Clustering and Inference Procedures for High-Dimensional Latent Variable Models

A complete suite of computationally efficient methods for high dimensional clustering and inference problems in G-Latent Models (a type of Latent Variable Gaussian graphical model). The main feature is the FORCE (First-Order, Certifiable, Efficient) clustering algorithm which is a fast solver for a semi-definite programming (SDP) relaxation of the K-means problem. For certain types of graphical models (G-Latent Models), with high probability the algorithm not only finds the optimal clustering, but produces a certificate of having done so. This certificate, however, is model independent and so can also be used to certify data clustering problems. The 'GFORCE' package also contains implementations of inferential procedures for G-Latent graphical models using n-fold cross validation. Also included are native code implementations of other popular clustering methods such as Lloyd's algorithm with kmeans++ initialization and complete linkage hierarchical clustering. The FORCE method is due to Eisenach and Liu (2019) .

Author: Carson Eisenach

Please send all correspondence to eisenach [AT]


This is the current development version of the GFORCE package.

This package provides implementations of state-of-the-art clustering algorithms and inference procedures introduced in

  • Eisenach, C. and Liu, H. (2017). Efficient, Certifiably Optimal High-Dimensional Clustering. arXiv:1806.00530.
  • Eisenach, C., Bunea, F., Ning, Y. and Dinicu, C. (2018). Efficient, High-Dimensional Inference for Cluster-Based Graphical Models. Manuscript submitted for publication.

The new methods implemented include:

  • FORCE - a fast solver for a semi-definite programming (SDP) relaxation of the K-means problem. For certain data generating distributions it produces a certificate of optimality with high probability, and
  • Inferential procedures and FDR control for cluster based graphical models.

Also provided are high quality implementations of traditional clustering algorithms:

  • Lloyd's algorithm,
  • kmeans++ initializations,
  • hierarchical clustering


Reference manual

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0.1.4 by Carson Eisenach, 3 months ago

Browse source code at

Authors: Carson Eisenach [aut, cre]

Documentation:   PDF Manual  

GPL-2 license

Imports MASS, lpSolve, stats

Suggests testthat

See at CRAN