| Citation: | HU G，LI Z X，ZHANG F M，et al. Dimension reduction of multivariate time series based on two-dimensional inter-class marginal Fisher analysis[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（12）：3537-3546 （in Chinese） doi: 10.13700/j.bh.1001-5965.2022.0128
|
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.
| [1] |
ALI M, BORGO R, JONES M W. Concurrent time-series selections using deep learning and dimension reduction[J]. Knowledge-Based Systems, 2021, 233: 107507. doi: 10.1016/j.knosys.2021.107507
|
| [2] |
LU M, HAMUNYELA E, VERBESSELT J, et al. Dimension reduction of multi-spectral satellite image time series to improve deforestation monitoring[J]. Remote Sensing, 2017, 9(10): 1025. doi: 10.3390/rs9101025
|
| [3] |
SIGGIRIDOU E, KUGIUMTZIS D. Dimension reduction of polynomial regression models for the estimation of granger causality in high-dimensional time series[J]. IEEE Transactions on Signal Processing, 2021, 69: 5638-5650. doi: 10.1109/TSP.2021.3114997
|
| [4] |
MA Q L, CHEN Z P, TIAN S, et al. Difference-guided representation learning network for multivariate time series classification[J]. IEEE Transactions on Cybernetics, 2022, 52(6): 4717-4727. doi: 10.1109/TCYB.2020.3034755
|
| [5] |
GUO H Y, WANG L D, LIU X D, et al. Information granulation-based fuzzy clustering of time series[J]. IEEE Transactions on Cybernetics, 2021, 51(12): 6253-6261. doi: 10.1109/TCYB.2020.2970455
|
| [6] |
JASTRZEBSKA A. Lagged encoding for image-based time series classification using convolutional neural networks[J]. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2020, 13(3): 245-260. doi: 10.1002/sam.11455
|
| [7] |
RAUBITZEK S, NEUBAUER T. A fractal interpolation approach to improve neural network predictions for difficult time series data[J]. Expert Systems with Applications, 2021, 169: 114474. doi: 10.1016/j.eswa.2020.114474
|
| [8] |
LAHRECHE A, BOUCHEHAM B. A fast and accurate similarity measure for long time series classification based on local extrema and dynamic time warping[J]. Expert Systems with Applications, 2021, 168: 1114374.
|
| [9] |
TAYALI H A, TOLUN S. Dimension reduction in mean-variance portfolio optimization[J]. Expert Systems with Applications, 2018, 92: 161-169. doi: 10.1016/j.eswa.2017.09.009
|
| [10] |
李海林, 杨丽彬. 时间序列数据降维和特征表示方法[J]. 控制与决策, 2013, 28(11): 1718-1722.
LI H L, YANG L B. Method of dimensionality reduction and feature representation for time series[J]. Control and Decision, 2013, 28(11): 1718-1722(in Chinese).
|
| [11] |
LIU C H, JAJA J, PESSOA L. LEICA: Laplacian eigenmaps for group ICA decomposition of fMRI data[J]. Neuroimage, 2018, 169(4): 363-373.
|
| [12] |
吴虎胜, 张凤鸣, 钟斌. 基于二维奇异值分解的多元时间序列相似匹配方法[J]. 电子与信息学报, 2014, 36(4): 847-854.
WU H S, ZHANG F M, ZHONG B. Similar pattern matching method for multivariate time series based on two-dimensional singular value decomposition[J]. Journal of Electronics & Information Technology, 2014, 36(4): 847-854(in Chinese).
|
| [13] |
周大镯, 吴晓丽, 闫红灿. 一种高效的多变量时间序列相似查询算法[J]. 计算机应用, 2008, 28(10): 2541-2543.
ZHOU D Z, WU X L, YAN H C. An efficient similarity search for multivariate time series[J]. Journal of Computer Applications, 2008, 28(10): 2541-2543(in Chinese).
