of vectors of length c containing component weights w_{l} summing to 1.

Theta:

a list of lists each containing c parametric family types pdfl. One of "normal", "lognormal", "Weibull", "gamma", "Gumbel", "binomial", "Poisson", "Dirac", "uniform" or circular "vonMises" defined for 0 \leq y_{i} \leq 2 \pi. Component parameters theta1.l follow the parametric family types. One of \mu_{il} for normal, lognormal, Gumbel and von Mises distributions, \theta_{il} for Weibull, gamma, binomial, Poisson and Dirac distributions and a for uniform distribution. Component parameters theta2.l follow theta1.l. One of \sigma_{il} for normal, lognormal and Gumbel distributions, \beta_{il} for Weibull and gamma distributions, p_{il} for binomial distribution, \kappa_{il} for von Mises distribution and b for uniform distribution. Component parameters theta3.l follow theta2.l. One of \xi_{il} for Gumbel distribution.

summary:

a data frame with additional information about dataset, preprocessing, c_{\mathrm{max}}, c_{\mathrm{min}}, information criterion type, a_{\mathrm{r}}, restraints type, mode type, optimal c, optimal v or k, K, y_{i0}, y_{i\mathrm{min}}, y_{i\mathrm{max}}, optimal h_{i}, information criterion \mathrm{IC}, log likelihood \mathrm{log}\, L and degrees of freedom M.

summary.EM:

a data frame with additional information about dataset, strategy for the EM algorithm strategy, variant of the EM algorithm variant, acceleration type acceleration, tolerance tolerance, acceleration multilplier acceleration.multiplier, maximum allowed number of iterations maximum.iterations, number of iterations used for obtaining optimal solution opt.iterations.nbr and total number of iterations of the EM algorithm total.iterations.nbr.

pos:

position in the summary data frame at which log likelihood \mathrm{log}\, L attains its maximum.

opt.c:

a list of vectors containing numbers of components for optimal v for the histogram and the kernel density estimation or for optimal number of nearest neighbours k for the k-nearest neighbour.

opt.IC:

a list of vectors containing information criteria for optimal v for the histogram and the kernel density estimation or for optimal number of nearest neighbours k for the k-nearest neighbour.

opt.logL:

a list of vectors containing log likelihoods for optimal v for the histogram and the kernel density estimation or for optimal number of nearest neighbours k for the k-nearest neighbour.

opt.Dmin:

a list of vectors containing D_{\mathrm{min}} values for optimal v for the histogram and the kernel density estimation or for optimal number of nearest neighbours k for the k-nearest neighbour.

opt.D:

a list of vectors containing totals of positive relative deviations for optimal v for the histogram and the kernel density estimation or for optimal number of nearest neighbours k for the k-nearest neighbour.

all.K:

a list of vectors containing all processed numbers of bins v for the histogram and the kernel density estimation or all processed numbers of nearest neighbours k for the k-nearest neighbour.

all.IC:

a list of vectors containing information criteria for all processed numbers of bins v for the histogram and the kernel density estimation or for all processed numbers of nearest neighbours k for the k-nearest neighbour.

Author(s)

Marko Nagode