Type:	Package
Title:	Functional Latent Data Models for Clustering Heterogeneous Curves ('FLaMingos')
Version:	0.1.0
Description:	Provides a variety of original and flexible user-friendly statistical latent variable models for the simultaneous clustering and segmentation of heterogeneous functional data (i.e time series, or more generally longitudinal data, fitted by unsupervised algorithms, including EM algorithms. Functional Latent Data Models for Clustering heterogeneous curves ('FLaMingos') are originally introduced and written in 'Matlab' by Faicel Chamroukhi https://github.com/fchamroukhi?utf8=?&tab=repositories&q=mix&type=public&language=matlab. The references are mainly the following ones. Chamroukhi F. (2010) https://chamroukhi.com/FChamroukhi-PhD.pdf. Chamroukhi F., Same A., Govaert, G. and Aknin P. (2010) <doi:10.1016/j.neucom.2009.12.023>. Chamroukhi F., Same A., Aknin P. and Govaert G. (2011). <doi:10.1109/IJCNN.2011.6033590>. Same A., Chamroukhi F., Govaert G. and Aknin, P. (2011) <doi:10.1007/s11634-011-0096-5>. Chamroukhi F., and Glotin H. (2012) <doi:10.1109/IJCNN.2012.6252818>. Chamroukhi F., Glotin H. and Same A. (2013) <doi:10.1016/j.neucom.2012.10.030>. Chamroukhi F. (2015) https://chamroukhi.com/FChamroukhi-HDR.pdf. Chamroukhi F. and Nguyen H-D. (2019) <doi:10.1002/widm.1298>.
URL:	https://github.com/fchamroukhi/FLaMingos
BugReports:	https://github.com/fchamroukhi/FLaMingos/issues
License:	GPL (≥ 3)
Depends:	R (≥ 2.10)
Imports:	methods, stats, Rcpp
Suggests:	knitr, rmarkdown
LinkingTo:	Rcpp, RcppArmadillo
Collate:	flamingos-package.R RcppExports.R utils.R kmeans.R mkStochastic.R FData.R ParamMixHMM.R ParamMixHMMR.R ParamMixRHLP.R StatMixHMM.R StatMixHMMR.R StatMixRHLP.R ModelMixHMMR.R ModelMixHMM.R ModelMixRHLP.R emMixHMM.R emMixHMMR.R emMixRHLP.R cemMixRHLP.R data-toydataset.R
VignetteBuilder:	knitr
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	6.1.1
NeedsCompilation:	yes
Packaged:	2019-08-05 19:08:18 UTC; lecocq191
Author:	Faicel Chamroukhi [aut], Florian Lecocq [aut, trl, cre] (R port), Marius Bartcus [aut, trl] (R port)
Maintainer:	Florian Lecocq <florian.lecocq@outlook.com>
Repository:	CRAN
Date/Publication:	2019-08-06 09:30:02 UTC

FLaMingos: Functional Latent datA Models for clusterING heterogeneOus curveS

Description

flamingos is an open-source toolbox for the simultaneous clustering (or classification) 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.

flamingos contains the following time series clustering and segmentation models:

• mixRHLP;

• mixHMM;

• mixHMMR.

For the advantages/differences of each of them, the user is referred to our mentioned paper references.

To learn more about flamingos, start with the vignettes: browseVignettes(package = "flamingos")

Author(s)

Maintainer: Florian Lecocq florian.lecocq@outlook.com (R port) [translator]

Authors:

• Faicel Chamroukhi faicel.chamroukhi@unicaen.fr (0000-0002-5894-3103)

• Marius Bartcus marius.bartcus@gmail.com (R port) [translator]

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), Universite de Toulon. https://chamroukhi.com/Dossier/FChamroukhi-Habilitation.pdf.

Chamroukhi, F., H. Glotin, and A. Same. 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.

Same, A., F. Chamroukhi, Gerard 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. Same, 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. Same, 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, Universite de Technologie de Compiegne. https://chamroukhi.com/papers/FChamroukhi-Thesis.pdf.

See Also

Useful links:

• https://github.com/fchamroukhi/FLaMingos

• Report bugs at https://github.com/fchamroukhi/FLaMingos/issues

A Reference Class which represents functional data.

