I implemented the EM algorithm for multivariate Gaussian Mixture Models from scratch and benchmarked it against sklearn.mixture.GaussianMixture. On a UMAP-reduced version of a high-dimensional text dataset, the results aligned almost perfectly:

Matching mixing weights, means, and covariances

Adjusted Rand Index = 1.0000

Component assignments match after greedy alignment via L2 distance

The implementation is object-oriented, numerically stable (with covariance regularization), and tracks parameter convergence across iterations. A direct comparison to scikit-learn is included.

Notebook:
06_em_algorithm_fit_gmm.ipynb

Core class:
ml_utils.py

Note: The convergence only matches this closely after dimensionality reduction with UMAP. On raw high-dimensional data, convergence is more sensitive to initialization.

Happy to share this as a learning tool or discussion starter around reproducibility and clustering convergence diagnostics.

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If you are interested in seeing the entire project:here