Dimension reduction of multivariate time series based on two-dimensional inter-class marginal Fisher analysis
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摘要:
针对传统边界Fisher分析及相关方法用于多元时间序列降维的局限性，提出一种基于二维类间边界Fisher分析的多元时间序列降维方法。针对边界Fisher分析进行模型改进，在本征图和惩罚图的基础上引入类间惩罚图，用来描述各个类中心之间的距离，并对目标函数进行改进，提出类间边界Fisher分析模型；对所提模型进行二维化拓展，提出基于二维类间边界Fisher分析的降维模型，使其能够直接处理二维矩阵数据，有效保留结构信息；通过计算协方差矩阵将多元时间序列集转化为等长特征集，利用降维模型将等长特征集投影到低维空间，达到数据降维和特征表示的目的。实验结果表明：所提方法能够有效对多元时间序列进行降维，达到良好的分类效果。
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关键词:
- 多元时间序列 /
- 降维 /
- 边界Fisher分析 /
- 协方差矩阵 /
- 分类
Abstract:In order to address the drawbacks of the traditional marginal Fisher analysis and related methods, a dimension reduction method for multivariate time series based on two-dimensional inter-class marginal Fisher analysis is proposed in this study. First, it conducts model improvement to cope with the limitation of marginal Fisher analysis, introduces an inter-class penalty graph based on eigenimage and penalty graph to describe the distance between the centers of each class, and improves objective function, then finally puts forward an inter-class marginal Fisher analysis model; then, by expanding the aforementioned model to two dimensions, we introduced the two-dimensional inter-class marginal Fisher analysis approach to directly analyze two-dimensional matrix data while successfully preserving structural information. Thereafter, by calculating the covariance matrix, the multivariate time series set is transformed into the equal-length feature set, and the equal-length feature set is projected into a low-dimensional space by using the dimension reduction model to achieve the purpose of data dimension reduction and feature representation. The experimental results show that this method can effectively reduce the dimension of multivariate time series and achieve good classification results compared with other methods.
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表 1 计算复杂度比较
Table 1. Comparison of computational complexity
降维方法 训练复杂度 投影复杂度 2DICMFA $O\left( {n{m^2}t + {n^2} + n{m^3}} \right)$ $O\left( {n{m^2}p} \right)$ PCA $O{\text{(}}n{m^2}t{\text{ + }}n{m^3}{\text{)}}$ $O\left( {nmpt} \right)$ SVD $O{\text{(}}n{m^3}{\text{)}}$ $O\left( {nmpt} \right)$ 
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表 2 MTS数据集信息
Table 2. MTS dataset information
数据集 类别数 特征维度 最短序列
时间长度最长序列
时间长度样本数 ASL 8 22 47 95 216 JV 9 12 7 29 640 NF 2 4 50 997 1337 WR 2 62 128 1918 44 EEG 2 64 256 256 22 LP1 4 6 15 15 88 LP2 5 6 15 15 47 LP3 4 6 15 15 47
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表 3 实验分类精度结果
Table 3. Experimental classification accuracy results
方法 K 分类精度 平均分类精度 ASL JV NF WR EEG LP1 LP2 LP3 PBLDA 1 0.71 0.48 0.84 0.73 0.68 0.38 0.51 0.47 0.60 5 0.69 0.43 0.82 0.73 0.50 0.30 0.45 0.40 0.54 10 0.62 0.40 0.81 0.73 0.55 0.27 0.43 0.47 0.54 S-DLPP 1 0.81 0.32 0.70 0.66 0.55 0.55 0.47 0.45 0.56 5 0.69 0.30 0.74 0.73 0.27 0.55 0.36 0.53 0.52 10 0.62 0.30 0.75 0.66 0.36 0.41 0.47 0.43 0.50 RFR 1 0.94 0.66 0.85 0.98 0.95 0.82 0.53 0.70 0.80 5 0.87 0.69 0.87 0.98 0.82 0.72 0.64 0.70 0.80 10 0.77 0.69 0.88 0.98 0.59 0.65 0.47 0.66 0.71 PCA 1 0.81 0.34 0.76 0.95 0.59 0.84 0.64 0.70 0.70 5 0.82 0.35 0.77 0.95 0.50 0.82 0.47 0.53 0.65 10 0.75 0.35 0.76 0.93 0.41 0.68 0.43 0.55 0.61 CPCA 1 0.94 0.48 0.76 0.98 0.59 0.83 0.68 0.72 0.75 5 0.93 0.52 0.76 0.98 0.45 0.75 0.57 0.53 0.69 10 0.89 0.52 0.75 0.98 0.32 0.68 0.45 0.51 0.64 2DICMFA 1 1.00 0.69 0.88 0.86 0.95 0.86 0.62 0.72 0.82 5 1.00 0.70 0.86 0.75 0.77 0.78 0.51 0.68 0.76 10 1.00 0.70 0.85 0.70 0.64 0.68 0.43 0.62 0.70
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表 4 p在不同数据集中的取值
Table 4. p values in different data sets
数据集 p 数据集 p ASL 10 EEG 10 JV 11 LP1 4 NF 4 LP2 2 WR 10 LP3 1
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