Description

FData is a reference class which represents general independent and identically distributed (i.i.d.) functional objects. The data can be ordered by time (functional time series). In the last case, the field X represents the time.

Fields

X

Numeric vector of length m representing the covariates/inputs.

Y

Matrix of size (n, m) representing the observed responses/outputs. Y consists of n functions of X observed at points 1,\dots,m.

A Reference Class which represents a fitted Mixture of HMM model.

Description

ModelMixHMM represents an estimated mixture of HMM model.

Fields

param

A ParamMixHMM object. It contains the estimated values of the parameters.

stat

A StatMixHMM object. It contains all the statistics associated to the MixHMM model.

Methods

plot(what = c("clustered", "smoothed", "loglikelihood"), ...)

Plot method

what

The type of graph requested:

• "clustered" = Clustered curves (field klas of class StatMixHMM).

• "smoothed" = Smoothed signal (field smoothed of class StatMixHMM).

• "loglikelihood" = Value of the log-likelihood for each iteration (field stored_loglik of class StatMixHMM).

...

Other graphics parameters.

summary(digits = getOption("digits"))

Summary method.

digits

The number of significant digits to use when printing.

See Also

ParamMixHMM, StatMixHMM

Examples

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

mixhmm <- emMixHMM(Y = Y, K = 3, R = 3, verbose = TRUE)

# mixhmm is a ModelMixHMM object. It contains some methods such as 'summary' and 'plot'
mixhmm$summary()
mixhmm$plot()

# mixhmm has also two fields, stat and param which are reference classes as well

# Log-likelihood:
mixhmm$stat$loglik

# Means
mixhmm$param$mu

A Reference Class which represents a fitted mixture of HMMR model.

Description

ModelMixHMMR represents an estimated mixture of HMMR model.

Fields

param

A ParamMixHMMR object. It contains the estimated values of the parameters.

stat

A StatMixHMMR object. It contains all the statistics associated to the MixHMMR model.

Methods

plot(what = c("clustered", "smoothed", "loglikelihood"), ...)

Plot method

what

The type of graph requested:

• "clustered" = Clustered curves (field klas of class StatMixHMMR).

• "smoothed" = Smoothed signal (field smoothed of class StatMixHMMR).

• "loglikelihood" = Value of the log-likelihood for each iteration (field stored_loglik of class StatMixHMMR).

...

Other graphics parameters.

summary(digits = getOption("digits"))

Summary method.

digits

The number of significant digits to use when printing.

See Also

ParamMixHMMR, StatMixHMMR

Examples

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

mixhmmr <- emMixHMMR(X = x, Y = Y, K = 3, R = 3, p = 1, verbose = TRUE)

# mixhmmr is a ModelMixHMMR object. It contains some methods such as 'summary' and 'plot'
mixhmmr$summary()
mixhmmr$plot()

# mixhmmr has also two fields, stat and param which are reference classes as well

# Log-likelihood:
mixhmmr$stat$loglik

# Parameters of the polynomial regressions:
mixhmmr$param$beta

A Reference Class which represents a fitted mixture of RHLP model.

Description

ModelMixRHLP represents an estimated mixture of RHLP model.

Fields

param

A ParamMixRHLP object. It contains the estimated values of the parameters.

stat

A StatMixRHLP object. It contains all the statistics associated to the MixRHLP model.

Methods

plot(what = c("estimatedsignal", "regressors", "loglikelihood"), ...)

Plot method.

what

The type of graph requested:

• "estimatedsignal" = Estimated signal (field Ey of class StatMixRHLP).

• "regressors" = Polynomial regression components (fields polynomials and pi_jkr of class StatMixRHLP).

• "loglikelihood" = Value of the log-likelihood for each iteration (field stored_loglik of class StatMixRHLP).

...

Other graphics parameters.

By default, all the above graphs are produced.

summary(digits = getOption("digits"))

Summary method.

digits

The number of significant digits to use when printing.

See Also

ParamMixRHLP, StatMixRHLP

Examples

data(toydataset)

# Let's fit a mixRHLP model on a dataset containing 2 clusters:
data <- toydataset[1:190,1:21]
x <- data$x
Y <- t(data[,2:ncol(data)])

mixrhlp <- cemMixRHLP(X = x, Y = Y, K = 2, R = 2, p = 1, verbose = TRUE)

# mixrhlp is a ModelMixRHLP object. It contains some methods such as 'summary' and 'plot'
mixrhlp$summary()
mixrhlp$plot()

# mixrhlp has also two fields, stat and param which are reference classes as well

# Log-likelihood:
mixrhlp$stat$loglik

# Parameters of the polynomial regressions:
mixrhlp$param$beta

A Reference Class which contains parameters of a mixture of HMM models.

Description

ParamMixHMM contains all the parameters of a mixture of HMM models.

Fields

fData

FData object representing the sample (covariates/inputs X and observed responses/outputs Y).

K

The number of clusters (Number of HMM models).

R

The number of regimes (HMM components) for each cluster.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

order_constraint

A logical indicating whether or not a mask of order one should be applied to the transition matrix of the Markov chain to provide ordered states. For the purpose of segmentation, it must be set to TRUE (which is the default value).

alpha

Cluster weights. Matrix of dimension (K, 1).

prior

The prior probabilities of the Markov chains. prior is a matrix of dimension (R, K). The k-th column represents the prior distribution of the Markov chain asociated to the cluster k.

trans_mat

The transition matrices of the Markov chains. trans_mat is an array of dimension (R, R, K).

mask

Mask applied to the transition matrices trans_mat. By default, a mask of order one is applied.

mu

Means. Matrix of dimension (R, K). The k-th column gives represents the k-th cluster and gives the means for the R regimes.

sigma2

The variances for the K clusters. If MixHMM model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size (R, K) (otherwise MixHMM model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size (1, K)).

nu

The degrees of freedom of the MixHMM model representing the complexity of the model.

Methods

initGaussParamHmm(Y, k, R, variance_type, try_algo)

Initialize the means mu and sigma2 for the cluster k.

initParam(init_kmeans = TRUE, try_algo = 1)

Method to initialize parameters alpha, prior, trans_mat, mu and sigma2.

If init_kmeans = TRUE then the curve partition is initialized by the K-means algorithm. Otherwise the curve partition is initialized randomly.

If try_algo = 1 then mu and sigma2 are initialized by segmenting the time series Y uniformly into R contiguous segments. Otherwise, mu and sigma2 are initialized by segmenting randomly the time series Y into R segments.

MStep(statMixHMM)

Method which implements the M-step of the EM algorithm to learn the parameters of the MixHMM model based on statistics provided by the object statMixHMM of class StatMixHMM (which contains the E-step).

A Reference Class which contains parameters of a mixture of HMMR models.

Description

ParamMixHMMR contains all the parameters of a mixture of HMMR models.

Fields

fData

FData object representing the sample (covariates/inputs X and observed responses/outputs Y).

K

The number of clusters (Number of HMMR models).

R

The number of regimes (HMMR components) for each cluster.

p

The order of the polynomial regression.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

order_constraint

A logical indicating whether or not a mask of order one should be applied to the transition matrix of the Markov chain to provide ordered states. For the purpose of segmentation, it must be set to TRUE (which is the default value).

alpha

Cluster weights. Matrix of dimension (K, 1).

prior

The prior probabilities of the Markov chains. prior is a matrix of dimension (R, K). The k-th column represents the prior distribution of the Markov chain asociated to the cluster k.

trans_mat

The transition matrices of the Markov chains. trans_mat is an array of dimension (R, R, K).

mask

Mask applied to the transition matrices trans_mat. By default, a mask of order one is applied.

beta

Parameters of the polynomial regressions. beta is an array of dimension (p + 1, R, K), with p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K clusters. If MixHMMR model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size (R, K) (otherwise MixHMMR model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size

nu

The degree of freedom of the MixHMMR model representing the complexity of the model.

phi

A list giving the regression design matrix for the polynomial regressions.

Methods

initParam(init_kmeans = TRUE, try_algo = 1)

Method to initialize parameters alpha, prior, trans_mat, beta and sigma2.

If init_kmeans = TRUE then the curve partition is initialized by the K-means algorithm. Otherwise the curve partition is initialized randomly.

If try_algo = 1 then beta and sigma2 are initialized by segmenting the time series Y uniformly into R contiguous segments. Otherwise, beta and sigma2 are initialized by segmenting randomly the time series Y into R segments.

initRegressionParam(Y, k, R, phi, variance_type, try_algo)

Initialize beta and sigma2 for the cluster k.

