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A flexible mixture model for simultaneous clustering and segmentation of functional data (time series). It uses the EM algorithm (or a CEM-like algorithm).
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DESCRIPTION
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README.Rmd
README.md
mixRHLP.Rproj

README.md

Overview

R code for the clustering and segmentation of time series (including with regime changes) by mixture of Hidden Logistic Processes (MixRHLP) and the EM algorithm; i.e functional data clustering and segmentation.

Installation

You can install the development version of mixRHLP from GitHub with:

# install.packages("devtools")
devtools::install_github("fchamroukhi/mixRHLP")

To build vignettes for examples of usage, type the command below instead:

# install.packages("devtools")
devtools::install_github("fchamroukhi/mixRHLP", 
                         build_opts = c("--no-resave-data", "--no-manual"), 
                         build_vignettes = TRUE)

Use the following command to display vignettes:

browseVignettes("mixRHLP")

Usage

library(mixRHLP)
# 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 (polynomial regression components)
p <- 1 # Degree of the polynomials
q <- 1 # Order of the logistic regression (by default 1 for contiguous segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model

n_tries <- 1
max_iter <- 1000
threshold <- 1e-5
verbose <- TRUE
verbose_IRLS <- FALSE
init_kmeans <- TRUE

mixrhlp <- emMixRHLP(X = x, Y = Y, K, R, p, q, variance_type, init_kmeans, 
                     n_tries, max_iter, threshold, verbose, verbose_IRLS)
#> EM - mixRHLP: Iteration: 1 | log-likelihood: -18129.8169520025
#> EM - mixRHLP: Iteration: 2 | log-likelihood: -16642.732267463
#> EM - mixRHLP: Iteration: 3 | log-likelihood: -16496.947898833
#> EM - mixRHLP: Iteration: 4 | log-likelihood: -16391.6755568235
#> EM - mixRHLP: Iteration: 5 | log-likelihood: -16308.151649539
#> EM - mixRHLP: Iteration: 6 | log-likelihood: -16242.6749975019
#> EM - mixRHLP: Iteration: 7 | log-likelihood: -16187.9951484578
#> EM - mixRHLP: Iteration: 8 | log-likelihood: -16138.360050325
#> EM - mixRHLP: Iteration: 9 | log-likelihood: -16092.9430959116
#> EM - mixRHLP: Iteration: 10 | log-likelihood: -16053.588838999
#> EM - mixRHLP: Iteration: 11 | log-likelihood: -16020.7365667916
#> EM - mixRHLP: Iteration: 12 | log-likelihood: -15993.7513179937
#> EM - mixRHLP: Iteration: 13 | log-likelihood: -15972.7088032469
#> EM - mixRHLP: Iteration: 14 | log-likelihood: -15957.3889127412
#> EM - mixRHLP: Iteration: 15 | log-likelihood: -15946.5663566082
#> EM - mixRHLP: Iteration: 16 | log-likelihood: -15938.693534838
#> EM - mixRHLP: Iteration: 17 | log-likelihood: -15932.584112949
#> EM - mixRHLP: Iteration: 18 | log-likelihood: -15927.5299507605
#> EM - mixRHLP: Iteration: 19 | log-likelihood: -15923.1499635319
#> EM - mixRHLP: Iteration: 20 | log-likelihood: -15919.2392546398
#> EM - mixRHLP: Iteration: 21 | log-likelihood: -15915.6795793534
#> EM - mixRHLP: Iteration: 22 | log-likelihood: -15912.3944381959
#> EM - mixRHLP: Iteration: 23 | log-likelihood: -15909.327585346
#> EM - mixRHLP: Iteration: 24 | log-likelihood: -15906.4326405988
#> EM - mixRHLP: Iteration: 25 | log-likelihood: -15903.6678636145
#> EM - mixRHLP: Iteration: 26 | log-likelihood: -15900.9933370165
#> EM - mixRHLP: Iteration: 27 | log-likelihood: -15898.3692402859
#> EM - mixRHLP: Iteration: 28 | log-likelihood: -15895.7545341827
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#> EM - mixRHLP: Iteration: 30 | log-likelihood: -15890.3751610539
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#> EM - mixRHLP: Iteration: 33 | log-likelihood: -15881.1193453446
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#> EM - mixRHLP: Iteration: 35 | log-likelihood: -15873.3037170772
#> EM - mixRHLP: Iteration: 36 | log-likelihood: -15868.595660791
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#> EM - mixRHLP: Iteration: 38 | log-likelihood: -15856.8678694783
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#> EM - mixRHLP: Iteration: 40 | log-likelihood: -15840.8778843568
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#> EM - mixRHLP: Iteration: 70 | log-likelihood: -15197.3697193674
#> EM - mixRHLP: Iteration: 71 | log-likelihood: -15187.8845852548
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#> EM - mixRHLP: Iteration: 77 | log-likelihood: -15155.1488045656
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#> EM - mixRHLP: Iteration: 80 | log-likelihood: -15144.078942659
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#> EM - mixRHLP: Iteration: 92 | log-likelihood: -15116.7874031382
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#> EM - mixRHLP: Iteration: 100 | log-likelihood: -15091.0341403017
#> EM - mixRHLP: Iteration: 101 | log-likelihood: -15085.5952981967
#> EM - mixRHLP: Iteration: 102 | log-likelihood: -15079.1100803411
#> EM - mixRHLP: Iteration: 103 | log-likelihood: -15071.2863215881
#> EM - mixRHLP: Iteration: 104 | log-likelihood: -15061.8155026615
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#> EM - mixRHLP: Iteration: 106 | log-likelihood: -15037.4728804542
#> EM - mixRHLP: Iteration: 107 | log-likelihood: -15023.5663638262
#> EM - mixRHLP: Iteration: 108 | log-likelihood: -15010.227713049
#> EM - mixRHLP: Iteration: 109 | log-likelihood: -14998.9216243488
#> EM - mixRHLP: Iteration: 110 | log-likelihood: -14990.3428946115
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mixrhlp$summary()
#> ------------------------
#> Fitted mixRHLP model
#> ------------------------
#> 
#> MixRHLP model with K = 3 clusters and R = 3 regimes:
#> 
#>  log-likelihood nu       AIC       BIC       ICL
#>       -14810.69 41 -14851.69 -14880.41 -14880.41
#> 
#> 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     6.8902863   5.1134337  3.90153421
#> X^1   0.9265632  -0.3959402  0.08748466
#> 
#> Variances:
#> 
#>  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
#>       0.981915     0.9787717     0.9702211
#> 
#> --------------------
#> Cluster 2 (k = 2):
#> 
#> Regression coefficients for each regime/segment r (r=1...R):
#> 
#>     Beta(r = 1) Beta(r = 2) Beta(r = 3)
#> 1    4.96556671   6.7326717   4.8807183
#> X^1  0.08880479   0.4984443   0.1350271
#> 
#> Variances:
#> 
#>  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
#>      0.9559969       1.03849     0.9506928
#> 
#> --------------------
#> Cluster 3 (k = 3):
#> 
#> Regression coefficients for each regime/segment r (r=1...R):
#> 
#>     Beta(r = 1) Beta(r = 2) Beta(r = 3)
#> 1     6.3513369    4.214736   6.6536553
#> X^1  -0.2449377    0.839666   0.1024863
#> 
#> Variances:
#> 
#>  Sigma2(r = 1) Sigma2(r = 2) Sigma2(r = 3)
#>      0.9498285     0.9270384      1.001413

mixrhlp$plot()

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