In this paper, we propose a novel video retrieval system using Generalized Eigenvalue Decomposition (GED). The system contains two major subsystems: database creation and database searching. In both subsystems, we propose new methods for shot-feature extraction, feature dimension transformation and feature similarity measuring base on GED. Experimental results confirm the effectiveness of our p...

1 Linear algebra 2 1.1 Inner product, norm, distance, and orthogonality . . . . . . . . . 2 1.2 Angle and inequality . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Vector projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Basics of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . ....

The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a speciied critical value.

A continuous wavelet transform, with Morlet wavelets as the basis functions, is used to map speech into the time-frequency domain. Forward and inverse FFT routines are used to implement the wavelet transforms. A coefficient covariance matrix is defined and an Eigenvalue decomposition is used to optimally determine significant wavelet based filters that accurately represent speech and potentiall...

The numerical calculation of traditional coherent-mode representations (CMRs) involves an eigenvalue decomposition of the cross-spectral density matrix. An efficient alternative modal representation of a partially coherent field can be realized using an LDL decomposition. Storage requirements are reduced by an amount on the order of the ratio between the coherence length and the source width. T...

We discuss a statistical model of social network data derived from matrix representations and symmetry considerations. The model can include known predictor information in the form of a regression term, and can represent additional structure via sender-specific and receiverspecific latent factors. This approach allows for the graphical description of a social network via the latent factors of t...

This paper proposes a new Bayesian non-parametric approach for clustering. It relies on an infinite Gaussian mixture model with a Chinese Restaurant Process (CRP) prior, and an eigenvalue decomposition of the covariance matrix of each cluster. The CRP prior allows to control the model complexity in a principled way and to automatically learn the number of clusters. The covariance matrix decompo...

Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing with the computational burden is via a tree decomposition of the output space. While this typically leads to training and inference that scales sublinearly with...

Spectral divide and conquer algorithms solve the eigenvalue problem by recursively computing an invariant subspace for a subset of the spectrum and using it to decouple the problem into two smaller subproblems. A number of such algorithms have been developed over the last forty years, often motivated by parallel computing and, most recently, with the aim of achieving minimal communication costs...

We present preliminary results of an ongoing project to develop codes of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems for hypre and PETSc software packages. hypre and PETSc provide high quality domain decomposition and multigrid preconditioning for parallel computers. Our LOBPCG implementation for hypre is publicly available in hy...