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List: kde-commits
Subject: kdesupport/eigen2/Eigen/src/Regression
From: Gael Guennebaud <g.gael () free ! fr>
Date: 2008-08-22 0:09:47
Message-ID: 1219363787.068873.325.nullmailer () svn ! kde ! org
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SVN commit 850674 by ggael:
Reimplement fitHyperplane such that the fit is done in a total LS sense
(use eigen decomposition).
Added optional feedback on the stability of the actual fit (think about fitting a 3D plane
on data lying on a line...)
M +28 -28 Regression.h
--- trunk/kdesupport/eigen2/Eigen/src/Regression/Regression.h #850673:850674
@@ -145,54 +145,54 @@
* Thus, the vector \a retCoefficients has size \f$n+1\f$, which is another
* difference from linearRegression().
*
- * This functions proceeds by first determining which coord has the smallest variance,
- * and then calls linearRegression() to express that coord as a function of the other ones.
+ * In practice, this function performs an hyper-plane fit in a total least square sense
+ * via the following steps:
+ * 1 - center the data to the mean
+ * 2 - compute the covariance matrix
+ * 3 - pick the eigenvector corresponding to the smallest eigenvalue of the covariance matrix
+ * The ratio of the smallest eigenvalue and the second one gives us a hint about the relevance
+ * of the solution. This value is optionally returned in \a soundness.
*
* \sa linearRegression()
*/
template<typename VectorType, typename BigVectorType>
void fitHyperplane(int numPoints,
VectorType **points,
- BigVectorType *result)
+ BigVectorType *result,
+ typename NumTraits<typename VectorType::Scalar>::Real* soundness = 0)
{
typedef typename VectorType::Scalar Scalar;
+ typedef Matrix<Scalar,VectorType::SizeAtCompileTime,VectorType::SizeAtCompileTime> CovMatrixType;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(BigVectorType)
ei_assert(numPoints >= 1);
int size = points[0]->size();
ei_assert(size+1 == result->size());
- // now let's find out which coord varies the least. This is
- // approximative. All that matters is that we don't pick a coordinate
- // that varies orders of magnitude more than another one.
- VectorType mean(size);
- Matrix<typename NumTraits<Scalar>::Real,
- VectorType::RowsAtCompileTime, VectorType::ColsAtCompileTime,
- VectorType::MaxRowsAtCompileTime, VectorType::MaxColsAtCompileTime
- > variance(size);
- mean.setZero();
- variance.setZero();
+ // compue the mean of the data
+ VectorType mean = VectorType::Zero(size);
for(int i = 0; i < numPoints; i++)
mean += *(points[i]);
mean /= numPoints;
- for(int j = 0; j < size; j++)
+
+ // compute the covariance matrix
+ CovMatrixType covMat = CovMatrixType::Zero(size, size);
+ VectorType remean = VectorType::Zero(size);
+ for(int i = 0; i < numPoints; i++)
{
- for(int i = 0; i < numPoints; i++)
- variance.coeffRef(j) += ei_abs2(points[i]->coeff(j) - mean.coeff(j));
+ VectorType diff = (*(points[i]) - mean).conjugate();
+ covMat += diff * diff.adjoint();
}
+
+ // now we just have to pick the eigen vector with smallest eigen value
+ SelfAdjointEigenSolver<CovMatrixType> eig(covMat);
+ result->start(size) = eig.eigenvectors().col(0);
+ if (soundness)
+ *soundness = eig.eigenvalues().coeff(0)/eig.eigenvalues().coeff(1);
- int coord_min_variance;
- variance.minCoeff(&coord_min_variance);
-
- // let's now perform a linear regression with respect to that
- // not-too-much-varying coord
- VectorType affine(size);
- linearRegression(numPoints, points, &affine, coord_min_variance);
-
- if(coord_min_variance>0)
- result->start(coord_min_variance) = affine.start(coord_min_variance);
- result->coeffRef(coord_min_variance) = static_cast<Scalar>(-1);
- result->end(size-coord_min_variance) = affine.end(size-coord_min_variance);
+ // let's compute the constant coefficient such that the
+ // plane pass trough the mean point:
+ result->coeffRef(size) = - (result->start(size).cwise()* mean).sum();
}
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