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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:
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.
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")library(flamingos)data("toydataset")
x <- toydataset$x
Y <- t(toydataset[,2:ncol(toydataset)])
K <- 3 # Number of clusters
R <- 3 # Number of regimes (polynomial regression components)
p <- 1 # Degree of the polynomials
q <- 1 # Order of the logistic regression (by default 1 for contiguous segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
n_tries <- 1
max_iter <- 1000
threshold <- 1e-5
verbose <- TRUE
verbose_IRLS <- FALSE
init_kmeans <- TRUE
mixrhlp <- emMixRHLP(X = x, Y = Y, K, R, p, q, variance_type, init_kmeans,
n_tries, max_iter, threshold, verbose, verbose_IRLS)
#> EM - mixRHLP: Iteration: 1 | log-likelihood: -18129.8169520025
#> EM - mixRHLP: Iteration: 2 | log-likelihood: -16642.732267463
#> EM - mixRHLP: Iteration: 3 | log-likelihood: -16496.947898833
#> EM - mixRHLP: Iteration: 4 | log-likelihood: -16391.6755568235
#> EM - mixRHLP: Iteration: 5 | log-likelihood: -16308.151649539
#> EM - mixRHLP: Iteration: 6 | log-likelihood: -16242.6749975019
#> EM - mixRHLP: Iteration: 7 | log-likelihood: -16187.9951484578
#> EM - mixRHLP: Iteration: 8 | log-likelihood: -16138.360050325
#> EM - mixRHLP: Iteration: 9 | log-likelihood: -16092.9430959116
#> EM - mixRHLP: Iteration: 10 | log-likelihood: -16053.588838999
#> EM - mixRHLP: Iteration: 11 | log-likelihood: -16020.7365667916
#> EM - mixRHLP: Iteration: 12 | log-likelihood: -15993.7513179937
#> EM - mixRHLP: Iteration: 13 | log-likelihood: -15972.7088032469
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mixrhlp$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 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 2 (k = 2):
#>
#> 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 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$plot()
data("toydataset")
Y <- t(toydataset[,2:ncol(toydataset)])
K <- 3 # Number of clusters
R <- 3 # Number of regimes (HMM states)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model
ordered_states <- TRUE
n_tries <- 1
max_iter <- 1000
init_kmeans <- TRUE
threshold <- 1e-6
verbose <- TRUE
mixhmm <- emMixHMM(Y = Y, K, R, variance_type, ordered_states, init_kmeans,
n_tries, max_iter, threshold, verbose)
#> EM - mixHMMs: Iteration: 1 | log-likelihood: -19054.7157954833
#> EM - mixHMMs: Iteration: 2 | log-likelihood: -15386.7973253636
#> EM - mixHMMs: Iteration: 3 | log-likelihood: -15141.8435629464
#> EM - mixHMMs: Iteration: 4 | log-likelihood: -15058.7251666378
#> EM - mixHMMs: Iteration: 5 | log-likelihood: -15055.5058566489
#> EM - mixHMMs: Iteration: 6 | log-likelihood: -15055.4877310423
#> EM - mixHMMs: Iteration: 7 | log-likelihood: -15055.4876146553
mixhmm$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$plot()
data("toydataset")
x <- toydataset$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()
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/Dossier/FChamroukhi-Habilitation.pdf.
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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/papers/FChamroukhi-Thesis.pdf.
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