在线性代数中,特征分解或谱分解是分解一个矩阵到一个标准形式,借此矩阵被表示在它的特征值和特征向量。只有可对角化的矩阵可以用这种方法分解.

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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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