Introduction

mixHMMR: Simultaneous model-based clustering and segmentation of heterogeneous and dynamical functional data (curves/times series) with changes in regime by a mixture of gaussian regression models with hidden Markov processes, fitted by the EM/Baum-Welch algorithm.

It was written in R Markdown, using the knitr package for production.

See help(package="flamingos") for further details and references provided by citation("flamingos").

Load data

data("toydataset")
x <- toydataset$x
Y <- t(toydataset[,2:ncol(toydataset)])

Set up mixHMMR model parameters

K <- 3 # Number of clusters
R <- 3 # Number of regimes/states
p <- 1 # Degree of the polynomial regression
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model

Set up EM parameters

ordered_states <- TRUE
n_tries <- 1
max_iter <- 1000
init_kmeans <- TRUE
threshold <- 1e-6
verbose <- TRUE

Estimation

mixhmmr <- emMixHMMR(X = x, Y = Y, K, R, p, variance_type, ordered_states, 
                     init_kmeans, n_tries, max_iter, threshold, verbose)
## EM - mixHMMR: Iteration: 1 || log-likelihood: -18975.6323298895
## EM - mixHMMR: Iteration: 2 || log-likelihood: -15198.5811534058
## EM - mixHMMR: Iteration: 3 || log-likelihood: -15118.0350455527
## EM - mixHMMR: Iteration: 4 || log-likelihood: -15086.2933826057
## EM - mixHMMR: Iteration: 5 || log-likelihood: -15084.2502053712
## EM - mixHMMR: Iteration: 6 || log-likelihood: -15083.7770153797
## EM - mixHMMR: Iteration: 7 || log-likelihood: -15083.3586992156
## EM - mixHMMR: Iteration: 8 || log-likelihood: -15082.8291034608
## EM - mixHMMR: Iteration: 9 || log-likelihood: -15082.2407744542
## EM - mixHMMR: Iteration: 10 || log-likelihood: -15081.6808462523
## EM - mixHMMR: Iteration: 11 || log-likelihood: -15081.175618676
## EM - mixHMMR: Iteration: 12 || log-likelihood: -15080.5819574865
## EM - mixHMMR: Iteration: 13 || log-likelihood: -15079.3118011276
## EM - mixHMMR: Iteration: 14 || log-likelihood: -15076.8073408977
## EM - mixHMMR: Iteration: 15 || log-likelihood: -15073.8399600893
## EM - mixHMMR: Iteration: 16 || log-likelihood: -15067.6884092483
## EM - mixHMMR: Iteration: 17 || log-likelihood: -15054.9127597413
## EM - mixHMMR: Iteration: 18 || log-likelihood: -15049.4000307536
## EM - mixHMMR: Iteration: 19 || log-likelihood: -15049.0221351022
## EM - mixHMMR: Iteration: 20 || log-likelihood: -15048.997021329
## EM - mixHMMR: Iteration: 21 || log-likelihood: -15048.9949507534

Summary

mixhmmr$summary()
## ------------------------
## Fitted mixHMMR model
## ------------------------
## 
## MixHMMR model with K = 3 clusters and R = 3 regimes:
## 
##  log-likelihood nu       AIC       BIC       ICL
##       -15048.99 50 -15098.99 -15134.02 -15134.02
## 
## Clustering table (Number of curves in each clusters):
## 
##  1  2  3 
## 10 10 10 
## 
## Mixing probabilities (cluster weights):
##          1         2         3
##  0.3333333 0.3333333 0.3333333
## 
## 
## --------------------
## Cluster 1 (k = 1):
## 
## Regression coefficients for each regime/segment r (r=1...R):
## 
##     Beta(r = 1) Beta(r = 2) Beta(r = 3)
## 1      6.870328   5.1511267   3.9901300
## X^1    1.204150  -0.4601777  -0.0155753
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9776399     0.9895623       0.96457
## 
## --------------------
## Cluster 2 (k = 2):
## 
## Regression coefficients for each regime/segment r (r=1...R):
## 
##     Beta(r = 1) Beta(r = 2) Beta(r = 3)
## 1     4.9512819   6.8393804   4.9076599
## X^1   0.2099508   0.2822775   0.1031626
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9576192      1.045043      0.952047
## 
## --------------------
## Cluster 3 (k = 3):
## 
## Regression coefficients for each regime/segment r (r=1...R):
## 
##     Beta(r = 1) Beta(r = 2) Beta(r = 3)
## 1     6.3552432   4.2868818   6.5327846
## X^1  -0.2865404   0.6907212   0.2429291
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9587975     0.9481068       1.01388

Plots

mixhmmr$plot()