Spectral methods

Belief Propagation and Spectral Methods Belief Propagation and Spectral Methods

We investigate an algorithm derived based on the belief propagation method of Pearl [11] applied to the (Min-)Bisection problem under the standard planted solution model (or more precisely the Most Likely Partition problem under the same planted solution model). We first point out that the algorithm (without thresholding) is nothing but the standard power method for computing an eigenvector wit...

Directed Spectral Methods Definition

Directed spectral measures quantify, in the frequency domain, directed statistical interactions between time-series variables. Most commonly, the various measures are computed based on a (linear) multi-variate autoregressive (MVAR) model of the data. The various methods quantify in different ways the strength of interaction terms in the Fourier transform of the MVAR model. While these methods a...

Spectral Projected Gradient Methods

The poor practical behavior of (1)-(2) has been known for many years. If the level sets of f resemble long valleys, the sequence {xk} displays a typical zig-zagging trajectory and the speed of convergence is very slow. In the simplest case, in which f is a strictly convex quadratic, the method converges to the solution with a Q-linear rate of convergence whose factor tends to 1 when the conditi...

Advanced Spectral Analysis Methods

The purpose of time-series analysis is to detect basic properties of the system that engenders a time series. The hope of predicting the system's future evolution is closely related to the possibility of such detection. The most easily predictable components of a system's evolution are the regular, deterministic ones; hence we look for trends and periodic oscillations. In doing so, it is often ...

Sparse Grid Spectral Methods