StatMixRHLP-class {flamingos}

A Reference Class which contains statistics of a mixture of RHLP models.

Description

StatMixRHLP contains all the statistics associated to a MixRHLP model, in particular the E-Step (and C-Step) of the (C)EM algorithm.

Fields

pi_jkr

Array of size (nm, R, K) representing the logistic proportion for cluster k.

tau_ik

Matrix of size (n, K) giving the posterior probabilities (fuzzy segmentation matrix) that the curve \boldsymbol{y}_{i} originates from the k-th RHLP model.

z_ik

Hard segmentation logical matrix of dimension (n, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ tau\_ik;\ 0 \ \textrm{otherwise}.

klas

Column matrix of the labels issued from z_ik. Its elements are klas[i] = z\_i, i = 1,\dots,n.

gamma_ijkr

Array of size (nm, R, K) giving the posterior probabilities that the observation \boldsymbol{y}_{ij} originates from the r-th regime of the k-th RHLP model.

polynomials

Array of size (m, R, K) giving the values of the estimated polynomial regression components.

weighted_polynomials

Array of size (m, R, K) giving the values of the estimated polynomial regression components weighted by the prior probabilities pi_jkr.

Ey

Matrix of size (m, K). Ey is the curve expectation (estimated signal): sum of the polynomial components weighted by the logistic probabilities pi_jkr.

loglik

Numeric. Observed-data log-likelihood of the MixRHLP model.

com_loglik

Numeric. Complete-data log-likelihood of the MixRHLP model.

stored_loglik

Numeric vector. Stored values of the log-likelihood at each EM iteration.

stored_com_loglik

Numeric vector. Stored values of the Complete log-likelihood at each EM iteration.

BIC

Numeric. Value of BIC (Bayesian Information Criterion).

ICL

Numeric. Value of ICL (Integrated Completed Likelihood).

AIC

Numeric. Value of AIC (Akaike Information Criterion).

log_fk_yij

Matrix of size (n, K) giving the values of the probability density function f(\boldsymbol{y}_{i} | z_i = k, \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

log_alphak_fk_yij

Matrix of size (n, K) giving the values of the logarithm of the joint probability density function f(\boldsymbol{y}_{i}, \ z_{i} = k | \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

log_gamma_ijkr

Array of size (nm, R, K) giving the logarithm of gamma_ijkr.

Methods

computeStats(paramMixRHLP)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramMixRHLP of class ParamMixRHLP.

CStep(reg_irls)

Method used in the CEM algorithm to update statistics.

EStep(paramMixRHLP)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramMixRHLP of class ParamMixRHLP (prior and posterior probabilities).

MAP()

MAP calculates values of the fields z_ik and klas by applying the Maximum A Posteriori Bayes allocation rule.

z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ tau\_ik;\ 0 \ \textrm{otherwise} .

See Also

ParamMixRHLP