StatMixRHLP-class function

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

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

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 $y_{i}$

   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: $z_ik = 1 if z_i = arg max_k tau_ik; 0 otherwise$.
  

• 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 $y_{ij}$

   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 $f(y_{i} | z_i = k, x, \Psi)$, c("$i =\n$", "$1,\\dots,n$").

• log_alphak_fk_yij: Matrix of size $(n, K)$ giving the values of the logarithm of the joint probability density function $f(y_{i}, z_{i} = k | x, \Psi)$, $i = 1,\dots,n$.

• 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.
   
    $z_ik = 1 if z_i = arg max_k tau_ik; 0 otherwise$.
  

See Also

ParamMixRHLP