MStep(statMixHMMR)

Method which implements the M-step of the EM algorithm to learn the parameters of the MixHMMR model based on statistics provided by the object statMixHMMR of class StatMixHMMR (which contains the E-step).

A Reference Class which contains parameters of a mixture of RHLP models.

Description

ParamMixRHLP contains all the parameters of a mixture of RHLP models.

Fields

fData

FData object representing the sample (covariates/inputs X and observed responses/outputs Y).

K

The number of clusters (Number of RHLP models).

R

The number of regimes (RHLP components) for each cluster.

p

The order of the polynomial regression.

q

The dimension of the logistic regression. For the purpose of segmentation, it must be set to 1.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

alpha

Cluster weights. Matrix of dimension (1, K).

W

Parameters of the logistic process. \boldsymbol{W} = (\boldsymbol{w}_{1},\dots,\boldsymbol{w}_{K}) is an array of dimension (q + 1, R - 1, K), with \boldsymbol{w}_{k} = (\boldsymbol{w}_{k,1},\dots,\boldsymbol{w}_{k,R-1}), k = 1,\dots,K, and q the order of the logistic regression. q is fixed to 1 by default.

beta

Parameters of the polynomial regressions. \boldsymbol{\beta} = (\boldsymbol{\beta}_{1},\dots,\boldsymbol{\beta}_{K}) is an array of dimension (p + 1, R, K), with \boldsymbol{\beta}_{k} = (\boldsymbol{\beta}_{k,1},\dots,\boldsymbol{\beta}_{k,R}), k = 1,\dots,K, p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K clusters. If MixRHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size (R, K) (otherwise MixRHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size (K, 1)).

nu

The degree of freedom of the MixRHLP model representing the complexity of the model.

phi

A list giving the regression design matrices for the polynomial and the logistic regressions.

Methods

CMStep(statMixRHLP, verbose_IRLS = FALSE)

Method which implements the M-step of the CEM algorithm to learn the parameters of the MixRHLP model based on statistics provided by the object statMixRHLP of class StatMixRHLP (which contains the E-step and the C-step).

initParam(init_kmeans = TRUE, try_algo = 1)

Method to initialize parameters alpha, W, beta and sigma2.

If init_kmeans = TRUE then the curve partition is initialized by the R-means algorithm. Otherwise the curve partition is initialized randomly.

If try_algo = 1 then beta and sigma2 are initialized by segmenting the time series Y uniformly into R contiguous segments. Otherwise, W, beta and sigma2 are initialized by segmenting randomly the time series Y into R segments.

initRegressionParam(Yk, k, try_algo = 1)

Initialize the matrix of polynomial regression coefficients beta_k for the cluster k.

MStep(statMixRHLP, verbose_IRLS = FALSE)

Method which implements the M-step of the EM algorithm to learn the parameters of the MixRHLP model based on statistics provided by the object statMixRHLP of class StatMixRHLP (which contains the E-step).

A Reference Class which contains statistics of a mixture of HMM model.

Description

StatMixHMM contains all the statistics associated to a MixHMM model, in particular the E-Step of the EM algorithm.

Fields

tau_ik

Matrix of size (n, K) giving the posterior probabilities that the curve \boldsymbol{y}_{i} originates from the k-th HMM model.

gamma_ikjr

Array of size (nm, R, K) giving the posterior probabilities that the observation \boldsymbol{y}_{ij} originates from the r-th regime of the k-th HMM model.

loglik

Numeric. Log-likelihood of the MixHMM model.

stored_loglik

Numeric vector. Stored values of the log-likelihood at each iteration of the EM algorithm.

klas

Row matrix of the labels issued from tau_ik. Its elements are klas[i] = z\_i, i = 1,\dots,n.

z_ik

Hard segmentation logical matrix of dimension (n, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ P(z_{ik} = 1 | \boldsymbol{y}_{i}; \boldsymbol{\Psi}) = tau\_tk;\ 0 \ \textrm{otherwise}.

smoothed

Matrix of size (m, K) giving the smoothed time series. The smoothed time series are computed by combining the time series \boldsymbol{y}_{i} with both the estimated posterior regime probabilities gamma_ikjr and the corresponding estimated posterior cluster probability tau_ik. The k-th column gives the estimated mean series of cluster k.

