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mixrhlp's Introduction

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
#> 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
#> EM - mixRHLP: Iteration: 46 | log-likelihood: -15760.2525673176
#> EM - mixRHLP: Iteration: 47 | log-likelihood: -15743.6600428386
#> EM - mixRHLP: Iteration: 48 | log-likelihood: -15725.8494727209
#> EM - mixRHLP: Iteration: 49 | log-likelihood: -15705.5392028324
#> EM - mixRHLP: Iteration: 50 | log-likelihood: -15681.0330055801
#> EM - mixRHLP: Iteration: 51 | log-likelihood: -15650.7058006772
#> EM - mixRHLP: Iteration: 52 | log-likelihood: -15614.1891628978
#> EM - mixRHLP: Iteration: 53 | log-likelihood: -15574.3209962234
#> EM - mixRHLP: Iteration: 54 | log-likelihood: -15536.9561042095
#> EM - mixRHLP: Iteration: 55 | log-likelihood: -15505.9888676546
#> EM - mixRHLP: Iteration: 56 | log-likelihood: -15480.3479747868
#> EM - mixRHLP: Iteration: 57 | log-likelihood: -15456.7432033066
#> EM - mixRHLP: Iteration: 58 | log-likelihood: -15432.855894347
#> EM - mixRHLP: Iteration: 59 | log-likelihood: -15408.4123139152
#> EM - mixRHLP: Iteration: 60 | log-likelihood: -15384.7708355233
#> EM - mixRHLP: Iteration: 61 | log-likelihood: -15363.3704926307
#> EM - mixRHLP: Iteration: 62 | log-likelihood: -15344.3247788467
#> EM - mixRHLP: Iteration: 63 | log-likelihood: -15326.444200793
#> 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
#> EM - mixRHLP: Iteration: 88 | log-likelihood: -15125.5797196054
#> EM - mixRHLP: Iteration: 89 | log-likelihood: -15123.4372146492
#> 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
#> EM - mixRHLP: Iteration: 105 | log-likelihood: -15050.4931948422
#> 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
#> EM - mixRHLP: Iteration: 111 | log-likelihood: -14984.2931646741
#> EM - mixRHLP: Iteration: 112 | log-likelihood: -14980.0317050997
#> EM - mixRHLP: Iteration: 113 | log-likelihood: -14976.7574542595
#> EM - mixRHLP: Iteration: 114 | log-likelihood: -14973.9768267566
#> EM - mixRHLP: Iteration: 115 | log-likelihood: -14971.5304235767
#> EM - mixRHLP: Iteration: 116 | log-likelihood: -14969.3710026547
#> EM - mixRHLP: Iteration: 117 | log-likelihood: -14967.3301314624
#> EM - mixRHLP: Iteration: 118 | log-likelihood: -14965.1319732928
#> EM - mixRHLP: Iteration: 119 | log-likelihood: -14962.818626259
#> EM - mixRHLP: Iteration: 120 | log-likelihood: -14961.1657986148
#> EM - mixRHLP: Iteration: 121 | log-likelihood: -14960.1001793804
#> EM - mixRHLP: Iteration: 122 | log-likelihood: -14959.2029493404
#> EM - mixRHLP: Iteration: 123 | log-likelihood: -14958.3643653619
#> EM - mixRHLP: Iteration: 124 | log-likelihood: -14957.5579272948
#> EM - mixRHLP: Iteration: 125 | log-likelihood: -14956.7769206505
#> EM - mixRHLP: Iteration: 126 | log-likelihood: -14956.0220832192
#> EM - mixRHLP: Iteration: 127 | log-likelihood: -14955.2990068376
#> EM - mixRHLP: Iteration: 128 | log-likelihood: -14954.6080936987
#> EM - mixRHLP: Iteration: 129 | log-likelihood: -14953.9546052572
#> EM - mixRHLP: Iteration: 130 | log-likelihood: -14953.3424683065
#> EM - mixRHLP: Iteration: 131 | log-likelihood: -14952.7742704947
#> EM - mixRHLP: Iteration: 132 | log-likelihood: -14952.2512735504
#> EM - mixRHLP: Iteration: 133 | log-likelihood: -14951.7732467988
#> EM - mixRHLP: Iteration: 134 | log-likelihood: -14951.3384384815
#> EM - mixRHLP: Iteration: 135 | log-likelihood: -14950.9439547413
#> EM - mixRHLP: Iteration: 136 | log-likelihood: -14950.5860673359
#> EM - mixRHLP: Iteration: 137 | log-likelihood: -14950.2605961901
#> EM - mixRHLP: Iteration: 138 | log-likelihood: -14949.9632302133
#> EM - mixRHLP: Iteration: 139 | log-likelihood: -14949.6897803656
#> EM - mixRHLP: Iteration: 140 | log-likelihood: -14949.4363440458
#> EM - mixRHLP: Iteration: 141 | log-likelihood: -14949.1993934329
#> EM - mixRHLP: Iteration: 142 | log-likelihood: -14948.9758045711
#> EM - mixRHLP: Iteration: 143 | log-likelihood: -14948.7628462595
#> EM - mixRHLP: Iteration: 144 | log-likelihood: -14948.5581447387
