| 4 | 0 | 11 |
| Downloads | Citas | Reads |
Functional canonical correlation analysis is a key method in multivariate statistics for identifying optimal linear correlations between two functional datasets. However, some functions within these datasets may exhibit anomalies such as sudden changes or fluctuations that deviate from the overall trend, resulting to inaccurate results. To address this, we propose an improved method: Sparse functional canonical correlation analysis based on the L2,1-norm. This approach reduces outliers by optimizing the selection of orthogonal basis functions, thereby enhancing the accuracy and reliability of the analysis. Numerical experiments show that the L2,1-norm-based method significantly outperforms traditional methods.
[1]Hotelling H.Relations between two sets of variates[J].Biometrika,1936,28(3/4):321-377.
[2]Ramsay J O.When the data are functions[J].Psychometrika,1982,47(4):379-396.
[3]Wang J L,Chiou J M,Müller H G.Functional data analysis[J].Annual Review of Statistics and Its Application,2016,3:257-295.
[4]López-Pintado S,Romo J.On the concept of depth for functional data[J].Journal of the American Statistical Association,2009,104(486):718-734.
[5]Cardot H,Ferraty F,Sarda P.Functional linear model[J].Statistics&Probability Letters,1999,45(1):11-22.
[6]Müller H G,Stadtmüller U.Generalized functional linear models[J].The Annals of Statistics,2005,33(2):774-805.
[7]Müller H G,Yao F.Functional additive models[J].Journal of the American Statistical Association,2008,103(484):1534-1544.
[8]Preda C.Regression models for functional data by reproducing kernel Hilbert spaces methods[J].Journal of Statistical Planning and Inference,2007,137(3):829-840.
[9]Chen D,Hall P,Müller H G.Single and multiple index functional regression models with nonparametric link[J].The Annals of Statistics,2011,39(3):1720-1747.
[10]Ferraty F,Vieu P.The functional nonparametric model and application to spectrometric data[J].Computational Statistics,2002,17(4):545-564.
[11]Hall P,Hosseini-Nasab M.On properties of functional principal components analysis[J].Journal of the Royal Statistical Society:Series B(Statistical Methodology),2006,68(1):109-126.
[12]Silverman B W.Smoothed functional principal components analysis by choice of norm[J].The Annals of Statistics,1996,24(1):1-24.
[13]Eubank R L,Hsing T.Canonical correlation for stochastic processes[J].Stochastic Processes and Their Applications,2008,118(9):1634-1661.
[14]Leurgans S E,Moyeed R A,Silverman B W.Canonical correlation analysis when the data are curves[J].Journal of the Royal Statistical Society:Series B(Methodological),1993,55(3):725-740.
[15]He G Z,Müller H G,Wang J L.Functional canonical analysis for square integrable stochastic processes[J].Journal of Multivariate Analysis,2003,85(1):54-77.
[16]Shin H,Lee S.Canonical correlation analysis for irregularly and sparsely observed functional data[J].Journal of Multivariate Analysis,2015,134:1-18.
[17]He G Z,Müller H G,Wang J L.Methods of canonical analysis for functional data[J].Journal of Statistical Planning and Inference,2004,122(1/2):141-159.
[18]Dragotti P L,Lu Y M.On sparse representation in Fourier and local bases[J].IEEE Transactions on Information Theory,2014,60(12):7888-7899.
[19]Ramsay J O,Dalzell C J.Some tools for functional data analysis[J].Journal of the Royal Statistical Society:Series B(Methodological),1991,53(3):539-561.
[20]Ramsay J O,Munhall K G,Gracco V L,et al.Functional data analyses of lip motion[J].Journal of the Acoustical Society of America,1996,99(6):3718-3727.
[21]Young N.An introduction to Hilbert space[M].New York:Cambridge University Press,1988.
[22]Berberian S K.Introduction to Hilbert space[M].New York:Oxford University Press,1961.
