挖掘最大和的子矩阵
Mining a Sub-Matrix of Maximal Sum
摘要：
双聚类技术已被广泛用于识别大数据矩阵中的同质亚组，例如在患者亚组中相似表达的基因亚组。挖掘最大和子矩阵是一个相关但不同的问题，其中寻找具有最大项和的（不一定连续的）矩形子矩阵。Le Van等人（Ranked Tiling，2014）已经说明了其对基因表达分析的适用性，并使用结合大邻域搜索（CP-LNS）的约束编程（CP）方法解决了这一问题。在这项工作中，我们展示了这个NP难问题的一些关键属性，并定义了一个边界函数，以便在合理的时间内解决更大的问题。两种不同的算法，以利用突出的特点的问题：CP方法与全局约束（CPGC）和混合整数线性规划（MILP）。在合成和真实基因表达数据上进行的实际实验显示了这些方法的特点及其相对于原始CP-LNS方法的优势。总的来说，CPGC方法往往是最快产生一个好的解决方案。然而，MILP公式可以说是最容易制定的，也可以是有竞争力的。
英文摘要：
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct problem for which one looks for a (non-necessarily contiguous) rectangular sub-matrix with a maximal sum of its entries. Le Van et al. (Ranked Tiling, 2014) already illustrated its applicability to gene expression analysis and addressed it with a constraint programming (CP) approach combined with large neighborhood search (CP-LNS). In this work, we exhibit some key properties of this NP-hard problem and define a bounding function such that larger problems can be solved in reasonable time. Two different algorithms are proposed in order to exploit the highlighted characteristics of the problem: a CP approach with a global constraint (CPGC) and mixed integer linear programming (MILP). Practical experiments conducted both on synthetic and real gene expression data exhibit the characteristics of these approaches and their relative benefits over the original CP-LNS method. Overall, the CPGC approach tends to be the fastest to produce a good solution. Yet, the MILP formulation is arguably the easiest to formulate and can also be competitive.
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