Transfer learning focuses on the reuse of supervised learning models in a new context. Prominent applications can be found in robotics, image processing or web mining. In these areas, learning scenarios change by nature, but often remain related and motivate the reuse of existing supervised models. While the majority of symmetric and asymmetric domain adaptation algorithms utilize all available source and target domain data, we show that domain adaptation requires only a substantial smaller subset. This makes it more suitable for real-world scenarios where target domain data is rare. The presented approach finds a target subspace representation for source and target data to address domain differences by orthogonal basis transfer. We employ Nystrom techniques and show the reliability of this approximation without a particular landmark matrix by applying post-transfer normalization. It is evaluated on typical domain adaptation tasks with standard benchmark data.
The polar decomposition @cite_7 is a universal decomposition applicable to an arbitrary matrix and is defined as @math . Where @math and @math with @math as singular values, @math and @math are left and right singular vectors respectively. If @math is a square matrix, the decomposition is unique and @math is orthogonal and a rotation matrix. @math is positive semi-definite and scaling factor of @math . then the eigenvectors and square root eigenvalues of @math are singular vectors and values of @math respectively. It is important to note that the spectral theorem is incorporated in Theorem , which in this context means that for the EVD and SVD are the same.
@cite_7
2088307891
A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed in practice.To add to the known best approximation property of the unitary polar factor, the Hermitian polar factor H of a nonsingular Hermitian matrix A is shown to be a good positive definite approximation to Aand @math is shown to be a best Hermitian positive semi-definite approximation to A. Perturbation bounds for the polar factors are derived.Applications of the polar decomposition to factor analysis, aerospace computations and optimisation are outlined; and a new method is derived for computing the square root of a symmetric positive definite matrix.