BIC

Numeric. Value of BIC (Bayesian Information Criterion).

AIC

Numeric. Value of AIC (Akaike Information Criterion).

ICL1

Numeric. Value of ICL (Integrated Completed Likelihood Criterion).

log_alpha_k_fyi

Private. Only defined for calculations.

exp_num_trans

Private. Only defined for calculations.

exp_num_trans_from_l

Private. Only defined for calculations.

Methods

computeStats(paramMixHMM)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramMixHMM of class ParamMixHMM.

EStep(paramMixHMM)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramMixHMM of class ParamMixHMM (prior and posterior probabilities).

MAP()

MAP calculates values of the fields z_ik and klas by applying the Maximum A Posteriori Bayes allocation rule.

z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ P(z_{ik} = 1 | \boldsymbol{y}_{i}; \boldsymbol{\Psi}) = tau\_tk;\ 0 \ \textrm{otherwise}.

See Also

ParamMixHMM

A Reference Class which contains statistics of a mixture of HMMR models.

Description

StatMixHMMR contains all the statistics associated to a MixHMMR model, in particular the E-Step of the EM algorithm.

Fields

tau_ik

Matrix of size (n, K) giving the posterior probabilities that the curve \boldsymbol{y}_{i} originates from the k-th HMMR model.

gamma_ikjr

Array of size (nm, R, K) giving the posterior probabilities that the observation \boldsymbol{y}_{ij} originates from the r-th regime of the k-th HMM model.

loglik

Numeric. Log-likelihood of the MixHMMR model.

stored_loglik

Numeric vector. Stored values of the log-likelihood at each iteration of the EM algorithm.

klas

Row matrix of the labels issued from tau_ik. Its elements are klas[i] = z\_i, i = 1,\dots,n.

z_ik

Hard segmentation logical matrix of dimension (n, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ P(z_{ik} = 1 | \boldsymbol{y}_{i}; \boldsymbol{\Psi}) = tau\_ik;\ 0 \ \textrm{otherwise}.

smoothed

Matrix of size (m, K) giving the smoothed time series. The smoothed time series are computed by combining the polynomial regression components with both the estimated posterior regime probabilities gamma_ikjr and the corresponding estimated posterior cluster probability tau_ik. The k-th column gives the estimated mean series of cluster k.

BIC

Numeric. Value of BIC (Bayesian Information Criterion).

AIC

Numeric. Value of AIC (Akaike Information Criterion).

ICL1

Numeric. Value of ICL (Integrated Completed Likelihood Criterion).

log_alpha_k_fyi

Private. Only defined for calculations.

exp_num_trans

Private. Only defined for calculations.

exp_num_trans_from_l

Private. Only defined for calculations.

Methods

computeStats(paramMixHMMR)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramMixHMMR of class ParamMixHMMR.

EStep(paramMixHMMR)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramMixHMMR of class ParamMixHMMR (prior and posterior probabilities).

MAP()

MAP calculates values of the fields z_ik and klas by applying the Maximum A Posteriori Bayes allocation rule.

z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ P(z_{ik} = 1 | \boldsymbol{y}_{i}; \boldsymbol{\Psi}) = tau\_ik;\ 0 \ \textrm{otherwise}.

See Also

ParamMixHMMR

A Reference Class which contains statistics of a mixture of RHLP models.

Description

StatMixRHLP contains all the statistics associated to a MixRHLP model, in particular the E-Step (and C-Step) of the (C)EM algorithm.

Fields

pi_jkr

Array of size (nm, R, K) representing the logistic proportion for cluster k.

tau_ik

Matrix of size (n, K) giving the posterior probabilities (fuzzy segmentation matrix) that the curve \boldsymbol{y}_{i} originates from the k-th RHLP model.

z_ik

Hard segmentation logical matrix of dimension (n, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ tau\_ik;\ 0 \ \textrm{otherwise}.

klas

Column matrix of the labels issued from z_ik. Its elements are klas[i] = z\_i, i = 1,\dots,n.

gamma_ijkr

Array of size (nm, R, K) giving the posterior probabilities that the observation \boldsymbol{y}_{ij} originates from the r-th regime of the k-th RHLP model.

polynomials

Array of size (m, R, K) giving the values of the estimated polynomial regression components.

weighted_polynomials

Array of size (m, R, K) giving the values of the estimated polynomial regression components weighted by the prior probabilities pi_jkr.

