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Overview

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.

Installation

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")

Usage

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()

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Clustering and segmentation of time series with regime changes by mixture of Hidden Markov Model Regressions (MixFHMMR) and the EM algorithm

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