SpectralMultivariateCalibration

Partial Least Squares implementation in Python

Provides

1. PartialLeastSquares(CrossValidation, ValsetValidation, Prediction)

• CrossValidation, cv
• ValsetValidation, vv
• Prediction, predict

It should be pointed out that before using 'predict', 'cv' or 'vv' must be run first.

Take 'cv' for example, its outputs include 'cv_result' and 'cal_result'.

Assume the DataSet consists of 80 spectra, 700 wavelength points, the max num of latent variable is 5. The cal_result's outputs are as following:

'cal_result' including:
    'b': (回归系数，(700,5))
    't2_limit': (t2阈值，(6,5))
    'leverage_limit': (杠杆值阈值，(5,))
    'q_limit': (Q残差阈值，(6,5)，最后一列nan)
    't_critical_value': (y学生化残差阈值，(6,5))
    'r2': (决定系数R2，(5,))
    'press': (预测残差平方和，(5,))
    'rmsec': (RMSEC校正均方根误差，(5,))
    'sec': (SEC校正标准偏差，(5,))
    'rpd': (RPD，(5,))
    'bias': (Bias，(5,))
    'x_loadings': (X载荷，(700,5))
    'x_scores_weights': (X权重，(700,5))
    'linear_regression_coefficient': (包含斜率Slope和截距Offset，(2,5))
    'fitting_x_list': (list, 每个元素代表1个隐变量下的拟合光谱矩阵)
    'residual_matrix_list': (list, 每个元素代表1个隐变量下的残差光谱矩阵)
    'fit_value': (拟合值，(80,5))
    'y_residual': (拟合残差，(80,5))
    'x_residual': (X残差，(80,5))
    't2': (T2，(80,5))
    'leverage': (Leverage，(80,5))
    'x_scores': (X得分，(80,5))
    'x_fvalue': (X残差F分布统计量，(80,5))
    'x_fprob': (X残差F分布累积概率值，(80,5))
    'y_fvalue': (y残差F分布统计量，(80,5))
    'y_fprob': (y残差F分布累积概率值，(80,5))
    'y_tvalue': (y学生化残差，(80,5))  # 学生化残差
    'x_sample_residuals': (80,5)
    'x_variable_residuals': (700,5)
    'x_total_residuals': (1,5)
    'explained_x_sample_variance': (80,5)
    'explained_x_variable_variance': (700,5)
    'explained_x_total_variance': (1,5)
    'explained_x_variance_ratio': (1,5)
    'x_outlier_indices_list':
    'y_outlier_indices_list':
    'just_x_outlier_list':
    'just_y_outlier_list':
    'both_xy_outlier_list':

2. Three PLS Algorithms:

• Improved Kernel Partial Least Squares, IKPLS
• Nonlinear Iterative Partial Least Squares，NIPALS
• Straightforward Implementation of a statistically inspired Modification of the Partial Least Squares, SIMPLS

3. Several Sampling Algorithms:

• montecarlo_sampling
• ks_sampling(Kennard-Stone)
• spxy_sampling

4. Several Samples split Algorithms:

• samples_systematic_split
• samples_ks_split
• samples_spxy_split
• samples_random_split

5. Popular Pretreat methods for Spectroscopy

• Multiplicative Scatter Correction (多元散射校正, MSC)
• Savitzky-Golay + Multiplicative Scatter Correction (一阶导+多元散射校正, SGMSC)
• Vector Normalization (矢量归一化, VN)
• Standard Normal Variate transformation (标准正态变量变换, SNV)
• Eliminate Constant Offset (消除常数偏移量, ECO)
• Subtract Straight Line (减去一条直线, SSL)
• De-Trending (去趋势, DT)
• Min-Max Normalization (最小最大归一化, MMN)
• Savitzky-Golay (平滑与求导), SG
• Savitzky-Golay + SNV (一阶导+标准正态变量变换, SGSNV)
• SNV + DT (标准正态变量变换+去趋势, SNVDT)
• SG + SSL (一阶导+减去一条直线, SGSSL)
• Mean Centering (均值中心化, MC)
• Zscore Standardization (Zscore标准化, ZS)

Dependencies

• Python 3.11.5
• numpy 1.24.3
• scipy 1.11.1

Acknowledgement

• OPUS by Bruker
• Unscrambler by CAMO
• Pirouette by Infometrix
• PLS_Toolbox by Eigenvector

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