A Multivariate Decision Tree for Big Data Classification of Distributed Data Streams
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摘要: 分布式数据流大数据中的类别边界不规则且易变，因此基于单变量决策树的集成分类器需要较大数量的基分类器才能准确地近似表达类别边界，这将降低集成分类器的学习与分类性能.因而，本文提出了基于几何轮廓相似度的多变量决策树.在最优基准向量的引导下将n维空间样本点投影到一维空间以建立有序投影点集合，然后通过类别投影边界将有序投影点集合划分为多个子集，接着分别对不同类别集合的交集递归投影分裂，最终生成决策树.实验表明，本文提出的多变量决策树GODT具有很高的分类精度和较低的训练时间，有效结合了单变量决策树学习效率高与多变量决策树表示能力强的优点.Abstract: Considering the irregularity and variability of the class boundaries of distributed big data streams, when the univariate decision tree is used as the base classifier in an ensemble classifier, large amounts of base classifiers are needed to accurately approximate class boundaries. This will reduce the learning and classification performance of ensemble classifiers. This article proposes a multivariate decision tree based on geometric outline similarity (GODT). Firstly, by using the optimal reference vector, the n-dimensional data points are projected onto the one-dimensional space, thus a set of ordered projection points are established. Secondly, the set of projection points are divided into several subsets, and the intersections of different subsets are projected and divided by recursive projecting and splitting. Finally, a decision tree is built. Experimental results show that GODT has a better classification accuracy and requires less training time. It combines the high learning efficiency of univariate decision tree algorithm with the strong representation power of multivariate decision tree.
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Key words:
- Distributed data streams /
- big data /
- classification /
- outline similarity /
- multivariate decision tree
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图 1 投影点集合$P_1 $与$P_2 $的位置关系
Fig. 1 The position relationship of projection point sets $P_1 $ and $P_2 $
图 3 分类精度随滑动窗口大小的变化情况
Fig. 3 The variation of classification accuracy with the sliding window size
图 4 $wt=5$时, 分类精度在整个挖掘序列的变化情况
Fig. 4 The variation of classification accuracy in the mining sequence when $wt=5$
图 5 训练时间随滑动窗口大小的变化情况
Fig. 5 The variation of training time with the sliding window size
图 6 分类精度随基分类器数量的变化情况
Fig. 6 The variation of classification accuracy with the number of base classifiers
表 1 数据集
Table 1 Dataset
Dataset Number of attributes Type of attributes Size Number of class KDDCUP99 42 Nominal, Numeric 5 209 460 23 Record Linkage 12 Numeric 4 587 620 2 Heterogeneity Activity 7 Numeric 13 062 475 7 
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表 2 EGODT的基分类器间的不合度量
Table 2 The disagreement measure between base classifiers of EGODT
GODT $c$1 $c$2 $c$3 $c$4 $c$5 $c$6 $c$7 $c$8 $c$9 $c$10 $c$1 0 0.43 0.52 0.55 0.51 0.41 0.43 0.43 0.41 0.48 $c$2 0 0.51 0.46 0.6 0.32 0.29 0.39 0.29 0.6 $c$3 0 0.24 0.24 0.56 0.6 0.56 0.6 0.52 $c$4 0 0.35 0.66 0.56 0.67 0.55 0.73 $c$5 0 0.53 0.64 0.52 0.57 0.58 $c$6 0 0.41 0.19 0.13 0.37 $c$7 0 0.12 0.19 0.68 $c$8 0 0.2 0.64 $c$9 0 0.6 $c$10 0
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表 3 EC45的基分类器间的不合度量
Table 3 The disagreement measure between base classifiers of EC45
C4.5 $c$1 $c$2 $c$3 $c$4 $c$5 $c$6 $c$7 $c$8 $c$9 $c$10 $c$1 0 0.31 0.44 0.44 0.35 0.3 0.31 0.31 0.29 0.35 $c$2 0 0.48 0.48 0.53 0.11 0.09 0.09 0.09 0.53 $c$3 0 0.02 0.53 0.55 0.53 0.52 0.51 0.55 $c$4 0 0.52 0.55 0.53 0.53 0.53 0.54 $c$5 0 0.48 0.51 0.53 0.49 0.04 $c$6 0 0.08 0.09 0.07 0.47 $c$7 0 0.02 0.07 0.53 $c$8 0 0.08 0.54 $c$9 0 0.49 $c$10 0
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表 4 ECart-LC的基分类器间的不合度量
Table 4 The disagreement measure between base classifiers of ECart-LC
Cart-LC $c$1 $c$2 $c$3 $c$4 $c$5 $c$6 $c$7 $c$8 $c$9 $c$10 $c$1 0 0.39 0.31 0.31 0.3 0.37 0.46 0.46 0.32 0.32 $c$2 0 0.22 0.22 0.36 0.57 0.48 0.47 0.48 0.6 $c$3 0 0 0.15 0.61 0.5 0.5 0.5 0.5 $c$4 0 0.15 0.61 0.5 0.5 0.5 0.5 $c$5 0 0.46 0.52 0.52 0.39 0.39 $c$6 0 0.57 0.57 0.2 0.16 $c$7 0 0 0.38 0.5 $c$8 0 0.38 0.5 $c$9 0 0.12 $c$10 0
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表 5 EHoeffdingTree的基分类器间的不合度量
Table 5 The disagreement measure between base classifiers of EHoeffdingTree
HoeffdingTree $c$1 $c$2 $c$3 $c$4 $c$5 $c$6 $c$7 $c$8 $c$9 $c$10 $c$1 0 0.26 0.53 0.54 0.38 0.3 0.36 0.31 0.24 0.47 $c$2 0 0.42 0.47 0.2 0.18 0.12 0.16 0.1 0.32 $c$3 0 0.45 0.45 0.43 0.58 0.58 0.46 0.45 $c$4 0 0.52 0.44 0.45 0.5 0.47 0.51 $c$5 0 0.54 0.57 0.56 0.58 0.07 $c$6 0 0.08 0.15 0.14 0.51 $c$7 0 0.19 0.12 0.58 $c$8 0 0.25 0.57 $c$9 0 0.56 $c$10 0
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