Diffusion tensor imaging (DTI) data differ from most medical images in that values at each voxel are not scalars, but 3×3 symmetric positive definite matrices called diffusion tensors (DTs). The anatomic characteristics of the tissue at each voxel are reflected by the DT eigenvalues and eigenvectors. In this article we consider the problem of testing whether the means of two groups of DT images...

A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalues and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved ...

A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

Spatial-correlation properties of the wave functions (eigenvectors) of a spin-one eigenproblem for dipole interaction is studied for random geometries of the underlying system. This problem describes, in particular, polar excitations (“plasmons”) of large clusters. In contrast to Berry’s conjecture of quantum chaos for massive particles, we have found long-range spatial correlations for wave fu...

The ability of humans to perceive the spatial orientation of an occluded arm was investigated. It was hypothesized that this ability is tied to the arm's inertial eigenvectors, invariant mechanical parameters corresponding to a limb's axes of rotational symmetry. By breaking the coincidence between the eigenvectors of the arm and its longitudinal axis, 3 experiments were directed at the possibi...

A new method for speech signal reconstruction is proposed by performing a nonlinear Kernel Principal Component Analysis (KPCA). By the use of kernel functions, one can efficiently compute principal components in high-dimensional feature spaces, and reconstruct vectors mapping from input space by those dominant principal components. As the reconstructed vectors is expressed in high dimensional f...

G. Birkhoff [l] and H. Samelson [4] have shown that a means of solving problems concerning the existence and uniqueness of eigenvectors of positive operators is given by introducing a suitable metric on a subset of the cone with respect to which the operators are contractions. More specifically, they have proved the Perron theorem for matrices with positive elements by intersecting the positive...

In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspac...

This part describes the results obtained in the simulations and experiments reported in the previous sessions of this report. A) Statistical comparison of the principal component analysis in various spaces The cumulative contributions of the eigenvectors in each space are summarized for multiple-of-three numbers of eigenvectors in Tables I to III. Table I. Cumulative contribution of the eigenve...

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing ...