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A-quick-tour-of-mixRHLP

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: 97 | log-likelihood: -15103.2137059945
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## 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
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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")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.