Related papers: Survey Propagation as local equilibrium equations
We study the task of finding good local optima in combinatorial optimization problems. Although combinatorial optimization is NP-hard in general, locally optimal solutions are frequently used in practice. Local search methods however…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
In this paper, we propose the first of its kind space-time dual-pairing summation by parts (DP-SBP) numerical framework for forward and adjoint wave propagation problems. This novel approach enables us to achieve spatial and temporal high…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
We introduce a principled and theoretically sound spectral method for $k$-way clustering in signed graphs, where the affinity measure between nodes takes either positive or negative values. Our approach is motivated by social balance…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions,…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation,…
Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…
The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased…