连续型数据的辨识矩阵属性约简方法

属性约简是粗糙集理论在数据处理方面的重要应用，已有的针对连续型数据的属性约简算法主要集中在基于正域的贪心算法，该方法只考虑了一致样本和其他样本的可辨识性，而忽略了边界样本点间可区分性。为了克服基于正域算法的缺点，提出了连续型数据的辨识矩阵属性约简模型，该模型不但考虑了正域样本的一致性，同时考虑了边界样本的可分性。基于该模型，分析了属性约简结构，定义了辨识矩阵来刻画特征子集的分类能力，构造了实值型数据的属性约简启发式算法，并利用UCI标准数据集进行了验证。理论分析和实验结果表明，提出的算法能够有效地处理连续型数据，提高了数据的分类精度。

A discernibility matrix-based attribute reduction for continuous data

In data processing, attribute reduction is an important application of rough set theory. The existing methods for continuous data mainly concentrate on the greedy algorithms based on the positive region. These methods take account of only the identifiability between consistent samples and other samples while ignoring distinguishability among the boundary samples. To overcome the disadvantage based on the positive domain algorithm, this paper proposed a new method for attribute reduction using a discernibility matrix. The model considers not only the consistency of samples in the positive region but also the reparability of boundary samples. On this basis, this paper analyzes the structure of attribute reduction and defines a discernibility matrix to characterize the discernibility ability of a subset of attributes. Next, an attribute reduction algorithm was designed based on the discernibility matrix. The validity of the proposed algorithm was verified using UCI standard data sets and theoretical analysis.