#> EM - mixRHLP: Iteration: 145 | log-likelihood: -14948.3596363733
#> EM - mixRHLP: Iteration: 146 | log-likelihood: -14948.1655161518
#> EM - mixRHLP: Iteration: 147 | log-likelihood: -14947.9741866833
#> EM - mixRHLP: Iteration: 148 | log-likelihood: -14947.7842100466
#> EM - mixRHLP: Iteration: 149 | log-likelihood: -14947.5942633197
#> EM - mixRHLP: Iteration: 150 | log-likelihood: -14947.4030977377
#> EM - mixRHLP: Iteration: 151 | log-likelihood: -14947.2095010109
#> EM - mixRHLP: Iteration: 152 | log-likelihood: -14947.0122620331
#> EM - mixRHLP: Iteration: 153 | log-likelihood: -14946.8101371804
#> EM - mixRHLP: Iteration: 154 | log-likelihood: -14946.6018173877
#> EM - mixRHLP: Iteration: 155 | log-likelihood: -14946.3858952193
#> EM - mixRHLP: Iteration: 156 | log-likelihood: -14946.1608312027
#> EM - mixRHLP: Iteration: 157 | log-likelihood: -14945.9249187549
#> EM - mixRHLP: Iteration: 158 | log-likelihood: -14945.676247118
#> EM - mixRHLP: Iteration: 159 | log-likelihood: -14945.4126618353
#> EM - mixRHLP: Iteration: 160 | log-likelihood: -14945.1317224602
#> EM - mixRHLP: Iteration: 161 | log-likelihood: -14944.8306573941
#> EM - mixRHLP: Iteration: 162 | log-likelihood: -14944.5063160023
#> EM - mixRHLP: Iteration: 163 | log-likelihood: -14944.1551184229
#> EM - mixRHLP: Iteration: 164 | log-likelihood: -14943.7730037188
#> EM - mixRHLP: Iteration: 165 | log-likelihood: -14943.355377134
#> EM - mixRHLP: Iteration: 166 | log-likelihood: -14942.8970570836
#> EM - mixRHLP: Iteration: 167 | log-likelihood: -14942.3922219831
#> EM - mixRHLP: Iteration: 168 | log-likelihood: -14941.8343559995
#> EM - mixRHLP: Iteration: 169 | log-likelihood: -14941.2161912546
#> EM - mixRHLP: Iteration: 170 | log-likelihood: -14940.5296397031
#> EM - mixRHLP: Iteration: 171 | log-likelihood: -14939.7657190993
#> EM - mixRHLP: Iteration: 172 | log-likelihood: -14938.9144460343
#> EM - mixRHLP: Iteration: 173 | log-likelihood: -14937.9647057519
#> EM - mixRHLP: Iteration: 174 | log-likelihood: -14936.9040831122
#> EM - mixRHLP: Iteration: 175 | log-likelihood: -14935.7186499891
#> EM - mixRHLP: Iteration: 176 | log-likelihood: -14934.3927038884
#> EM - mixRHLP: Iteration: 177 | log-likelihood: -14932.9084527435
#> EM - mixRHLP: Iteration: 178 | log-likelihood: -14931.245639997
#> EM - mixRHLP: Iteration: 179 | log-likelihood: -14929.3811026273
#> EM - mixRHLP: Iteration: 180 | log-likelihood: -14927.2882537299
#> EM - mixRHLP: Iteration: 181 | log-likelihood: -14924.9364821865
#> EM - mixRHLP: Iteration: 182 | log-likelihood: -14922.2904675358
#> EM - mixRHLP: Iteration: 183 | log-likelihood: -14919.3094231961
#> EM - mixRHLP: Iteration: 184 | log-likelihood: -14915.9463144684
#> EM - mixRHLP: Iteration: 185 | log-likelihood: -14912.1471647651
#> EM - mixRHLP: Iteration: 186 | log-likelihood: -14907.8506901999
#> EM - mixRHLP: Iteration: 187 | log-likelihood: -14902.9887290339
#> EM - mixRHLP: Iteration: 188 | log-likelihood: -14897.4883102736
#> EM - mixRHLP: Iteration: 189 | log-likelihood: -14891.27676833
#> EM - mixRHLP: Iteration: 190 | log-likelihood: -14884.2919447409
#> EM - mixRHLP: Iteration: 191 | log-likelihood: -14876.4995909623
#> EM - mixRHLP: Iteration: 192 | log-likelihood: -14867.9179321727
#> EM - mixRHLP: Iteration: 193 | log-likelihood: -14858.6442978196
#> EM - mixRHLP: Iteration: 194 | log-likelihood: -14848.8804338117
#> EM - mixRHLP: Iteration: 195 | log-likelihood: -14838.9872847758
#> EM - mixRHLP: Iteration: 196 | log-likelihood: -14829.6292321768
#> EM - mixRHLP: Iteration: 197 | log-likelihood: -14821.8717823403
#> EM - mixRHLP: Iteration: 198 | log-likelihood: -14816.6461672058
#> EM - mixRHLP: Iteration: 199 | log-likelihood: -14813.7497363742
#> EM - mixRHLP: Iteration: 200 | log-likelihood: -14812.2267827519
#> EM - mixRHLP: Iteration: 201 | log-likelihood: -14811.4198287137
#> EM - mixRHLP: Iteration: 202 | log-likelihood: -14811.0049217051
#> EM - 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     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()