[23]Debnath L,Mikusinski P.Introduction to Hilbert spaces with applications[M].New York:Academic Press,1990.
[24]Ramsay J O,Silverman B W.Applied functional data analysis:Methods and case studies[M].New York:Springer,2002.
[25]Parkhomenko E,Tritchler D,Beyene J.Sparse canonical correlation analysis with application to genomic data integration[J].Statistical Applications in Genetics and Molecular Biology,2009,8(1):1.
[26]Hardoon D R,Shawe-Taylor J.Sparse canonical correlation analysis[J].Machine Learning,2011,83(3):331-353.
[27]Liu J,Ji S W,Ye J P.Multi-task feature learning via efficientℓ2,1-norm minimization[PP/OL]. V1. arXiv(2012-05-09)[2025-01-15].https：//arxiv.org/pdf/1205.2631.
[28]Zhang Z,Li F Z,Zhao M B,et al.Robust neighborhood preserving projection by nuclear/L2,1-norm regularization for image feature extraction[J].IEEE Transactions on Image Processing,2017,26(4):1607-1622.
[29]Ren C X,Dai D Q,Yan H.Robust classification usingℓ2,1-norm based regression model[J]. Pattern Recognition,2012,45(7):2708-2718.
[30]An X M,Shen L,Hu H,et al.Federated learning with manifold regularization and normalized update reaggregation[PP/OL].V1.arXiv(2023-11-10)[2025-01-15].https：//arxiv.org/pdf/2311.05924.
[31]Tang S Q,Yu S J,Dong Y N,et al.Deep dynamic probabilistic canonical correlation analysis[C]//ICASSP 2025-2025 IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP),April 6-11,2025,Hyderabad,India. New York:IEEE,2025:1-5.
[32]PatanèG,Nicolussi F,Krauth A,et al.Functional-ordinal canonical correlation analysis with application to data from optical sensors[PP/OL].V1.arXiv(2025-01-30)[2025-03-15].https：//arxiv.org/pdf/2501.18317.
[33]Yang W J,Müller H G,Stadtmüller U.Functional singular component analysis[J].Journal of the Royal Statistical Society:Series B(Statistical Methodology),2011,73(3):303-324.
[34]Krzyśko M,WaszakŁ．Canonical correlation analysis for functional data[J].Biometrical Letters,2013,50(2):95-105.
[35]Chakraborty R,Vemuri B C.Statistics on the Stiefel manifold:Theory and applications[J].The Annals of Statistics,2019,47(1):415-438.
[36]Chen S X,Ma S Q,So A M C,et al.Proximal gradient method for nonsmooth optimization over the Stiefel manifold[J].SIAM Journal on Optimization,2020,30(1):210-239.
[37]Chen S X,Ma S Q,Xue L Z,et al.An alternating manifold proximal gradient method for sparse principal component analysis and sparse canonical correlation analysis[J].INFORMS Journal on Optimization,2020,2(3):192-208.
[38]Moe-Nilssen R,Helbostad J L.Estimation of gait cycle characteristics by trunk accelerometry[J].Journal of Biomechanics,2004,37(1):121-126.
[39]Capra B,Müller H G.An accelerated-time model for response curves[J].Journal of the American Statistical Association,1997,92(437):72-83.
Basic Information:
DOI：10.13568/j.cnki.651094.651316.2025.06.24.0001
China Classification Code:O212
Citation Information:
[1]Zhang Zejiang,Yang Zhixia,Ye Junyou ,et al.Sparse Canonical Correlation Analysis with L_(2,1)-Norm for Functional Data[J].Journal of Xinjiang University (Natural Science Edition in Chinese and English),2026,43(03):305-323.DOI:10.13568/j.cnki.651094.651316.2025.06.24.0001.
Fund Information:
The National Natural Science Foundation of China “Optimization models and algorithms for interpretable learning machines on complex data”(12461058); Xinjiang Key Laboratory of Applied Mathematics (XJDX1401)
2026-05-15
2026-05-15