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Python codes for functional data clustering and segmentation with the mixture of regressions with hidden logistic processes (MixRHLP) model:

<< R and Matlab versions are aslo available on Github>>

python codes written by

Faicel Chamrouckhi & Marius Bartcus

firstname.lastname@unicaen.fr

The needed packages to run our code are: NumPy and matplotlib.

SHORT DESCRIPTION OF EACH PYTHON FILE. For more detailed description, please see the individual files

  1. main_MixFRHLP_EM Main script to run the EM or CEM algorithm
  2. ModelLearner.py Contains the two functions of the EM and the CEM algorithms.
  3. datasets Contains the object to load (mainly the dataset)
  4. MixModel.py The MixModel class containts the data object and the model settings (number of clusters, the number of segments, the degree of polynomials, the order of the logistic regression)
  5. MixParam.py Initializes and updates (the M-step) the model parameters.
  6. MixStats.py Calculates the conditional memberships (responsibilities) (E-step), the loglikelihood, the data partition, and information criterias BIC, ICL, etc
  7. ModelOptions.py contains algorithm settings (like the number of runs/iterations, convergence threshold, type of initialization, etc).
  8. enums.py Used to enumerate the variance type (heteroskedastic or homoscedastic)
  9. RegressionDesinger.py Design matrices for the polynomial regression and the logistic regression
  10. utils.py _Contains mainly the model_logit function that calculates the multinomial logistic pobabilities, and an efficient Iteratively Reweighted Least-Squares (IRLS) algorithm.

When using this code please cite the following papers : The two first ones concern the model and its use in clustering and the last ones concern the model and its use in discrimination.

 @article{Chamroukhi-RHLP-2009,
 	Author = {Chamroukhi, F. and Sam\'{e}, A. and Govaert, G. and Aknin, P.},
 	Journal = {Neural Networks},
 	Number = {5-6},
 	Pages = {593--602},
	Publisher = {Elsevier Science Ltd.},
 	Title = {Time series modeling by a regression approach based on a latent process},
 	Volume = {22},
 	Year = {2009}
     }
 @article{Chamroukhi-MixRHLP-2011,
 	Author = {Sam{\'e}, A. and Chamroukhi, F. and Govaert, G{\'e}rard and Aknin, P.},
 	Issue = 4,
 	Journal = {Advances in Data Analysis and Classification},
 	Pages = {301--321},
 	Publisher = {Springer Berlin / Heidelberg},
 	Title = {Model-based clustering and segmentation of time series with changes in regime},
 	Volume = 5,
 	Year = {2011}
     }

 @article{Chamroukhi-RHLP-FLDA,
 	Author = {Chamroukhi, F. and Sam\'{e}, A. and Govaert, G. and Aknin, P.},
 	Journal = {Neurocomputing},
 	Number = {7-9},
 	Pages = {1210--1221},
 	Title = {A hidden process regression model for functional data description. Application to curve discrimination},
 	Volume = {73},
 	Year = {2010}
     }

 @article{Chamroukhi-FMDA-2013,
 	Author = {Chamroukhi, F. and Glotin, H. and Sam{\'e}, A.},
 	Journal = {Neurocomputing},
 	Pages = {153-163},
 	Title = {Model-based functional mixture discriminant analysis with hidden process regression for curve classification},
 	Volume = {112},
 	Year = {2013}
     }  
@article{Chamroukhi-FDA-2018,
 	Journal = {Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery},
 	Author = {Faicel Chamroukhi and Hien D. Nguyen},
 	Note = {DOI: 10.1002/widm.1298.},
 	Volume = {},
 	Title = {Model-Based Clustering and Classification of Functional Data},
 	Year = {2019},
 	Month = {to appear},
 	url =  {https://chamroukhi.com/papers/MBCC-FDA.pdf}
    }

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A flexible mixture model for simultaneous clustering and segmentation of functional data (time series). It uses the EM algorithm (or a CEM-like algorithm).

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