基于多元函数主成分表示的识别学习

doi:10.6040/j.issn.1672-3961.0.2021.314

Abstract

Abstract:

Aiming at the problem of multi-dimensional information fusion in recognition learning, a recognition method based on multivariate functional principal component representation was proposed. The numerical calculation method of multivariate functional principal components was given. The joint covariance operator was used to calculate eigenvalues and eigenvectors, and the key distinguishing features were extracted. Based on these comprehensive features, the random forest method was used to recognize and learn multivariate functional data. The recognition performance of multivariate functional principal component representation method was compared with other representation methods on simulated data and real data. The experimental results showed that the accuracy was equal to 1 in the simulation dataset, English handwritten dataset and Chinese handwritten dataset, and 0.954 4 in the motion dataset. Compared with other methods, multivariate functional principal component analysis (MFPCA) had better recognition effect and improved the recognition accuracy effectively.

Key words: functional data, basis function, MFPCA, random forest, accuracy

CLC Number:

TP391

Yinfeng MENG,Qingfang LI. Recognition learning based on multivariate functional principal component representation[J].Journal of Shandong University(Engineering Science), 2022, 52(3): 1-8.

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阶数	E_MS1	E_MS2
2	0.104 0	0.103 5
3	0.097 4	0.097 4
4	0.096 8	0.096 9
5	0.057 9	0.059 2
6	0.057 4	0.058 6
7	0.038 4	0.038 7

主成分	贡献率	累计贡献率
Z₁	64.76	64.76
Z₂	24.86	89.62
Z₃	4.58	94.20
Z₄	2.27	96.47
Z₅	1.34	97.81

特征抽取方法	准确率均值	准确率方差
B-spline	1.000 0	0
Fourier	1.000 0	0
Polygonal	1.000 0	0
Exponential	1.000 0	0
Monomial	1.000 0	0
Power	1.000 0	0
MFPCA	1.000 0	0

特征抽取方法	准确率均值	准确率方差
B-spline	0.999 1	0.006 1
Fourier	1.000 0	0
Polygonal	1.000 0	0
Exponential	1.000 0	0
Monomial	0.986 1	0.024 6
Power	0.989 1	0.019 9
MFPCA	1.000 0	0

特征抽取方法	准确率均值	准确率方差
B-spline	0.922 8	0.061 6
Fourier	0.928 3	0.055 4
Polygonal	0.932 8	0.060 8
Exponential	0.907 2	0.064 7
Monomial	0.862 2	0.083 7
Power	0.858 9	0.078 7
MFPCA	0.954 4	0.053 2

Recognition learning based on multivariate functional principal component representation

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