Ey

Matrix of size (m, K). Ey is the curve expectation (estimated signal): sum of the polynomial components weighted by the logistic probabilities pi_jkr.

loglik

Numeric. Observed-data log-likelihood of the MixRHLP model.

com_loglik

Numeric. Complete-data log-likelihood of the MixRHLP model.

stored_loglik

Numeric vector. Stored values of the log-likelihood at each EM iteration.

stored_com_loglik

Numeric vector. Stored values of the Complete log-likelihood at each EM iteration.

BIC

Numeric. Value of BIC (Bayesian Information Criterion).

ICL

Numeric. Value of ICL (Integrated Completed Likelihood).

AIC

Numeric. Value of AIC (Akaike Information Criterion).

log_fk_yij

Matrix of size (n, K) giving the values of the probability density function f(\boldsymbol{y}_{i} | z_i = k, \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

log_alphak_fk_yij

Matrix of size (n, K) giving the values of the logarithm of the joint probability density function f(\boldsymbol{y}_{i}, \ z_{i} = k | \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

log_gamma_ijkr

Array of size (nm, R, K) giving the logarithm of gamma_ijkr.

Methods

computeStats(paramMixRHLP)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramMixRHLP of class ParamMixRHLP.

CStep(reg_irls)

Method used in the CEM algorithm to update statistics.

EStep(paramMixRHLP)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramMixRHLP of class ParamMixRHLP (prior and posterior probabilities).

MAP()

MAP calculates values of the fields z_ik and klas by applying the Maximum A Posteriori Bayes allocation rule.

z\_ik = 1 \ \textrm{if} \ z\_i = \textrm{arg} \ \textrm{max}_{k} \ tau\_ik;\ 0 \ \textrm{otherwise} .

See Also

ParamMixRHLP

cemMixRHLP implements the CEM algorithm to fit a MixRHLP model.

Description

cemMixRHLP implements the maximum complete likelihood parameter estimation of mixture of RHLP models by the Classification Expectation-Maximization algorithm (CEM algorithm).

Usage

cemMixRHLP(X, Y, K, R, p = 3, q = 1,
  variance_type = c("heteroskedastic", "homoskedastic"),
  init_kmeans = TRUE, n_tries = 1, max_iter = 100,
  threshold = 1e-05, verbose = FALSE, verbose_IRLS = FALSE)

Arguments

Details

cemMixRHLP function implements the CEM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixRHLP, then it alternates between the E-Step, the C-Step (methods of the class StatMixRHLP), and the CM-Step (method of the class ParamMixRHLP) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixRHLP.

See Also

ModelMixRHLP, ParamMixRHLP, StatMixRHLP

Examples

data(toydataset)

#' # Let's fit a mixRHLP model on a dataset containing 2 clusters:
data <- toydataset[1:190,1:21]
x <- data$x
Y <- t(data[,2:ncol(data)])

mixrhlp <- cemMixRHLP(X = x, Y = Y, K = 2, R = 2, p = 1, verbose = TRUE)

mixrhlp$summary()

mixrhlp$plot()

emMixHMM implemens the EM (Baum-Welch) algorithm to fit a mixture of HMM models.

Description

emMixHMM implements the maximum-likelihood parameter estimation of a mixture of HMM models by the Expectation-Maximization (EM) algorithm, known as Baum-Welch algorithm in the context of mixHMM.

Usage

emMixHMM(Y, K, R, variance_type = c("heteroskedastic", "homoskedastic"),
  order_constraint = TRUE, init_kmeans = TRUE, n_tries = 1,
  max_iter = 1000, threshold = 1e-06, verbose = FALSE)

Arguments

Details

emMixHMM function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixHMM, then it alternates between the E-Step (method of the class StatMixHMM) and the M-Step (method of the class ParamMixHMM) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixHMM.

