## 1 Introduction
OPLS decomposes X-variation into Y-correlated and orthogonal subspaces, preserving predictive power while clarifying spectral feature attribution--particularly effective for wood chip NIR analysis and metabolomics, though validation must prevent signal loss. 2. Scatter Correction and Baseline Methods: MSC corrects additive/scattering effects by linear regression to a reference spectrum, effectively mitigating path-length variations in diffuse reflectance powder analysis. Its performance hinges critically on reference spectrum selection and struggles with nonlinear scattering. SNV applies row-wise normalization (mean-centering and scaling), providing parameter-free baseline stabilization for heterogeneous samples but attenuating Y-relevant amplitude differences. Both methods prioritize physical artifact removal over chemical feature enhancement. 3. Smoothing and Filtering Techniques: SG Filtering leverages polynomial convolution for simultaneous noise reduction and derivative computation, resolving overlapping peaks in IR/Raman spectra while preserving peak morphology. Optimal performance requires careful tuning of window size and polynomial order. LoPLS integrates low-pass frequency filtering into PLS to suppress high-frequency noise from portable spectrometers, but may blur sharp spectral features critical for analyte identification. PLS Variants: VCPLS constrains PLS loadings to high-variance spectral regions, reducing overfitting from low-variance noise in collinear datasets but risking omission of subtle Y-correlated signals. PoPLS amplifies weak spectral features through the exponentiation of loadings, enhancing trace analyte detection in complex matrices like pharmaceuticals; however, arbitrary exponent selection may amplify artifacts. Additionally, methods like Lasso regularization have been investigated to handle high-dimensional data and prevent overfitting. While these approaches have shown promise, they often rely on predefined transformations or regularization strategies that may not fully adapt to the unique characteristics of each spectral dataset. Despite advancements in spectral data analysis, several limitations persist in current research. Firstly, existing methods often lack the flexibility to adapt to the specific noise patterns and spectral complexities inherent in individual datasets. Secondly, the predictive performance of these methods can degrade significantly when faced with substantial spectral overlap or high noise levels. Furthermore, the theoretical foundations of some of these techniques are not fully developed, making it challenging to rigorously assess their convergence properties and prediction variances. These limitations can result in inaccurate predictions and reduced reliability in practical applications, potentially compromising the integrity of analytical results and decision-making processes. The objective of this study is to develop and validate the FPLS model, which integrates an adaptive filter within the PLS framework to improve the accuracy and robustness of spectral-based predictions. By optimizing the filter parameters alongside the PLS regression coefficients, the FPLS model aims to adaptively mitigate the effects of noise and spectral overlap, thereby enhancing the predictive performance. The proposed model will be evaluated through rigorous theoretical analysis and experimental validation using diverse spectral datasets, including Corn, Octane, Mango, and Soil Nitrogen. The scope of this study focuses on the enhancement of PLS regression through adaptive filtering techniques. We summarize our main contributions of this study as follows:  
1. Introduction of FPLS Model: We propose the filter learning-based Partial Least Squares (FPLS) model, which incorporates an adaptive filter into the traditional PLS framework. This innovation allows the model to adaptively learn the optimal filter during training, thereby improving its ability to handle noisy data and extract relevant features. 2.