Introduction

mixHMM: Clustering and segmentation of heterogeneous curves/time series by mixture of gaussian Hidden Markov Models (MixHMMs) 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")
Y <- t(toydataset[,2:ncol(toydataset)])

Set up mixHMM model parameters

K <- 3 # Number of clusters
R <- 3 # Number of regimes (HMM states)
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

mixhmm <- emMixHMM(Y = Y, K, R, variance_type, ordered_states, init_kmeans, 
                   n_tries, max_iter, threshold, verbose)
## EM - mixHMMs: Iteration: 1 | log-likelihood: -19054.7157954833
## EM - mixHMMs: Iteration: 2 | log-likelihood: -15386.7973253636
## EM - mixHMMs: Iteration: 3 | log-likelihood: -15141.8435629464
## EM - mixHMMs: Iteration: 4 | log-likelihood: -15058.7251666378
## EM - mixHMMs: Iteration: 5 | log-likelihood: -15055.5058566489
## EM - mixHMMs: Iteration: 6 | log-likelihood: -15055.4877310423
## EM - mixHMMs: Iteration: 7 | log-likelihood: -15055.4876146553

Summary

mixhmm$summary()
## -----------------------
## Fitted mixHMM model
## -----------------------
## 
## MixHMM model with K = 3 clusters and R = 3 regimes:
## 
##  log-likelihood nu       AIC       BIC
##       -15055.49 41 -15096.49 -15125.21
## 
## 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):
## 
## Means:
## 
##    r = 1    r = 2    r = 3
##  7.00202 4.964273 3.979626
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9858726     0.9884542     0.9651437
## 
## -------------------
## Cluster 2 (k = 2):
## 
## Means:
## 
##     r = 1    r = 2    r = 3
##  4.987066 6.963998 4.987279
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9578459      1.045573      0.952294
## 
## -------------------
## Cluster 3 (k = 3):
## 
## Means:
## 
##     r = 1    r = 2    r = 3
##  6.319189 4.583954 6.722627
## 
## Variances:
## 
##  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
##      0.9571803     0.9504731       1.01553

Plots

mixhmm$plot()