基于多重奇异值分解熵的属性约简方法研究及应用

发布时间：2018-06-03 08:08

本文选题：奇异值分解 + 偏熵　；参考：《安徽大学》2017年硕士论文

【摘要】：现实世界地大物博,缤纷复杂.现实世界具有太多的不确定性,导致了人类对世界认知的不完善.粗糙集作为不确定性的问题的有效工具,近些年来被人们广泛的研究,并应用于处理现实生活中遇到不确定问题,其中属性约简作为粗糙集研究的主要方向被学者们广泛关注.本文主要提出基于奇异值分解偏熵和关联熵的关联系数概念,通过比较关联系数进行属性约简,实验证明了该方法的有效性.本文主要工作如下:(1)奇异值能充分反映轨迹矩阵的奇异特征,关联系数能够较好地刻画数据之间的关联性,本文提出了一种基于奇异值分解熵的属性约简算法,该算法通过对时间序列的轨迹矩阵进行奇异值分解,得到两条时间序列间的关联系数.剔除与决策属性值关联系数较小的属性,从而进行属性约简.通过具体实例,并与条件信息熵等算法进行了对比,表明奇异值分解方法在约简结果和识别精度方面均表现出优势.(2)通过分割整体序列为若干个子序列,并借助于滑动窗方法,得到两个序列的关联系数谱.实验说明该关联系数谱能更加准确刻画数据间的相关程度,从而更有效用于数据约简.进一步,提出了基于多重奇异值分解偏熵和关联熵的关联系数谱,通过重数在正负值之间的调节,刻画不同标度下奇异值的大小对关联系数的影响,实验证明该方法可以更加细致刻画两序列的关联系数谱的稳定程度,从而更加精确刻画条件属性与决策属性间的关联.
[Abstract]:The real world is vast and complex. There is too much uncertainty in the real world, which leads to the imperfect cognition of the world. Rough set, as an effective tool for uncertain problems, has been widely studied in recent years and applied to deal with uncertain problems in real life. Among them, attribute reduction, as the main research direction of rough sets, has been widely concerned by scholars. In this paper, the concept of correlation coefficient based on singular value decomposition partial entropy and correlation entropy is proposed, and the effectiveness of the method is proved by comparing the correlation coefficient with attribute reduction. The main work of this paper is as follows: (1) the singular value can fully reflect the singular characteristics of the locus matrix, and the correlation coefficient can better describe the correlation between the data. In this paper, an attribute reduction algorithm based on singular value decomposition entropy is proposed. The correlation coefficient between two time series is obtained by the singular value decomposition of the locus matrix of the time series. The attribute is reduced by eliminating the attribute with low correlation coefficient with the value of decision attribute. Compared with the conditional information entropy algorithm, it is shown that the singular value decomposition method has advantages in both the reduction result and the recognition accuracy) by dividing the global sequence into several sub-sequences, and by using the sliding window method, the singular value decomposition method can be used to solve the problem. The correlation coefficient spectrum of two sequences is obtained. The experimental results show that the correlation coefficient spectrum can more accurately describe the correlation degree between the data, so that the correlation coefficient spectrum can be more effectively used in data reduction. Furthermore, the correlation coefficient spectrum based on the partial entropy and correlation entropy of multiple singular value decomposition is proposed. By adjusting the multiplicity between positive and negative values, the influence of singular value on the correlation coefficient under different scales is described. Experimental results show that this method can describe the stability of correlation coefficient spectrum of two sequences in more detail, so that the correlation between conditional attributes and decision attributes can be described more accurately.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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