R code for the clustering and segmentation of time series (including with regime changes) by mixture of gaussian Hidden Markov Models Regression (MixHMMR) and the EM algorithm, i.e functional data clustering and segmentation.
You can install the development version of mixHMMR from GitHub with:
# install.packages("devtools")
devtools::install_github("fchamroukhi/mixHMMR")
To build vignettes for examples of usage, type the command below instead:
# install.packages("devtools")
devtools::install_github("fchamroukhi/mixHMMR",
build_opts = c("--no-resave-data", "--no-manual"),
build_vignettes = TRUE)
Use the following command to display vignettes:
browseVignettes("mixHMMR")
library(mixHMMR)
# Application to a toy data set
data("toydataset")
x <- toydataset$x
Y <- t(toydataset[,2:ncol(toydataset)])
K <- 3 # Number of clusters
R <- 3 # Number of regimes/states
p <- 1 # Degree of the polynomial regression
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
ordered_states <- TRUE
n_tries <- 1
max_iter <- 1000
init_kmeans <- TRUE
threshold <- 1e-6
verbose <- TRUE
mixhmmr <- emMixHMMR(X = x, Y = Y, K, R, p, variance_type, ordered_states,
init_kmeans, n_tries, max_iter, threshold, verbose)
#> EM - mixHMMR: Iteration: 1 || log-likelihood: -18975.6323298895
#> EM - mixHMMR: Iteration: 2 || log-likelihood: -15198.5811534058
#> EM - mixHMMR: Iteration: 3 || log-likelihood: -15118.0350455527
#> EM - mixHMMR: Iteration: 4 || log-likelihood: -15086.2933826057
#> EM - mixHMMR: Iteration: 5 || log-likelihood: -15084.2502053712
#> EM - mixHMMR: Iteration: 6 || log-likelihood: -15083.7770153797
#> EM - mixHMMR: Iteration: 7 || log-likelihood: -15083.3586992156
#> EM - mixHMMR: Iteration: 8 || log-likelihood: -15082.8291034608
#> EM - mixHMMR: Iteration: 9 || log-likelihood: -15082.2407744542
#> EM - mixHMMR: Iteration: 10 || log-likelihood: -15081.6808462523
#> EM - mixHMMR: Iteration: 11 || log-likelihood: -15081.175618676
#> EM - mixHMMR: Iteration: 12 || log-likelihood: -15080.5819574865
#> EM - mixHMMR: Iteration: 13 || log-likelihood: -15079.3118011276
#> EM - mixHMMR: Iteration: 14 || log-likelihood: -15076.8073408977
#> EM - mixHMMR: Iteration: 15 || log-likelihood: -15073.8399600893
#> EM - mixHMMR: Iteration: 16 || log-likelihood: -15067.6884092484
#> EM - mixHMMR: Iteration: 17 || log-likelihood: -15054.9127597414
#> EM - mixHMMR: Iteration: 18 || log-likelihood: -15049.4000307536
#> EM - mixHMMR: Iteration: 19 || log-likelihood: -15049.0221351022
#> EM - mixHMMR: Iteration: 20 || log-likelihood: -15048.997021329
#> EM - mixHMMR: Iteration: 21 || log-likelihood: -15048.9949507534
mixhmmr$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
mixhmmr$plot()