{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T20:03:16Z","timestamp":1767211396548,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,9]],"date-time":"2025-07-09T00:00:00Z","timestamp":1752019200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100012554","name":"Hubei Provincial Department of Education","doi-asserted-by":"publisher","award":["B2020061"],"award-info":[{"award-number":["B2020061"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Partial Least Squares (PLS) regression has been widely used to model the relationship between predictors and responses. However, PLS may be limited in its capacity to handle complex spectral data contaminated with significant noise and interferences. In this paper, we propose a novel filter learning-based PLS (FPLS) model that integrates an adaptive filter into the PLS framework. The FPLS model is designed to maximize the covariance between the filtered spectral data and the response. This modification enables FPLS to dynamically adapt to the characteristics of the data, thereby enhancing its feature extraction and noise suppression capabilities. We have developed an efficient algorithm to solve the FPLS optimization problem and provided theoretical analyses regarding the convergence of the model, the prediction variance, and the relationships among the objective functions of FPLS, PLS, and the filter length. Furthermore, we have derived bounds for the Root Mean Squared Error of Prediction (RMSEP) and the Cosine Similarity (CS) to evaluate model performance. Experimental results using spectral datasets from Corn, Octane, Mango, and Soil Nitrogen show that the FPLS model outperforms PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso in terms of prediction accuracy. The theoretical analyses align with the experimental results, emphasizing the effectiveness and robustness of the FPLS model in managing complex spectral data.<\/jats:p>","DOI":"10.3390\/a18070424","type":"journal-article","created":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:26:53Z","timestamp":1752229613000},"page":"424","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Filter Learning-Based Partial Least Squares Regression and Its Application in Infrared Spectral Analysis"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5227-5159","authenticated-orcid":false,"given":"Yi","family":"Mou","sequence":"first","affiliation":[{"name":"School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Long","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Wuhan Polytechnic University, Wuhan 430024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weizhen","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6420-8984","authenticated-orcid":false,"given":"Teng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0169-7439(01)00155-1","article-title":"PLS-regression: A basic tool of chemometrics","volume":"58","author":"Wold","year":"2001","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.jcp.2015.04.015","article-title":"On computing first and second order derivative spectra","volume":"295","author":"Roy","year":"2015","journal-title":"J. Comput. Phys."},{"key":"ref_3","unstructured":"Zhang, X.D. (2022). Modern Signal Processing, Walter de Gruyter GmbH & Co KG."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0169-7439(01)00156-3","article-title":"Some recent developments in PLS modeling","volume":"58","author":"Wold","year":"2001","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0169-7439(89)80111-X","article-title":"Nonlinear PLS modeling","volume":"7","author":"Wold","year":"1989","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/j.neuroimage.2010.07.034","article-title":"Partial Least Squares (PLS) methods for neuroimaging: A tutorial and review","volume":"56","author":"Krishnan","year":"2011","journal-title":"Neuroimage"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1002\/cem.1180070104","article-title":"The kernel algorithm for PLS","volume":"7","author":"Lindgren","year":"1993","journal-title":"J. Chemom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/cem.1180080208","article-title":"Comments on the PLS kernel algorithm","volume":"8","year":"1994","journal-title":"J. Chemom."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0169-7439(93)85002-X","article-title":"SIMPLS: An alternative approach to partial least squares regression","volume":"18","year":"1993","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/cem.1180080204","article-title":"A PLS kernel algorithm for data sets with many variables and fewer objects. Part 1: Theory and algorithm","volume":"8","author":"Lindgren","year":"1994","journal-title":"J. Chemom."