摘要
随着数据量的爆炸性增长以及信息技术的高速发展,数据挖掘与机器学习已成为当今研究的热点。目前,现实世界中往往呈现连续属性值的数据,而很多数据挖掘与机器学习分类算法仅仅适用离散属性值的数据。因此,必须将连续属性值的数据进行离散化,否则,这些分类学习算法无法正常工作。针对此问题,本文系统分析了现有的连续数据离散化方法,并从离散化标准等方面进行了深入研究,主要包括：
(1)提出一种单属性与多属性相结合的自底向上离散化方法,在考虑属性间关系的同时,综合衡量各相邻区间对之间的差异,寻找最好的合并区间。首先,我们通过最小描述长度理论和连续属性中相邻区间对的重要性,提出一种结合单属性与多属性的离散化标准,并在理论上分析了此标准的优势；进一步,基于此标准,提出一种启发式的自底向上离散化算法,寻找最优的离散化结果；最后,在UCI数据集上的实验结果表明,与现有的离散化方法相比,此方法显著提高了C4.5决策树与支持向量机分类器的学习精度。
(2)提出一种基于非线性降维技术的高维数据离散化方法,有效解决了高维非线性数据的离散化问题。首先,我们提出一种基于局部邻域优化的线性嵌入算法,将高维数据降维至低维空间中,有效保持了原始数据的几何关系结构。该算法克服了数据的几何关系结构容易被扭曲的缺陷；其次,提出一种基于面积的卡方离散化算法,从概率的角度考虑每对区间被合并的可能性,有效离散低维数据空间中的每个连续属性。实验结果表明,此方法得到了较好的离散化结果以及更简化的知识,提高了分类器的学习精度。另外,此方法应用在计算机视觉和图像分类中,取得了很好的效果。
(3)提出一种改进卡方统计的数据离散化方法,提高了基于统计独立性离散化方法的质量。首先,我们分析了卡方函数中自由度选取的不足,给出了自由度选取的修正方案；其次,根据数据类分布等特点,提出了期望频数的改进方案,克服了不同数据集赋予相同期望频数的缺陷,提高了卡方计算的准确性。实验结果表明,改进的方法产生了较高的类属性相互依赖冗余值,并显著提高了C4.5决策树与Naive贝叶斯分类器的学习精度。
With the explosive growth of the amount of data and the rapid development of information technology, data mining and machine learning have become a hot research currently. At present, a large number of data with continuous attribute values are presented in the real world. However, many classification algorithms in data mining and machine learning are only applied to data with discrete attribute values. Therefore, data with continuous attribute values must be discretized. Otherwise, these classification algorithms do not work properly. To solve this problem, we systematically analyze existing discretization methods of continuous data and study them in-depth from different aspects such as discretization criterion. The main contributions of this dissertation can be summarized as follows:
(1) A combined single attribute and multi-attribute bottom-up discretization method is pro-posed. It not only considers the correlations among the attributes, but also synthetically evalu-ates the variance among the adjacent interval pairs. This aims to find the best merged intervals. First, we propose a combined single attribute and multi-attribute discretization criterion, which is derived by minimum description length principle and significance of adjacent interval pairs among continuous attributes. The advantage of the criterion is further analyzed. Furthermore, we develop a heuristic bottom-up discretization algorithm to find the optimal discretization result based on the criterion. Finally, empirical experiments on UCI data sets show that the proposed method significantly improves the learning accuracy of C4.5decision tree and support vector machine classifier compared with existing discretization methods.
(2) A discretization method for disposing high-dimensional data based on nonlinear dimension reduction technique is proposed. It solves the discretization problem of high-dimensional data. First, we propose a locally linear embedding algorithm based on local neigh-borhood optimization. It maps high-dimensional data into a low-dimensional space and ensures to keep geometric correlation structure of the original data. This algorithm overcomes the defi-ciency that the geometric correlation structure of the data is easily distorted when mapping data. Second, we propose an area-based chi-square discretization algorithm. It effectively discretizes each continuous attribute in the low-dimensional space by considering the possibility of being merged for each interval pair from the view of probability. The experimental results show that the proposed method yields a better discretization result and more concise knowledge of the data. It improves the learning accuracy of classifiers. In addition, the proposed discretization method has been applied to computer vision and image classification, and achieves a good result.
(3) A data discretization method based on improved chi-square statistic is proposed. It im-proves the quality of discretization methods based on statistical independence. First, we analyze the deficiency of the selection of degree of freedom in chi-square function and give a modified scheme for selection of degree of freedom. Second, we propose an improved scheme for ex-pected frequency according to data distribution, which overcomes the deficiency that different datasets have the same expected frequency. This improves the accuracy of chi-square calcula-tion. The experimental results show that the improved method generates higher class-attribute interdependence redundancy value and significantly improves the learning accuracy of C4.5de-cision tree and Naive bayes classifier.
引文
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