#### SaMUraiS:

StAtistical Models for the UnsupeRvised segmentAtIon of time-Series.

SaMUraiS is an open source toolbox (available in R and in Matlab) including many original and flexible user-friendly statistical latent variable models and unsupervised algorithms to segment and represent, time-series data (univariate or multivariate), and more generally, longitudinal data which include regime changes. Our samurais use mainly the following efficient "sword" packages to segment data: RHLP; HMM/HMMR; PWR; MRHLP; MHMMR; MPWR.

#### 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 (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. Our nice FLaMingoS are mainly: mixRHLP, mixHMM, mixHMMR, PWRM, MixReg, unsupMixReg.

#### MEteorits:

Mixtures-of-ExperTs modEling for cOmplex and non-noRmal dIsTributionS

MEteoritS is an open source toolbox (available in R and in Matlab) providing a unified mixture-of-experts (ME) modeling and estimation framework with several original and flexible ME models to model, cluster and classify heterogeneous data. It deals with many complex situations where the data are distributed according non-normal, possibly skewed distributions, and when they might be corrupted by atypical observations. Our (dis-)covered meteorites are for instance the following ones: NMoE, tMoE, SNMoE, StMoE, RMoE. The toolbox contains in particular sparse mixture-of-experts models for high-dimensional data.

#### HMMR:

Hidden Markov model regression (HMMR)

Time-series segmentation: User-friendly and flexible algorithm for time series segmentation with a regression model governed by a hidden Markov process. Hidden Markov Model Regression (HMMR) for segmentation of time series with regime changes. The model assumes that the time series is governed by a sequence of hidden discrete regimes/states, where each regime/state has Gaussian regressors as observations. The model parameters are estimated by MLE via the EM algorithm

#### MRHLP:

Multivariate Regression with Hidden Logistic Process (MRHLP)

Joint segmentation of multivariate time-series: Flexible and user-friendly probabilistic joint segmentation of time-series with smooth and/or abrupt regime changes by a mixture model-based regression approach with a hidden logistic process, fitted by the EM algorithm.

#### MHMMR:

Multivariate Hidden Markov Model Rgression (MRHMM)

Joint segmentation of multivariate time-series: Modeling and segmentation of multivariate time series with regime changes via Multivariate Hidden Markov Model Regression (HMMR). The model assumes that the time series is governed by a sequence of hidden discrete regimes/states, where each regime/state has multivariate Gaussian regressors emission densities. The model parameters are estimated by MLE via the Baum-Welch (EM) algorithm.

#### mixRHLP

Functional Data Clustering and Segmentation using flexible Functional Mixture Models: Mixture of regressions with hidden logistic processes A flexible mixture model for simultaneous clustering and segmentation of functional data (time-series). It uses the EM algorithm (or a CEM-like algorithm). 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.

#### mixHMM

Functional Data Clustering and Segmentation using flexible Functional Mixture Models: R code for the clustering and segmentation of time-series (including with regime changes) by mixture of hidden Markov models (mixHMM) and the Baum-Welch (EM) algorithm; i.e functional data clustering and segmentation, the latter can be performed by Viterbi decoding.

#### mixHMMR

Functional Data Clustering and Segmentation using flexible Functional Mixture Models: Flexible simultaneous clustering and segmentation of functional data (time-series) with regime changes by mixture of hidden Markov model regressions (mixHMMR). The learning is performed by the Baum-Welch (EM) algorithm and the segmentation can be performed by Viterbi decoding.

#### HDME

High-Dimensional Mixtures-of-Experts

High-dimensional Mixtures-of-Experts: Estimation and Feature Selection in Mixtures of Generalized Linear Experts Models with prEMME : proximal Newton EM for estimation and feature selection in high-dimensional Mixtures-of-Experts [Huynh and Chamroukhi, 2019] Unsupervised regularised MLE for high-dimensional regression/clustering Regularized mixtures-of-experts and a hybrib EM/MM algorithm Regularized mixtures-of-experts and a hybrib EM/Proximal Newton algorithm

#### uRMix

Fully unsupervised learning of regression mixtures

uRMix is a toolbox for unsupervised (curve) clustering with regression mixtures, including polynomial, spline, B-spline, and random effects regression mixture models, by robust EM algorithms. The algorithm simultaneously estimates the model parameters, and the number of mixture components, by a regularized likelihood estimation approach. The algorithms are applied to the clustering of functional data sets (phoneme data clustering, yeast-cycle, satellite, waveform, etc).

