# demix: Empirical Density Calculation In rebmix: Finite Mixture Modeling, Clustering & Classification

## Description

Returns the data frame containing observations \bm{x}_{1}, …, \bm{x}_{n} and empirical densities f_{1}, …, f_{n} for the Parzen window or k-nearest neighbour or bin means \bar{\bm{x}}_{1}, …, \bar{\bm{x}}_{v} and empirical densities f_{1}, …, f_{v} for the histogram preprocessing. Vectors \bm{x} and \bar{\bm{x}} are subvectors of \bm{y} = (y_{1}, …, y_{d})^{\top} and \bar{\bm{y}} = (\bar{y}_{1}, …, \bar{y}_{d})^{\top}.

## Usage

 1 2 3 ## S4 method for signature 'REBMIX' demix(x = NULL, pos = 1, variables = expression(1:d), ...) ## ... and for other signatures 

## Arguments

 x see Methods section below. pos a desired row number in [email protected] for which the empirical densities are calculated. The default value is 1. variables a vector containing indices of variables in subvectors \bm{x} or \bar{\bm{x}}. The default value is 1:d. ... currently not used.

## Methods

signature(x = "REBMIX")

an object of class REBMIX.

signature(x = "REBMVNORM")

an object of class REBMVNORM.

Marko Nagode

## References

M. Nagode and M. Fajdiga. The rebmix algorithm for the univariate finite mixture estimation. Communications in Statistics - Theory and Methods, 40(5):876-892, 2011a. http://dx.doi.org/10.1080/03610920903480890.

M. Nagode and M. Fajdiga. The rebmix algorithm for the multivariate finite mixture estimation. Communications in Statistics - Theory and Methods, 40(11):2022-2034, 2011b. http://dx.doi.org/10.1080/03610921003725788.

M. Nagode. Finite mixture modeling via REBMIX. Journal of Algorithms and Optimization, 3(2):14-28, 2015. http://dx.doi.org/10.5963/JAO0302001.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 # Generate simulated dataset. n <- c(15, 15) Theta <- list(pdf1 = rep("normal", 3), theta1.1 = c(10, 20, 30), theta2.1 = c(3, 2, 1), pdf2 = rep("normal", 3), theta1.2 = c(3, 4, 5), theta2.2 = c(15, 10, 5)) simulated <- RNGMIX(Dataset.name = paste("simulated_", 1:4, sep = ""), rseed = -1, n = n, Theta = Theta) # Number of classes or nearest neighbours to be processed. K <- c(as.integer(1 + log2(sum(n))), # Minimum v follows Sturges rule. as.integer(10 * log10(sum(n)))) # Maximum v follows log10 rule. # Estimate number of components, component weights and component parameters. simulatedest <- REBMIX(model = "REBMVNORM", Dataset = simulated@Dataset, Preprocessing = "h", cmax = 4, Criterion = "BIC", pdf = c("n", "n", "n"), K = K[1]:K[2]) # Preprocess simulated dataset. f <- demix(simulatedest, pos = 3, variables = c(1, 3)) f # Plot finite mixture. opar <- plot(simulatedest, pos = 3, nrow = 3, ncol = 1) par(usr = opar[[2]]\$usr, mfg = c(2, 1)) text(x = f[, 1], y = f[, 2], labels = format(f[, 3], digits = 3), cex = 0.8, pos = 1) 

rebmix documentation built on April 7, 2018, 5:03 p.m.