mixrhlp's People

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fchamroukhi avatar florian-lecocq avatar mbartcus avatar

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mixrhlp's Issues

some EM try does not converge

This error is occurs randomly. For example this is at try 15.

EM : Iteration : 11 log-likelihood : -17134.6939558614
EM : Iteration : 12 log-likelihood : -17131.8105618592
Error in modele_logit(W_old, phiW, tauijk, cluster_weights) :
Probleme loglik NaN (!!!)

The problem comes from the IRLS, because here the loglikelihood does not increase.
I think we need to see in detail this lines of code in the "utils", that are for now commented.

## Verifier si Qw1(w^(c+1),w^(c))> Qw1(w^(c),w^(c))
# # (adaptation) de Newton Raphson : W(c+1) = W(c) - pas*H(W)^(-1)*g(W)
# pas <- 1
# alpha <- 2
#
# while(loglik < loglik_old){
#   pas <- pas/alpha # pas d'adaptation de l'algo Newton raphson
#   #recalcul du parametre W et de la loglik
#   #Hw_old = Hw_old + lambda*I;
#   w <- as.vector(W_old) - pas * solve(Hw_old)%*%gw_old
#   W = matrix(w,q,K-1)
#   problik <- modele_logit(W, phiW, tauijk, cluster_weights)
#   piik <- problik[[1]]
#   loglik <- problik[[2]]
#   loglik <- loglik - lambda*(norm(as.vector(W_old),"2"))^2
# }

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