Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization

TL;DR

This paper introduces a novel, projection-free neural network architecture for binary graph classification that leverages the GDPA theorem to reduce computational complexity and improve interpretability, outperforming traditional model-based methods.

Contribution

It proposes an unfolding method for a semi-definite relaxation of graph classifiers using linear constraints, avoiding costly eigen-decompositions, and integrates parameter optimization via SGD.

Findings

Outperforms pure model-based graph classifiers.

Achieves comparable performance to data-driven networks.

Uses fewer parameters than traditional models.

Abstract

Algorithm unfolding creates an interpretable and parsimonious neural network architecture by implementing each iteration of a model-based algorithm as a neural layer. However, unfolding a proximal splitting algorithm with a positive semi-definite (PSD) cone projection operator per iteration is expensive, due to the required full matrix eigen-decomposition. In this paper, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we unroll a projection-free algorithm for semi-definite programming relaxation (SDR) of a binary graph classifier, where the PSD cone constraint is replaced by a set of "tightest possible" linear constraints per iteration. As a result, each iteration only requires computing a linear program (LP) and one extreme eigenvector. Inside the unrolled network, we optimize parameters via stochastic gradient descent (SGD) that determine graph edge weights in two ways: i) a metric matrix that computes feature distances, and ii) a sparse weight matrix computed via local linear embedding (LLE). Experimental results show that our unrolled network outperformed pure model-based graph classifiers, and achieved comparable performance to pure data-driven networks but using far fewer parameters.