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Ilya Safro

Publications and source records attributed to Ilya Safro.

100 records · Page 6Linked to original sources
arXiv2014

Fast Multilevel Support Vector Machines

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training set in one optimization process, the support vectors are obtained and gradually refined at multiple levels of coarseness of the data. The proposed framework includes: (a) construction of hierarchy of large-scale data coarse representations, and (b) a local processing of updating the hyperplane throughout this hierarchy. Our multilevel framework substantially improves the computational time without loosing the quality of classifiers. The algorithms are demonstrated for both regular and weighted support vector machines. Experimental results are presented for balanced and imbalanced classification problems. Quality improvement on several imbalanced data sets has been observed.

stat.ML↗
arXiv2013

A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators

The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size. Recently, Hager and Hungerford [1] developed a continuous bilinear programming formulation of the VSP. In this paper, we reinforce the bilinear programming approach with a multilevel scheme for learning the structure of the graph.

cs.DS↗
arXiv2012

Multiscale Network Generation

Networks are widely used in science and technology to represent relationships between entities, such as social or ecological links between organisms, enzymatic interactions in metabolic systems, or computer infrastructure. Statistical analyses of networks can provide critical insights into the structure, function, dynamics, and evolution of those systems. However, the structures of real-world networks are often not known completely, and they may exhibit considerable variation so that no single network is sufficiently representative of a system. In such situations, researchers may turn to proxy data from related systems, sophisticated methods for network inference, or synthetic networks. Here, we introduce a flexible method for synthesizing realistic ensembles of networks starting from a known network, through a series of mappings that coarsen and later refine the network structure by randomized editing. The method, MUSKETEER, preserves structural properties with minimal bias, including unknown or unspecified features, while introducing realistic variability at multiple scales. Using examples from several domains, we show that MUSKETEER produces the intended stochasticity while achieving greater fidelity across a suite of network properties than do other commonly used network generation algorithms.

cs.DM↗
arXiv2012

Fast Response to Infection Spread and Cyber Attacks on Large-Scale Networks

We present a strategy for designing fast methods of response to cyber attacks and infection spread on complex weighted networks. In these networks, nodes can be interpreted as primitive elements of the system, and weighted edges reflect the strength of interaction among these elements. The proposed strategy belongs to the family of multiscale methods whose goal is to approximate the system at multiple scales of coarseness and to obtain a solution of microscopic scale by combining the information from coarse scales. In recent years these methods have demonstrated their potential for solving optimization and analysis problems on large-scale networks. We consider an optimization problem that is based on the SIS epidemiological model. The objective is to detect the network nodes that have to be immunized in order to keep a low level of infection in the system.

cs.SI↗
arXiv2012

Advanced Coarsening Schemes for Graph Partitioning

The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.

cs.DS↗
arXiv2010

Multiscale approach for the network compression-friendly ordering

We present a fast multiscale approach for the network minimum logarithmic arrangement problem. This type of arrangement plays an important role in a network compression and fast node/link access operations. The algorithm is of linear complexity and exhibits good scalability which makes it practical and attractive for using on large-scale instances. Its effectiveness is demonstrated on a large set of real-life networks. These networks with corresponding best-known minimization results are suggested as an open benchmark for a research community to evaluate new methods for this problem.

cs.DS↗
arXiv2010

Relaxation-based coarsening and multiscale graph organization

In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at each coarser level. We demonstrate the use of this measure in multiscale methods for several important combinatorial optimization problems and discuss the multiscale graph organization.

cs.DS↗
arXiv2009

A Measure of the Connection Strengths between Graph Vertices with Applications

We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the convergence property, we propose a mutually reinforcing model to explain the intuition behind the strategy. The practical effectiveness of this measure is demonstrated through several combinatorial optimization problems on graphs and hypergraphs.

cs.DM↗
arXiv2009

A Fast Multigrid Algorithm for Energy Minimization Under Planar Density Constraints

The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving correction to this problem. The method is demonstrated on various graph drawing (visualization) instances.

cs.DS↗