See Also

ModelMixHMM, ParamMixHMM, StatMixHMM

Examples

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

mixhmm <- emMixHMM(Y = Y, K = 3, R = 3, verbose = TRUE)

mixhmm$summary()

mixhmm$plot()

emMixHMMR implements the EM algorithm to fit a mixture if HMMR models.

Description

emMixHMMR implements the maximum-likelihood parameter estimation of a mixture of HMMR models by the Expectation-Maximization (EM) algorithm.

Usage

emMixHMMR(X, Y, K, R, p = 3, variance_type = c("heteroskedastic",
  "homoskedastic"), order_constraint = TRUE, init_kmeans = TRUE,
  n_tries = 1, max_iter = 1000, threshold = 1e-06, verbose = FALSE)

Arguments

Details

emMixHMMR function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixHMMR, then it alternates between the E-Step (method of the class StatMixHMMR) and the M-Step (method of the class ParamMixHMMR) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixHMMR.

See Also

ModelMixHMMR, ParamMixHMMR, StatMixHMMR

Examples

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

mixhmmr <- emMixHMMR(X = x, Y = Y, K = 3, R = 3, p = 1, verbose = TRUE)

mixhmmr$summary()

mixhmmr$plot()

emMixRHLP implements the EM algorithm to fit a mixture of RHLP models.

Description

emMixRHLP implements the maximum-likelihood parameter estimation of a mixture of RHLP models by the Expectation-Maximization (EM) algorithm.

Usage

emMixRHLP(X, Y, K, R, p = 3, q = 1,
  variance_type = c("heteroskedastic", "homoskedastic"),
  init_kmeans = TRUE, n_tries = 1, max_iter = 1000,
  threshold = 1e-05, verbose = FALSE, verbose_IRLS = FALSE)

Arguments

Details

emMixRHLP function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixRHLP, then it alternates between the E-Step (method of the class StatMixRHLP) and the M-Step (method of the class ParamMixRHLP) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixRHLP.

See Also

ModelMixRHLP, ParamMixRHLP, StatMixRHLP

Examples

data(toydataset)

# Let's fit a mixRHLP model on a dataset containing 2 clusters:
data <- toydataset[1:190,1:21]
x <- data$x
Y <- t(data[,2:ncol(data)])

mixrhlp <- emMixRHLP(X = x, Y = Y, K = 2, R = 2, p = 1, verbose = TRUE)

mixrhlp$summary()

mixrhlp$plot()

mkStochastic ensures that it is a stochastic vector, matrix or array.

Description

mkStochastic ensures that it is a stochastic vector, matrix or array.

Usage

mkStochastic(M)

Arguments

Details

mkStochastic ensures that the giving argument is a stochastic vector, matrix or array, i.e., that the sum over the last dimension is 1.

Value

A vector, matrix or array for which the sum over the last dimension is 1.

A dataset composed of simulated time series with regime changes.

Description

A dataset composed of 30 simulated time series with regime changes.

Usage

toydataset

Format

A data frame with 350 rows and 31 variables:

x

The covariate variable which is the time in that case.

y1

Times series with a wave form shape and for which a normally distributed random noise has been added.

y2

Same as y1.

y3

Same as y1.

y4

Same as y1.

y5

Same as y1.

y6

Same as y1.

y7

Same as y1.

y8

Same as y1.

y9

Same as y1.

y10

Same as y1.

y11

Time series generated as follows:

• First regime: 120 values of Normally distributed random numbers with mean 5 and variance 1.

• Second regime: 70 values of Normally distributed random numbers with mean 7 and variance 1.

• Third regime: 160 values of Normally distributed random numbers with mean 5 variance 1.

y12

Same as y11.

y13

Same as y11.

y14

Same as y11.

y15

Same as y11.

y16

Same as y11.

y17

Same as y11.

y18

Same as y11.

y19

Same as y11.

y20

Same as y11.

y21

Time series generated as follows:

• First regime: 80 values of Normally distributed random numbers with mean 7 variance 1.

• Second regime: 130 values of Normally distributed random numbers with mean 5 variance 1.

• Third regime: 140 values of Normally distributed random numbers with mean 4 variance 1.

y22

Same as y21.

y23

Same as y21.

y24

Same as y21.

y25

Same as y21.

y26

Same as y21.

y27

Same as y21.

y28

Same as y21.

y29

Same as y21.

y30

Same as y21.