[计算机科学] 粗糙集与矩阵压缩 [推广有奖]

摘要翻译：
粗糙集是数据挖掘中有效的数据预处理方法。作为向量空间线性无关性的推广，拟阵为贪婪算法提供了良好的平台。本文将粗糙集应用于拟阵，研究了相应拟阵对偶的压缩性。首先，对于论域上的等价关系，通过下近似算子建立粗糙集的矩阵结构。其次，研究了拟阵的对偶及其独立集、基、秩函数等性质。最后，研究了对偶拟阵对单点集的补的收缩与对偶拟阵对单点集的等价类的补的收缩之间的关系。
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英文标题：
《Rough sets and matroidal contraction》
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作者：
Jingqian Wang and William Zhu
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.
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PDF链接：
https://arxiv.org/pdf/1209.5482