Multidimensional Partial Least Squares Method for Multidimensional Data Fitting
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In the field of data analysis, multidimensional partial least squares (MPLS) serves as a fundamental data fitting methodology. This algorithm not only efficiently handles collinear data but also processes complex datasets containing multiple independent variables. During implementation, data preprocessing steps such as normalization using z-score standardization and noise removal through filtering techniques are essential prerequisites. The method employs latent variable extraction to maximize covariance between predictor and response matrices, typically implemented through iterative NIPALS (Nonlinear Iterative Partial Least Squares) algorithms. Furthermore, this approach finds extensive applications in signal processing for feature extraction, image recognition for pattern classification, and machine learning domains for multivariate calibration. Key MATLAB functions include plsregress for model development and cross-validation techniques for parameter optimization.
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