MATLAB和C#（Accord.NET）中的PLS回归系数

我试图在C#中执行偏最小二乘回归分析。在MATLAB中执行的pls技术使用SIMPLS算法，该算法提供了beta（回归系数矩阵）

• 我不明白为什么两种情况下矩阵都不同，我将输入传递到C版本的方式是否有错误

• 此外，两者的输入是相同的，并且参考了此处包含的文件

最小工作示例：

MATLAB：遵循HervéAbdi的小示例（HervéAbdi，偏最小二乘回归）。参考资料：

雅阁网：

double[][] inputs = new double[][]
    {
        //      Wine | Price | Sugar | Alcohol | Acidity
        new double[] {   7,     7,      13,        7 },
        new double[] {   4,     3,      14,        7 },
        new double[] {  10,     5,      12,        5 },
        new double[] {  16,     7,      11,        3 },
        new double[] {  13,     3,      10,        3 },
    };

double[][] outputs = new double[][]
    {
        //             Wine | Hedonic | Goes with meat | Goes with dessert
        new double[] {           14,          7,                 8 },
        new double[] {           10,          7,                 6 },
        new double[] {            8,          5,                 5 },
        new double[] {            2,          4,                 7 },
        new double[] {            6,          2,                 4 },
    };

var pls = new PartialLeastSquaresAnalysis()
        {
            Method = AnalysisMethod.Center,
            Algorithm = PartialLeastSquaresAlgorithm.NIPALS
        };

var regression = pls.Learn(inputs, outputs);

double[][] coeffs = regression.Weights;
>>
-1.69811320754717 -0.0566037735849056   0.0707547169811322
1.27358490566038   0.29245283018868     0.571933962264151
-4                 1                    0.5
1.17924528301887   0.122641509433962    0.159198113207547

---

我认为在调用MATLAB和Accord.NET版本PLS的方式之间至少存在三个差异

正如您所提到的，MATLAB使用的是SIMPLS。然而，Accord.NET被告知使用NIPALS

MATLAB版本被称为plsregress（输入、输出，1），这意味着回归计算只考虑PLS中的一个潜在成分，但Accord.NET没有指示您这样做

Accord.NET返回一个多变量回归对象，该对象包含权重矩阵和截距向量，而MATLAB将截距作为权重矩阵的第一列返回

一旦考虑到所有这些因素，就可以生成与MATLAB版本完全相同的结果：

double[][] inputs = new double[][]
{
    //      Wine | Price | Sugar | Alcohol | Acidity
    new double[] {   7,     7,      13,        7 },
    new double[] {   4,     3,      14,        7 },
    new double[] {  10,     5,      12,        5 },
    new double[] {  16,     7,      11,        3 },
    new double[] {  13,     3,      10,        3 },
};

double[][] outputs = new double[][]
{
    //             Wine | Hedonic | Goes with meat | Goes with dessert
    new double[] {           14,          7,                 8 },
    new double[] {           10,          7,                 6 },
    new double[] {            8,          5,                 5 },
    new double[] {            2,          4,                 7 },
    new double[] {            6,          2,                 4 },
};

// Create the Partial Least Squares Analysis
var pls = new PartialLeastSquaresAnalysis()
{
    Method = AnalysisMethod.Center,
    Algorithm = PartialLeastSquaresAlgorithm.SIMPLS, // First change: use SIMPLS
};

// Learn the analysis
pls.Learn(inputs, outputs);

// Second change: Use just 1 latent factor/component
var regression = pls.CreateRegression(factors: 1);

// Third change: present results as in MATLAB
double[][] w = regression.Weights.Transpose();
double[] b = regression.Intercepts;

// Add the intercepts as the first column of the matrix of
// weights and transpose it as in the way MATLAB presents it
double[][] coeffs = (w.InsertColumn(b, index: 0)).Transpose();

// Show results in MATLAB format
string str = coeffs.ToOctave();

随着这些变化，上述系数矩阵应变为

[ 10.4844779770616    6.18986077674717    6.28413863347486    ;
  -0.634878923091644 -0.304054829845448  -0.0726082626993539  ;
   0.0219492754418065 0.0105118991463605  0.00251024045589416 ;
   0.192261724966225  0.0920775662006966  0.0219881135215502  ; 
   0.289484835410222  0.13863944631343    0.033107085796122   ]

[ 10.4844779770616    6.18986077674717    6.28413863347486    ;
  -0.634878923091644 -0.304054829845448  -0.0726082626993539  ;
   0.0219492754418065 0.0105118991463605  0.00251024045589416 ;
   0.192261724966225  0.0920775662006966  0.0219881135215502  ; 
   0.289484835410222  0.13863944631343    0.033107085796122   ]