The {\em tensor power method} generalizes the matrix method to higher order arrays, or tensors. Like in case, fixed points of are eigenvectors tensor. While every real symmetric has an eigendecomposition, vectors generating a decomposition not always In this paper we show that whenever eigenvector is} generator tensor, then (if is sufficiently high) robust} , i.e., it attracting point method....

We analyze the eigenvectors of generalized Laplacian for two metric graphs occurring in practical applications. In accordance with random network theory, localization an eigenvector is rare and should be tuned to observe exactly localized eigenvectors. derive resonance conditions obtain various geometric configurations their combinations form more complicated resonant structures. These suggest ...

A method for object recognition and pose estimation for robotic bin picking is presented. The approach discussed is a variant on current approaches to eigenimage analysis. Compared to traditional approaches which use object geometry only (shape invariants), the implementation described uses the eigenspace determined by processing the eigenvalues and eigenvectors of the image set. The image set ...

We show that averaging eigenvectors of randomly sampled submatrices efficiently approximates the true eigenvectors of the original matrix under certain conditions on the incoherence of the spectral decomposition. This incoherence assumption is typically milder than those made in matrix completion and allows eigenvectors to be sparse. We discuss applications to spectral methods in dimensionality...

We extend the classical problem of predicting a sequence of outcomes from a finite alphabet to the matrix domain. In this extension, the alphabet of n outcomes is replaced by the set of all dyads, i.e. outer products uu> where u is a vector in R of unit length. Whereas in the classical case the goal is to learn (i.e. sequentially predict as well as) the best multinomial distribution, in the mat...

In this paper a new completely unsupervised mesh segmentation algorithm is proposed, which is based on the PCA interpretation of the Laplacian eigenvectors of the mesh and on parametric clustering using Gaussian mixtures. We analyse the geometric properties of these vectors and we devise a practical method that combines single-vector analysis with multiple-vector analysis. We attempt to charact...

By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the componentwise bounds for unitary factors upper triangular of generalized Schur decomposition. The diagonal elements invariant subspace are also derived. From former, present an bound a condition number eigenvalue. Furthermore, with numerical iterative method, nonlinear decompositio...