基于量子计算的粗糙集核属性求解算法

段隆振; 谢旭明; 邱桃荣; 杨舒晴

doi:10.16383/j.aas.2018.c170328

基于量子计算的粗糙集核属性求解算法

doi: 10.16383/j.aas.2018.c170328

段隆振^1,,
谢旭明^{1, 2,},
邱桃荣^1, ,,
杨舒晴^1,

1.
南昌大学信息工程学院南昌 330031
2.
南昌大学图书馆南昌 330031

基金项目:

国家自然科学基金 61070139

国家自然科学基金 81460769

国家自然科学基金 61762045

江西省科技化项目 20112BBG70087

详细信息

作者简介:
段隆振   南昌大学教授.主要研究方向为数据挖掘, 并行计算与大数据. E-mail:lzhduan@126.com

谢旭明   南昌大学博士研究生.主要研究方向为粗糙集与量子计算. E-mail: xiexuming@ncu.edu.cn

杨舒晴   南昌大学博士研究生.主要研究方向为粗糙集与量子计算. E-mail:ysqsinuo@163.com

通讯作者:
邱桃荣南昌大学教授.主要研究方向为粗糙集, 粒计算与量子计算.本文通信作者. E-mail: qiutaorong@ncu.edu.cn

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出版历程
- 收稿日期: 2017-06-16
- 录用日期: 2018-01-01
- 刊出日期: 2020-08-26

A Quantum Algorithm of the Computation of Core in Rough Set

DUAN Long-Zhen^1
,,
XIE Xu-Ming^{1, 2
,},
QIU Tao-Rong^{1
, ,},
YANG Shu-Qing^1
,

1.
College of Information Engineering, Nanchang University, Nanchang 330031
2.
Library of Nanchang University, Nanchang 330031

Funds:

National Natural Science Foundation of China 61070139

National Natural Science Foundation of China 81460769

National Natural Science Foundation of China 61762045

Scientiflc and Technological Project of Jiangxi Province 20112BBG70087

More Information

Author Bio:
DUAN Long-Zhen    Professor at Nanchang University. His research interest covers data mining, parallel computing and big data

XIE Xu-Ming    Ph. D. candidate at Nanchang University. His research interest covers rough set and quantum computing

YANG Shu-Qing   Ph. D. candidate at Nanchang University. Her research interest covers rough set and quantum computing

Corresponding author: QIU Tao-Rong Professor at Nanchang University. His research interest covers rough set, granular computing and quantum computing. Corresponding author of this paper

摘要

摘要: 粗糙集的核属性求解问题在经典计算中是一个NP问题.现有的方法中最优的时间复杂度也需要${\rm O}$$ \left(|C||U|\right)$($U$为论域、$C$为属性列数).由于量子计算的并行性特点, 本文致力于采用量子计算的方法来求解粗糙集的核属性, 拟提出了一种基于量子计算的粗糙集核属性求解算法.经过仿真实验, 在任何情况下, 该算法都能以1的总概率得到目标分量; 且通过理论分析证明了算法的时间复杂度不会高于${\rm O}$$\left(|\frac{{\rm{ \mathsf{ π}}}}{2\arcsin\sqrt {\frac{M}{C}}}+1||U|\right)$.
- 量子计算 /
- 粗糙集 /
- 核属性 /
- 算法设计
Abstract: The computation of core in rough set is an NP-hard problem in classic computing. The best time complexity of the existing algorithms is ${\rm O}$$\left(|C||U|\right)$ ($U$ stands for Universe, $C$ stands for the number of attributes). Due to its ability to compute in parallel, quantum computing, is adopted to find the core in rough set in this research. Thus, a quantum algorithm of the computation of core in rough set is proposed. Based on simulation experiment, the proposed algorithm is able to get one target out of the target set with the probability of 1. And the time complexity of the new algorithm is proved to be no more than ${\rm O}$$ \left(|\frac{{\rm{ \mathsf{ π}}}}{2\arcsin\sqrt {\frac{M}{C}}}+1||U|\right)$ by theoretical analysis.
- Quantum computing /
- rough set /
- core /
- algorithm design
Recommended by Associate Editor ZHANG Min-Ling
注释:

1) 本文责任编委张敏灵

HTML全文

图 1 $G$算子内部结构

Fig. 1 Inner structure of $G$

下载: 全尺寸图片幻灯片

图 2 Grover算法示意图

Fig. 2 Diagram of Grover algorithm

下载: 全尺寸图片幻灯片

图 3 核属性个数与目标分量概率的关系

Fig. 3 Comparing the number of core attributes and percentage of targets

下载: 全尺寸图片幻灯片

图 4 Comparing the number of core attributes and percentage of targets

Fig. 4 Comparing the number of core attributes and the number of iterations

下载: 全尺寸图片幻灯片

表 1 UCI数据集实验结果

Table 1 The test result of UCI sets

数据集	算法	迭代次数	概率
Iris数据集	Grover算法	失效	失效
Iris数据集	文献[15]算法	2	0.9686
Iris数据集	文献[16]算法	1	1.0000
Iris数据集	$\textbf{本文算法}$	$\textbf{1}$	$\textbf{1.0000}$
Soybean数据集	Grover算法	1	0.8815
Soybean数据集	文献[15]算法	3	0.9723
Soybean数据集	文献[16]算法	2	0.9766
Soybean数据集	$\textbf{本文算法}$	$\textbf{2}$	$\textbf{1.0000}$
Dermatology数据集	Grover算法	6	0.9983
Dermatology数据集	文献[15]算法	12	1.0000
Dermatology数据集	文献[16]算法	8	0.9978
Dermatology数据集	$\textbf{本文算法}$	$\textbf{6}$	$\textbf{1.0000}$
Balloons数据集	Grover算法	失效	失效
Balloons数据集	文献[15]算法	2	0.9686
Balloons数据集	文献[16]算法	1	1.0000
Balloons数据集	$\textbf{本文算法}$	$\textbf{1}$	$\textbf{1.0000}$
Breast Cancer数据集	Grover算法	1	1.0000
Breast Cancer数据集	文献[15]算法	3	0.9688
Breast Cancer数据集	文献[16]算法	2	0.9451
Breast Cancer数据集	$\textbf{本文算法}$	$\textbf{1}$	$\textbf{1.0000}$

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