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1002\/cem.1248","article-title":"A comparison of nine PLS1 algorithms","volume":"23","author":"Andersson","year":"2009","journal-title":"J. Chemom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.chemolab.2007.10.006","article-title":"LPLS-regression: A method for prediction and classification under the influence of background information on predictor variables","volume":"91","author":"Flatberg","year":"2008","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0169-7439(98)00109-9","article-title":"Orthogonal signal correction of near-infrared spectra","volume":"44","author":"Wold","year":"1998","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1002\/cem.695","article-title":"Orthogonal projections to latent structures (O-PLS)","volume":"16","author":"Trygg","year":"2002","journal-title":"J. Chemom."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0169-7439(01)00102-2","article-title":"Direct orthogonal signal correction","volume":"56","author":"Westerhuis","year":"2001","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1366\/0003702854248656","article-title":"Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat","volume":"39","author":"Geladi","year":"1985","journal-title":"Appl. Spectrosc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1366\/0003702894202201","article-title":"Standard Normal Variate Transformation and De-trending of Near-Infrared Diffuse Reflectance Spectra","volume":"43","author":"Barnes","year":"1989","journal-title":"Appl. Spectrosc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1016\/j.trac.2009.07.007","article-title":"Review of the most common pre-processing techniques for near-infrared spectra","volume":"28","author":"Rinnan","year":"2009","journal-title":"Trend. Anal. Chem."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1504\/IJDMB.2015.066768","article-title":"Probabilistic partial least squares regression for quantitative analysis of Raman spectra","volume":"11","author":"Li","year":"2015","journal-title":"Int. J. Data Min. Bioinform."},{"key":"ref_20","first-page":"3000109","article-title":"Robust Mixture Probabilistic Partial Least Squares Model for Soft Sensing With Multivariate Laplace Distribution","volume":"70","author":"Yang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_21","first-page":"97","article-title":"Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space","volume":"2","author":"Rosipal","year":"2002","journal-title":"J. Mach. Learn. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1109\/TNNLS.2018.2844866","article-title":"Solving Partial Least Squares Regression via Manifold Optimization Approaches","volume":"30","author":"Chen","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104486","DOI":"10.1016\/j.chemolab.2021.104486","article-title":"Partial least trimmed squares regression","volume":"221","author":"Xie","year":"2022","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Mohammadi, A., Almasganj, F., Taherkhani, A., and Naderkhani, F. (2008, January 12\u201314). Missing Feature reconstruction with Multivariate Laplace distribution (MLD) for noise robust phoneme recognition. Proceedings of the 2008 3rd International Symposium on Communications, Control and Signal Processing, Saint Julian\u2019s, Malta.","DOI":"10.1109\/ISCCSP.2008.4537339"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.aca.2013.01.022","article-title":"A consensus orthogonal partial least squares discriminant analysis (OPLS-DA) strategy for multiblock Omics data fusion","volume":"769","author":"Boccard","year":"2013","journal-title":"Anal. Chim. Acta"},{"key":"ref_26","unstructured":"Wang, H. (1999). Partial Least-Squares Regression Method and Applications, National Defense Industry Press."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1002\/cem.1180020306","article-title":"PLS regression methods","volume":"2","year":"1988","journal-title":"J. Chemom."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.chemolab.2015.04.014","article-title":"Variance constrained partial least squares","volume":"145","author":"Jiang","year":"2015","journal-title":"Chemom. Intell. Lab. Syst"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1002\/cem.904","article-title":"A twist to partial least squares regression","volume":"19","author":"Indahl","year":"2005","journal-title":"J. Chemom."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.csda.2013.03.022","article-title":"M-type smoothing spline estimators for principal functions","volume":"66","author":"Lee","year":"2013","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_32","unstructured":"Esbensen, K.H., Guyot, D., Westad, F., and Houm\u00f8ller, L.P. (2002). Multivariate Data Analysis-In Practise: An Introduction to Multivariate Data Analysis and Experimental Design, Wiley. Gtap Technical Papers."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.3788\/fgxb20183907.1016","article-title":"Optimization for Vis\/NIRS Prediction Model of Soil Available Nitrogen Content","volume":"39","author":"Wang","year":"2018","journal-title":"Chin. J. 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