const MatrixX& Jacobian::GetNullspace()
{
if(computeNullSpace_)
{
computeNullSpace_ = false;
/*jacobianInverseNoDls_ = jacobian_;
PseudoInverse(jacobianInverseNoDls_); // tmp while figuring out how to chose lambda*/
//ComputeSVD();
MatrixX id = MatrixX::Identity(jacobian_.cols(), jacobian_.cols());
ComputeSVD();
//Eigen::JacobiSVD<MatrixX> svd(jacobian_, Eigen::ComputeThinU | Eigen::ComputeThinV);
MatrixX res = MatrixX::Zero(id.rows(), id.cols());
for(int i =0; i < svd_.matrixV().cols(); ++ i)
{
VectorX v = svd_.matrixV().col(i);
res += v * v.transpose();
}
Identitymin_ = id - res;
//Identitymin_ = id - (jacobianInverseNoDls_* jacobian_);
}
return Identitymin_;
}
TYPED_TEST(TestSecondOrderMultinomialLogisticRegression, MinimizerOverfitSmall) {
MatrixX<TypeParam> X(2, 10);
VectorXi y(10);
X << 0.6097662 , 0.53395565, 0.9499446 , 0.67289898, 0.94173948,
0.56675891, 0.80363783, 0.85303565, 0.15903886, 0.99518533,
0.41655682, 0.29256121, 0.36103228, 0.29899503, 0.4957268 ,
-0.04277318, -0.28038614, -0.12334621, -0.17497722, 0.1492248;
y << 0, 0, 0, 0, 0, 1, 1, 1, 1, 1;
std::vector<MatrixX<TypeParam> > X_var;
for (int i=0; i<10; i++) {
//X_var.push_back(MatrixX<TypeParam>::Random(2, 2).array().abs() * 0.01);
//X_var.push_back(MatrixX<TypeParam>::Zero(2, 2));
VectorX<TypeParam> a = VectorX<TypeParam>::Random(2).array() * 0.01;
X_var.push_back(
a * a.transpose()
);
}
SecondOrderLogisticRegressionApproximation<TypeParam> mlr(X, X_var, y, 0);
MatrixX<TypeParam> eta = MatrixX<TypeParam>::Zero(2, 3);
GradientDescent<SecondOrderLogisticRegressionApproximation<TypeParam>, MatrixX<TypeParam>> minimizer(
std::make_shared<
ArmijoLineSearch<
SecondOrderLogisticRegressionApproximation<TypeParam>,
MatrixX<TypeParam>
>
>(),
[](TypeParam value, TypeParam gradNorm, size_t iterations) {
return iterations < 5000;
}
);
minimizer.minimize(mlr, eta);
EXPECT_GT(0.1, mlr.value(eta));
}