DP-GLPCA

DP-GLPCA performs constrained clustering by integrating dissimilarity propagation into Graph-Laplacian Principal Component Analysis (GLPCA) to produce a convex semisupervised low-dimensional embedding guided by pairwise similarity and dissimilarity constraints.

Key Features:

• Dissimilarity-regularized GLPCA: integrates a dissimilarity regularizer into Graph-Laplacian Principal Component Analysis to enforce similarity and dissimilarity constraints between low-dimensional representations.
• Convex semisupervised embedding: formulates a convex semisupervised low-dimensional embedding model that incorporates pairwise constraints.
• Dissimilarity Propagation (DP) model: refines the dissimilarity regularizer by propagating cannot-link (dissimilarity) constraints.
• Iterative optimization: solves the Dissimilarity Propagation model iteratively using an inexact augmented Lagrange multiplier method.
• Convergence guarantees: optimization is proven to achieve global convergence and reach a Karush–Kuhn–Tucker (KKT) point.
• Enhanced cluster discriminability: enforcement of both similarity and dissimilarity constraints improves discriminability of clusters.
• Benchmark validation: experimentally validated across nine benchmark datasets, achieving superior clustering accuracy compared to existing constrained clustering methods.

Scientific Applications:

• Constrained clustering: applicable to clustering tasks where pairwise supervisory constraints are available.
• Dimensionality reduction: produces low-dimensional embeddings that preserve similarity and dissimilarity relationships for downstream analyses.
• Cluster discriminability enhancement: suitable for analyses requiring improved separability of similar and dissimilar samples.

Methodology:

Formulate a convex semisupervised low-dimensional embedding by incorporating a dissimilarity regularizer into GLPCA, refine that regularizer by propagating cannot-link constraints via a Dissimilarity Propagation model, and solve the DP model iteratively using an inexact augmented Lagrange multiplier method with global convergence to a KKT point.