SubspaceClustering

Repository for the paper Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap.

An illustration of the phase diagram for the clustering of two-classes sparse homogeneous Gaussian Mixture. We colour each region according to the associated *reconstruction phase* . The different phases are separated by the associated *thresholds* .

Structure

In this repository we provide the code and some guided example to help the reader to reproduce the figures of the paper [1]. The repository is structured as follows.

File	Description
/AMP_SE	Solver for AMP and its State Evolution (SE) equations. The notebook [/AMP_SE/how_to_AMP/SE.ipynb] provides a step-by-step explanation on how to use the package. This implementation has been used to produce the results in Sections 4/5/6 of the paper.
/Miscellaneous	Solver for the general-purpose algorithms PCA, sparse PCA and Diagonal Thresholding. The notebook [/Miscellaneous/how_to_mix.ipynb] provides a step-by-step explanation on how to use the package. This implementation has been used to produce the results in Sections 4/5/6 of the paper.

Reference

[1]Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap, Luca Pesce, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová arXiv: 2205.13527[stat.ML]