Introduction

mixRHLP: Simultaneous model-based clustering and segmentation of heterogeneous and dynamical functional data (curves/times series) with smooth and/or abrupt changes in regime by a mixture of regression models with hidden logistic processes, fitted by the EM algorithm and extensions.

It was written in R Markdown, using the knitr package for production.

See help(package="flamingos") for further details and references provided by citation("flamingos").

Load data

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

Set up mixRHLP model parameters

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

Set up EM parameters

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

Estimation

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
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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
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## EM - mixRHLP: Iteration: 204 | log-likelihood: -14810.6883875777

Summary

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     6.3513369    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 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    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

Plots

Estimated signal

mixrhlp$plot(what = "estimatedsignal")

Regressors

mixrhlp$plot(what = "regressors")

Log-likelihood

mixrhlp$plot(what = "loglikelihood")

A-quick-tour-of-mixRHLP