/// <summary>
/// Ridge回帰のパラメータ学習
/// </summary>
/// <param name="design_matrix_without_constant"></param>
/// <param name="target_y"></param>
/// <param name="alpha"></param>
/// <returns></returns>
public static double[,] RidgeLearn(double[,] design_matrix_without_constant, double[,] target_y, double alpha)
{
if (design_matrix_without_constant.GetLength(0) - target_y.GetLength(0) != 0)
{
throw new FormatException(nameof(design_matrix_without_constant) + "の行" + design_matrix_without_constant.GetLength(0) + "と、" + nameof(target_y) + "の行" + target_y.GetLength(0) + "が異なります。");
}
double[,] design_matrix_with_constant_1 = LinerRegression.AddConstant1(design_matrix_without_constant);
double[,] X_T = Matrix.Transpose(design_matrix_with_constant_1);
double[,] X_T_cross_X = Matrix.Multiply(X_T, design_matrix_with_constant_1);
double hyper_parameter = Math.Abs(alpha);
double[,] I = new double[X_T_cross_X.GetLength(0), X_T_cross_X.GetLength(0)];
for (int j = 0; j < X_T_cross_X.GetLength(0); j++)
{
I[j, j] = hyper_parameter;
}
double[,] X_T_cross_X_add_I = Matrix.Add(X_T_cross_X, I);
double[,] X_T_cross_X_Inverse = Matrix.Inverse(X_T_cross_X_add_I);
double[,] w = Matrix.Multiply(X_T_cross_X_Inverse, X_T);
w = Matrix.Multiply(w, target_y);
return(w);
}
/// <summary>
/// Lerning Liner_Regression .
/// Return w ( Colmun Vector )
/// </summary>
/// <param name="design_matrix_without_constant"></param>
/// <param name="column_vector_y"></param>
/// <returns></returns>
public static double[,] Learn(double[,] design_matrix_without_constant, double[,] column_vector_y)
{
if (design_matrix_without_constant.GetLength(0) - column_vector_y.GetLength(0) != 0)
{
throw new FormatException(nameof(design_matrix_without_constant) + "の行" + design_matrix_without_constant.GetLength(0) + "と、" + nameof(column_vector_y) + "の行" + column_vector_y.GetLength(0) + "が異なります。");
}
double[,] design_matrix_with_constant_1 = LinerRegression.AddConstant1(design_matrix_without_constant);
double[,] X_T = Matrix.Transpose(design_matrix_with_constant_1);
double[,] X_T_cross_X = Matrix.Multiply(X_T, design_matrix_with_constant_1);
double[,] X_T_cross_X_Inverse = Matrix.Inverse(X_T_cross_X);
double[,] w = Matrix.Multiply(X_T_cross_X_Inverse, X_T);
w = Matrix.Multiply(w, column_vector_y);
return(w);
}
/// <summary>
/// 線形回帰 X_T × w ( w : Colmun_Vector )
/// </summary>
/// <param name="row_Vector_or_Design_Matrix_without_Constant"></param>
/// <param name="columnVector_w"></param>
/// <returns></returns>
public static double[,] Regression(double[,] row_Vector_or_Design_Matrix_without_Constant, double[,] columnVector_w)
{
double[,] row_vector_or_design_matrix_with_constant_1 = LinerRegression.AddConstant1(row_Vector_or_Design_Matrix_without_Constant);
return(Matrix.Multiply(row_vector_or_design_matrix_with_constant_1, columnVector_w));
}