论文标题
种植的准分子集团恢复的级别表格分解
Rank-sparsity decomposition for planted quasi clique recovery
论文作者
论文摘要
在本文中，我们将等级 - 表格矩阵分解应用于种植的最大准粘液问题（MQCP）。这个问题将种植的最大集团问题（MCP）作为特殊情况。最大集团问题是NP-HARD。准胶合物或$γ$ -Clique是一个密集的图表，边缘密度至少为$γ$，其中$γ\ in（0，1] $。最大的准清算问题旨在找到与给定图中最大的基数相关的，我们选择的方法是较低的植物，当时我们的选择是一个较低的跨度跨度。最大的准胶合，我们在双矩阵的标准上得出了一个新的结合，该矩阵使用$ l _ {\ infty，2} norm进行恢复。
In this paper, we apply the Rank-Sparsity Matrix Decomposition to the planted Maximum Quasi-Clique Problem (MQCP). This problem has the planted Maximum Clique Problem (MCP) as a special case. The maximum clique problem is NP-hard. A Quasi-clique or $γ$-clique is a dense graph with the edge density of at least $γ$, where $γ\in (0, 1]$. The maximum quasi-clique problem seeks to find such a subgraph with the largest cardinality in a given graph. Our method of choice is the low-rank plus sparse matrix splitting technique. We present a theoretical basis for when our convex relaxation problem recovers the planted maximum quasi-clique. We derived a new bound on the norm of the dual matrix that certifies the recovery using $l_{\infty,2} norm. We showed that when certain conditions are met, our convex formulation recovers the planted quasi-clique exactly. The numerical experiments we performed corroborated our theory.
