Shot boundary detection is the first step of the video analysis, summarization and retrieval. In this paper, we propose a novel shot boundary detection algorithm using Generalized Eigenvalue Decomposition (GED) and modeling of gradual transitions by Gaussian functions. Especially, we focus on the challenges of detecting the gradual shots and extracting appropriate spatio-temporal features, whic...

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of bivariate phase synchronization strength. The resulting method is able to identify clusters of synchronized oscillators, and to quantify their strength as wel...

This paper is focused on estimators, both batch and adaptive, of the eigenvalue decomposition (EVD) of centrosymmetric (CS) covariance matrices. These estimators make use of the property that eigenvectors and eigenvalues of such structured matrices can be estimated via two decoupled eigensystems. As a result, the number of operations is roughly halved, and moreover, the statistical properties o...

To find the position of an acoustic source in a room, the relative delay between two (or more) microphone signals for the direct sound must be determined. The generalized cross-correlation method is the most popular technique to do so and is well explained in a landmark paper by Knapp and Carter. In this paper, a new approach is proposed that is based on eigenvalue decomposition. Indeed, the ei...

The simple Lanczos process is very eeective for nding a few extreme eigenvalues of a large symmetric matrix. The main task in each iteration step consists in evaluating a matrix-vector product. It is shown in this paper how to apply a fast wavelet-based product in order to speed up computations. Some numerical results are given for the simple case of the Harmonic Oscillator.

We study domain decomposition methods for fourth-order plate problems. The well-known von K arm an equations are used as our model problem. By exploiting the symmetry of the domain, the solution of the original problem can be obtained by solving those associated reduced problems, which are defined on subdomains with appropriate boundary conditions. We show how nonoverlapping and overlapping dom...

In this paper, we address the problem of adaptive eigenvalue decomposition (EVD). We propose a new approach, based on the optimization of the log-likelihood criterion. The parameters of the log-likelihood to be estimated are the eigenvectors and the eigenvalues of the data covariance matrix. They are actualized by means of a stochastic algorithm that requires little computational cost. Furtherm...

Sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis and sparse canonical correlation analysis. However, this problem is difficult to solve since it is NP-hard. In this paper, we consider a new decomposition method to tackle this problem. Specifically, we us...

The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each can be called a binary matrix) eigenvalues whose negatives $-\lambda = c$ give periodic orbits under the iteration, namely $z_k z_{k-1}^2+c$ with $z_0=0$, are thus contained in set. By Perron--Frobenius theorem, dominant real positive eigenvalue, wh...