|
| [14] |
李正欣, 郭建胜, 惠晓滨, 等. 基于共同主成分的多元时间序列降维方法[J]. 控制与决策, 2013, 28(4): 531-536. doi: 10.13195/j.cd.2013.04.54.lizhx.002
LI Z X, GUO J S, HUI X B, et al. Dimension reduction method for multivariate time series based on common principal component[J]. Control and Decision, 2013, 28(4): 531-536(in Chinese). doi: 10.13195/j.cd.2013.04.54.lizhx.002
|
| [15] |
LI H L. Accurate and efficient classification based on common principal components analysis for multivariate time series[J]. Neurocomputing, 2016, 171: 744-753. doi: 10.1016/j.neucom.2015.07.010
|
| [16] |
HE H, TAN Y H. Unsupervised classification of multivariate time series using VPCA and fuzzy clustering with spatial weighted matrix distance[J]. IEEE Transactions on Cybernetics, 2020, 50(3): 1096-1105. doi: 10.1109/TCYB.2018.2883388
|
| [17] |
SUNDARARAJAN R R. Principal component analysis using frequency components of multivariate time series[J]. Computational Statistics & Data Analysis, 2021, 157: 107164.
|
| [18] |
DONG Y N, QIN S J, BOYD S P. Extracting a low-dimensional predictable time series[J]. Optimization and Engineering, 2022, 23(2): 1189-1214. doi: 10.1007/s11081-021-09643-x
|
| [19] |
李海林. 基于变量相关性的多元时间序列特征表示[J]. 控制与决策, 2015, 30(3): 441-447.
LI H L. Feature representation of multivariate time series based on correlation among variables[J]. Control and Decision, 2015, 30(3): 441-447(in Chinese).
|
| [20] |
李海林, 梁叶. 基于关键形态特征的多元时间序列降维方法[J]. 控制与决策, 2020, 35(3): 629-636.
LI H L, LIANG Y. Dimension reduction for multivariate time series based on crucial shape features[J]. Control and Decision, 2020, 35(3): 629-636(in Chinese).
|
| [21] |
WENG X Q, SHEN J Y. Classification of multivariate time series using locality preserving projections[J]. Knowledge-Based Systems, 2008, 21(7): 581-587. doi: 10.1016/j.knosys.2008.03.027
|
| [22] |
WENG X Q. Classification of multivariate time series using supervised locality preserving projection[C]//Proceedings of the 3rd International Conference on Intelligent System Design and Engineering Applications. Piscataway: IEEE Press, 2013: 428-431.
|
| [23] |
董红玉, 陈晓云. 基于奇异值分解和判别局部保持投影的多变量时间序列分类[J]. 计算机应用, 2014, 34(1): 239-243.
DONG H Y, CHEN X Y. Classification of multivariate time series classification based on singular value decomposition and discriminant locality preserving projection[J]. Journal of Computer Applications, 2014, 34(1): 239-243(in Chinese).
|
| [24] |
ZHAO J H, SUN F, LIANG H Y, et al. Pseudo bidirectional linear discriminant analysis for multivariate time series classification[J]. IEEE Access, 2021, 9: 88674-88684. doi: 10.1109/ACCESS.2021.3089839
|
| [25] |
YAN S C, XU D, ZHANG B Y, et al. Graph embedding and extensions: A general framework for dimensionality reduction[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40-51. doi: 10.1109/TPAMI.2007.250598
|
| [26] |
CHEN J H, WAN Y, WANG X Y, et al. Learning-based shapelets discovery by feature selection for time series classification[J]. Applied Intelligence, 2022, 52(8): 9460-9475. doi: 10.1007/s10489-021-03009-7
|
| [27] |
LIU Y, GAO J E, CAO W, et al. A hybrid double-density dual-tree discrete wavelet transformation and marginal Fisher analysis for scoring sleep stages from unprocessed single-channel electroencephalogram[J]. Quantitative Imaging in Medicine and Surgery, 2020, 10(3): 766-778. doi: 10.21037/qims.2020.02.01
|
| [28] |
李峰, 王正群, 周中侠, 等. 半监督的稀疏保持二维边界Fisher分析降维算法[J]. 计算机辅助设计与图形学学报, 2014, 26(6): 923-931.
LI F, WANG Z Q, ZHOU Z X, et al. Semi-supervised sparsity preserving two-dimensional marginal fisher analysis dimensionality reduction algorithm[J]. Journal of Computer-Aided Design & Computer Graphics, 2014, 26(6): 923-931(in Chinese).
|
| [29] |
WANG Z, ZHANG L, WANG B J. Sparse modified marginal Fisher analysis for facial expression recognition[J]. Applied Intelligence, 2019, 49(7): 2659-2671. doi: 10.1007/s10489-018-1388-7
|
Figures(6) / Tables(4)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
