Related papers: Analysis of large sparse graphs using regular deco…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
Lifelong SLAM considers long-term operation of a robot where already mapped locations are revisited many times in changing environments. As a result, traditional graph-based SLAM approaches eventually become extremely slow due to the…
Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model, clusters are generally defined as cliques. However, such an approach might be too…
The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…
Component-centric distributed graph processing platforms that use a bulk synchronous parallel (BSP) programming model have gained traction. These address the short-comings of Big Data abstractions/platforms like MapReduce/Hadoop for…
Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a…