论文标题
学习图与MCP的Laplacian
Learning Graph Laplacian with MCP
论文作者
论文摘要
我们考虑在拉普拉斯（Laplacian）约束下学习图形的问题，并以非凸面惩罚：minimax凹惩罚（MCP）。为了求解MCP惩罚图形模型，我们设计了一个不精确的近端差异算法（DCA），并证明其收敛到临界点。我们注意到，近端DCA的每个子问题都享有一个不错的属性，即其双重问题中的目标函数在半齿梯度中是不断区分的。因此，我们将有效的半齿牛顿方法应用于近端DCA的子问题。对各种合成和真实数据集的数值实验证明了非凸位惩罚MCP在促进稀疏性方面的有效性。与现有的最新方法相比，我们的方法被证明在学习图Laplacian的MCP中更有效和可靠。
We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP). For solving the MCP penalized graphical model, we design an inexact proximal difference-of-convex algorithm (DCA) and prove its convergence to critical points. We note that each subproblem of the proximal DCA enjoys the nice property that the objective function in its dual problem is continuously differentiable with a semismooth gradient. Therefore, we apply an efficient semismooth Newton method to subproblems of the proximal DCA. Numerical experiments on various synthetic and real data sets demonstrate the effectiveness of the non-convex penalty MCP in promoting sparsity. Compared with the existing state-of-the-art method, our method is demonstrated to be more efficient and reliable for learning graph Laplacian with MCP.
