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...

This paper focuses on obtaining clustering information in a distribution when iid data are given. First, we develop theoretical results for understanding and using clustering information contained in the eigenvectors of data adjacency matrices based on a radial kernel function (with a sufficiently fast tail decay). We provide population analyses to give insights into which eigenvectors should b...

In this paper, we study the asymptotic behavior of extreme eigenvalues and eigenvectors high-dimensional spiked sample covariance matrices, in supercritical case when a reliable detection spikes is possible. particular, derive joint distribution generalized components associated eigenvectors, that is, projections onto arbitrary given direction, assuming dimension size are comparably large. gene...

We present an automatic mesh segmentation framework, which achieves 3D segmentation in two stages, comprising hierarchical spectral analysis and isolinebased boundary detection. During hierarchical spectral analysis, a novel single segmentation field is defined to capture concavity-aware decompositions of eigenvectors from a concavity-aware Laplacian. Specifically, on the eigenvector hierarchy,...

This paper presents and analyzes a new algorithm for computing eigenvectors of symmetric tridiagonal matrices factored as LDLt, with D diagonal and L unit bidiagonal. If an eigenpair is well behaved in a certain sense with respect to the factorization, the algorithm is shown to compute an approximate eigenvector which is accurate to working precision. As a consequence, all the eigenvectors comp...

In this paper, we focus on differential privacy preserving spectral graph analysis. Spectral graph analysis deals with the analysis of the spectra (eigenvalues and eigenvector components) of the graph’s adjacency matrix or its variants. We develop two approaches to computing the ε-differential eigen decomposition of the graph’s adjacency matrix. The first approach, denoted as LNPP, is based on ...

Spectral Clustering has reached a wide level of diffusion among unsupervised learning applications. Despite its practical success we believe that for a correct usage one has to face a difficult problem: given a target number of classes K the optimal K-dimensional subspace is not necessarily spanned by the first K eigenvectors of the graph Normalized Laplacian. The contribution of this paper is ...