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Functional Latent datA Models for clusterING heterogeneOus curveS
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README.md

FLaMingos: Functional Latent datA Models for clusterING heterogeneOus curveS

Travis build status CRAN versions CRAN logs

flamingos is an open-source toolbox (available in R and in Matlab) for the simultaneous clustering and segmentation of heterogeneous functional data (i.e time-series ore more generally longitudinal data), with original and flexible functional latent variable models, fitted by unsupervised algorithms, including EM algorithms.

Our nice FLaMingos are mainly:

  • mixRHLP;
  • mixHMM;
  • mixHMMR.

The models and algorithms are developped and written in Matlab by Faicel Chamroukhi, and translated and designed into R packages by Florian Lecocq, Marius Bartcus and Faicel Chamroukhi.

Installation

You can install the flamingos package from GitHub with:

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

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

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

Use the following command to display vignettes:

browseVignettes("flamingos")

Usage

library(flamingos)
mixRHLP
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
#> EM - mixRHLP: Iteration: 29 | log-likelihood: -15893.1056775993
#> EM - mixRHLP: Iteration: 30 | log-likelihood: -15890.3751610539
#> EM - mixRHLP: Iteration: 31 | log-likelihood: -15887.5097378815
#> EM - mixRHLP: Iteration: 32 | log-likelihood: -15884.4482946475
#> EM - mixRHLP: Iteration: 33 | log-likelihood: -15881.1193453446
#> EM - mixRHLP: Iteration: 34 | log-likelihood: -15877.4381561224
#> EM - mixRHLP: Iteration: 35 | log-likelihood: -15873.3037170772
#> EM - mixRHLP: Iteration: 36 | log-likelihood: -15868.595660791
#> EM - mixRHLP: Iteration: 37 | log-likelihood: -15863.171868441
#> EM - mixRHLP: Iteration: 38 | log-likelihood: -15856.8678694783
#> EM - mixRHLP: Iteration: 39 | log-likelihood: -15849.5002500459
#> EM - mixRHLP: Iteration: 40 | log-likelihood: -15840.8778843568
#> EM - mixRHLP: Iteration: 41 | log-likelihood: -15830.8267303162
#> EM - mixRHLP: Iteration: 42 | log-likelihood: -15819.2343887404
#> EM - mixRHLP: Iteration: 43 | log-likelihood: -15806.11425583
#> EM - mixRHLP: Iteration: 44 | log-likelihood: -15791.6651550126
#> EM - mixRHLP: Iteration: 45 | log-likelihood: -15776.2575311116
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#> EM - mixRHLP: Iteration: 60 | log-likelihood: -15384.7708355233
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#> EM - mixRHLP: Iteration: 64 | log-likelihood: -15308.1502066517
#> EM - mixRHLP: Iteration: 65 | log-likelihood: -15288.3650661699
#> EM - mixRHLP: Iteration: 66 | log-likelihood: -15267.1380314858
#> EM - mixRHLP: Iteration: 67 | log-likelihood: -15245.8151021308
#> EM - mixRHLP: Iteration: 68 | log-likelihood: -15226.3007649639
#> EM - mixRHLP: Iteration: 69 | log-likelihood: -15209.9671868432
#> EM - mixRHLP: Iteration: 70 | log-likelihood: -15197.3697193674
#> EM - mixRHLP: Iteration: 71 | log-likelihood: -15187.8845852548
#> EM - mixRHLP: Iteration: 72 | log-likelihood: -15180.4065779427
#> EM - mixRHLP: Iteration: 73 | log-likelihood: -15174.1897193241
#> EM - mixRHLP: Iteration: 74 | log-likelihood: -15168.8680084075
#> EM - mixRHLP: Iteration: 75 | log-likelihood: -15164.1615627415
#> EM - mixRHLP: Iteration: 76 | log-likelihood: -15159.6679572457
#> EM - mixRHLP: Iteration: 77 | log-likelihood: -15155.1488045656
#> EM - mixRHLP: Iteration: 78 | log-likelihood: -15150.9231858137
#> EM - mixRHLP: Iteration: 79 | log-likelihood: -15147.2212168192
#> EM - mixRHLP: Iteration: 80 | log-likelihood: -15144.078942659
#> EM - mixRHLP: Iteration: 81 | log-likelihood: -15141.3516305636
#> EM - mixRHLP: Iteration: 82 | log-likelihood: -15138.8602529876
#> EM - mixRHLP: Iteration: 83 | log-likelihood: -15136.5059345662
#> EM - mixRHLP: Iteration: 84 | log-likelihood: -15134.2384537766
#> EM - mixRHLP: Iteration: 85 | log-likelihood: -15132.0298589309
#> EM - mixRHLP: Iteration: 86 | log-likelihood: -15129.8608706576
#> EM - mixRHLP: Iteration: 87 | log-likelihood: -15127.7157936565
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#> EM - mixRHLP: Iteration: 90 | log-likelihood: -15121.2712280838
#> EM - mixRHLP: Iteration: 91 | log-likelihood: -15119.0622569401
#> EM - mixRHLP: Iteration: 92 | log-likelihood: -15116.7874031382
#> EM - mixRHLP: Iteration: 93 | log-likelihood: -15114.4192658119
#> EM - mixRHLP: Iteration: 94 | log-likelihood: -15111.9245293407
#> EM - mixRHLP: Iteration: 95 | log-likelihood: -15109.262047444
#> EM - mixRHLP: Iteration: 96 | log-likelihood: -15106.3802520661
#> EM - mixRHLP: Iteration: 97 | log-likelihood: -15103.2137059945
#> EM - mixRHLP: Iteration: 98 | log-likelihood: -15099.6787565231
#> EM - mixRHLP: Iteration: 99 | log-likelihood: -15095.6664401258
#> 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: 108 | log-likelihood: -15010.227713049
#> EM - mixRHLP: Iteration: 109 | log-likelihood: -14998.9216243488
#> EM - mixRHLP: Iteration: 110 | log-likelihood: -14990.3428946115
#> EM - mixRHLP: Iteration: 111 | log-likelihood: -14984.2931646741
#> EM - mixRHLP: Iteration: 112 | log-likelihood: -14980.0317050997
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#> EM - mixRHLP: Iteration: 116 | log-likelihood: -14969.3710026547
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#> EM - mixRHLP: Iteration: 204 | log-likelihood: -14810.6883875777

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     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
#> 
#> --------------------
#> Cluster 3 (k = 3):
#> 
#> 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

mixrhlp$plot()

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

K <- 3 # Number of clusters
R <- 3 # Number of regimes (HMM states)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model

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

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

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

mixhmm$plot()

mixHMMR
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     6.3552432   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
#> 
#> --------------------
#> Cluster 2 (k = 2):
#> 
#> 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 3 (k = 3):
#> 
#> 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

mixhmmr$plot()

References

Chamroukhi, Faicel, and Hien D. Nguyen. 2019. “Model-Based Clustering and Classification of Functional Data.” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery. https://chamroukhi.com/papers/MBCC-FDA.pdf.

Chamroukhi, F. 2016. “Unsupervised Learning of Regression Mixture Models with Unknown Number of Components.” Journal of Statistical Computation and Simulation 86 (November): 2308–34. https://chamroukhi.com/papers/Chamroukhi-JSCS-2015.pdf.

Chamroukhi, Faicel. 2016. “Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation.” Journal of Classification 33 (3): 374–411. https://chamroukhi.com/papers/Chamroukhi-PWRM-JournalClassif-2016.pdf.

Chamroukhi, F. 2015. “Statistical Learning of Latent Data Models for Complex Data Analysis.” Habilitation Thesis (HDR), Université de Toulon. https://chamroukhi.com/FChamroukhi-HDR.pdf.

Chamroukhi, F., H. Glotin, and A. Samé. 2013. “Model-Based Functional Mixture Discriminant Analysis with Hidden Process Regression for Curve Classification.” Neurocomputing 112: 153–63. https://chamroukhi.com/papers/chamroukhi_et_al_neucomp2013a.pdf.

Chamroukhi, F., and H. Glotin. 2012. “Mixture Model-Based Functional Discriminant Analysis for Curve Classification.” In Proceedings of the International Joint Conference on Neural Networks (IJCNN), IEEE, 1–8. Brisbane, Australia. https://chamroukhi.com/papers/Chamroukhi-ijcnn-2012.pdf.

Samé, A., F. Chamroukhi, Gérard Govaert, and P. Aknin. 2011. “Model-Based Clustering and Segmentation of Time Series with Changes in Regime.” Advances in Data Analysis and Classification 5 (4): 301–21. https://chamroukhi.com/papers/adac-2011.pdf.

Chamroukhi, F., A. Samé, P. Aknin, and G. Govaert. 2011. “Model-Based Clustering with Hidden Markov Model Regression for Time Series with Regime Changes.” In Proceedings of the International Joint Conference on Neural Networks (IJCNN), IEEE, 2814–21. https://chamroukhi.com/papers/Chamroukhi-ijcnn-2011.pdf.

Chamroukhi, F., A. Samé, G. Govaert, and P. Aknin. 2010. “A Hidden Process Regression Model for Functional Data Description. Application to Curve Discrimination.” Neurocomputing 73 (7-9): 1210–21. https://chamroukhi.com/papers/chamroukhi_neucomp_2010.pdf.

Chamroukhi, F. 2010. “Hidden Process Regression for Curve Modeling, Classification and Tracking.” Ph.D. Thesis, Université de Technologie de Compiègne. https://chamroukhi.com/FChamroukhi-PhD.pdf.

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