README

FLaMingos: Functional Latent datA Models for clusterING heterogeneOus curveS

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

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

Usage

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 - 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mixRHLP: Iteration: 203 | log-likelihood: -14810.7960368513 #> 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 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()

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/Dossier/FChamroukhi-Habilitation.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/papers/FChamroukhi-Thesis.pdf.

FLaMingos: Functional Latent datA Models for clusterING heterogeneOus curveS

Installation

Usage

References