基于GDPA线性化的二值图分类器的无投影展开SDP松弛
Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization
摘要：
算法展开通过将基于模型的算法的每次迭代实现为神经层来创建可解释且简约的神经网络架构。然而，由于需要全矩阵特征分解，因此每次迭代使用半正定（PSD）锥投影算子展开邻近分裂算法是昂贵的。在本文中，利用最近的线性代数定理称为Gershgorin盘完美对齐（GDPA），我们展开的二进制图分类器的半定规划松弛（SDR）的无投影算法，其中PSD锥约束被替换为一组“最紧密的可能”的线性约束每次迭代。因此，每次迭代只需要计算一个线性规划（LP）和一个极端的特征向量。在展开的网络内部，我们通过随机梯度下降（SGD）优化参数，SGD以两种方式确定图边缘权重：i）计算特征距离的度量矩阵，以及ii）通过局部线性嵌入（LLE）计算的稀疏权重矩阵。实验结果表明，我们的展开网络优于纯基于模型的图分类器，并实现了与纯数据驱动网络相当的性能，但使用的参数要少得多。
英文摘要：
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.
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