Belief Propagation and Spectral Methods Belief Propagation and Spectral Methods
نویسندگان
چکیده
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 with the largest eigenvalue used by some spectral method for the Bisection problem. We then show that the thresholding helps to improve an approximate solution (by the spectral method) to the exact solution. Through our analysis, we prove that, at least for the Bisection problem, the belief propagation can be regarded as a unified spectral type algorithm for obtaining the exact solution with high probability.
منابع مشابه
Comparative Study for Inference of Hidden Classes in Stochastic Block Models
Inference of hidden classes in stochastic block model is a classical problem with important applications. Most commonly used methods for this problem involve näıve mean field approaches or heuristic spectral methods. Recently, belief propagation was proposed for this problem. In this contribution we perform a comparative study between the three methods on synthetically created networks. We show...
متن کاملPairwise Clustering and Graphical Models
Significant progress in clustering has been achieved by algorithms that are based on pairwise affinities between the datapoints. In particular, spectral clustering methods have the advantage of being able to divide arbitrarily shaped clusters and are based on efficient eigenvector calculations. However, spectral methods lack a straightforward probabilistic interpretation which makes it difficul...
متن کاملMixture Modeling by Affinity Propagation
Clustering is a fundamental problem in machine learning and has been approached in many ways. Two general and quite different approaches include iteratively fitting a mixture model (e.g., using EM) and linking together pairs of training cases that have high affinity (e.g., using spectral methods). Pair-wise clustering algorithms need not compute sufficient statistics and avoid poor solutions by...
متن کاملLearning and Inferring Image Segmentations using the GBP Typical Cut Algorithm
Significant progress in image segmentation has been made by viewing the problem in the framework of graph partitioning. In particular, spectral clustering methods such as “normalized cuts” (ncuts) can efficiently calculate good segmentations using eigenvector calculations. However, spectral methods when applied to images with local connectivity often oversegment homogenous regions. More importa...
متن کاملGaussian Belief with dynamic data and in dynamic network
In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol (“Consensus Propagation”, Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averag...
متن کامل