#### uRMix

Fully unsupervised learning of regression mixtures

uRMix is a toolbox for unsupervised (curve) clustering with regression mixtures, including polynomial, spline, B-spline, and random effects regression mixture models, by robust EM algorithms. The algorithm simultaneously estimates the model parameters, and the number of mixture components, by a regularized likelihood estimation approach. The algorithms are applied to the clustering of functional data sets (phoneme data clustering, yeast-cycle, satellite, waveform, etc).

#### mixPWR

Functional Mixture of PieceWise Regressions for clustering and segmentation

Functional Data Clustering and Segmentation using flexible Functional Mixture Models: introduces a finite mixture of piece-wise polynomial regressions to the simultaneous clustering and optimal segmentation of functional data (curves or time series presenting regime changes). Each piecewise polynomial regression model of the mixuture is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification EM (CEM) algorithm in which the optimal curve segmentation is performed by using dynamic programming.

#### DPPM

Dirichlet Process Parsimonious Mixtures: Bayesian Parsimonious Non-Parametric Clustering

DPPM offer a fully unsupervised and sparse clustering of high-dimensional data using Dirichlet Process Parsimonious Mixtures (DPPM). DPPM are constructed as a Bayesian nonparametric formulation of the parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices. DPPM thus allow to simultaneously infer the model parameters, the optimal number of mixture components and the optimal parsimonious covariance structure, from the data. The parameter estimation is performed by maximum a posteriori estimation by Gibbs sampling and the model selection is performed by using Bayes factors.

#### BSSRM

Bayesian Spatial Spline Regression Mixtures

Model-based clustering for spatial functional data: introduces a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data, and a Bayesian mixture of spatial spline regressions with mixed-effects (BMSSR) for modeling, density estimation and model-based surface clustering. The Bayesian model inference is performed by Markov Chain Monte Carlo (MCMC) sampling. We derive two Gibbs samplers to infer the BSSR and the BMSSR models.

credit: the first three funny pictures above created via dreamscopeapp.com

##### Robust Mixture-of-Experts

t Mixture-of-Experts >> TMoE

##### Functional Data Clustering and Segmentation

##### using flexible Functional Mixture Models:

Mixture of regressions with hidden logistic processes >> MixRHLP

Mixture of hidden Markov models >> MixHMM

Mixture of hidden Markov model regressions >> MixHMMR

Piece-wise regression mixture model >> PWRM

Mixture of regressions >> MixRreg

Mixture of spline regressions >> PSRM and B-spline regressions
>> bSPRM

##### Fully unsupervised non-parametric signal decomposition

Bayesian sparse non-parametric Dirichlet process mixture models >> DPPM

##### Bayesian spatial functional data clustering

Bayesian mixture of spatial spline regressions for functional data clustering >> BSSRM

##### Bayesian Non-Parametric Clustering

Fully unsupervised and sparse clustering of high-dimensional data using Dirichlet Process Parsimonious Mixtures >> DPPM

##### Fully unsupervised regression mixtures for functional data clustering

Unsupervised learning of regression mixture models with unknown number of components:

Robust EM and regression mixture >> RobustEM-PRM

Robust EM and spline regression mixture >> RobustEM-SRM

Robust EM and B-spline regression mixture >> RobustEM-bSRM

##### Unsupervised regularised MLE for high-dimensional regression/clustering

Regularized mixtures-of-experts and a hybrib EM/MM algorithm
>> RMoE-EM/MM

Regularized mixtures-of-experts and a hybrib EM/Proximal Newton algorithm
>> RMoE-EM/PLN