Online EM Algorithm for HD-MED

This is the code of the online EM algorithm for HD-MED and MED currently this package has online EM versions of:

• Standard Gaussian Mixture Model and t-distribution Mixture Model
• High-Dimensional Gaussian Mixture Model and High Dimensional t-distribtuion Mixture Model

Basic Usage

Training of the dataset X

from onlineEM import em_config
from onlineEM.hd import hdgmm



config = {
    "n_components": 3, # Number of component of the mixture
    "num_features": 5,  # Number of features
    "num_epochs": 3, # Number of epochs
    "mini_batch_size": 256, # Size of the mini-batched
}

config = em_config(**config) # Create the configuration object

model_hd = hdgmm()

config_hd, params_hd, stats_hd = model_hd.burnin(X, config) # Initialize the model
params_hd, stats_hd = model_hd.online_epochs(X, params_hd, stats_hd, config_hd) # Train the model

Dimension reduction

🚨 This only works for High-Dimensional models 🚨

X_red, idx_clf = hdgmm.project(X, params_hd, config) # Project the initial high-dimensional data to lower different subspaces

# outputs low dimensional data X_red in a form of a list of arrays  for different clusters along with their associated index idx_clf in the original array

X_decompressed = hdgmm.inv_project(X_red, idx_clf)

👩‍💻 Basic exemple in notebook/. 👨‍💻

References

• [1] Oudoumanessah, G., Coudert, T., Meyer, L., Delphin, A., Dojat, M., Lartizien, C., & Forbes, F. Cluster globally, Reduce locally: Scalable efficient dictionary compression for magnetic resonance fingerprinting. In 2025 IEEE 22th International Symposium on Biomedical Imaging (ISBI).

• [2] Oudoumanessah, G., Coudert, T., Lartizien, C., Dojat, M., Christen, T., & Forbes, F. (2024). Scalable magnetic resonance fingerprinting: Incremental inference of high dimensional elliptical mixtures from large data volumes. arXiv preprint arXiv:2412.10173.

Todo

• Implement Ruppert-Polyak Averaging and find a way to average variables in the Stiefel manifold