  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.
