40,848 research outputs found
A smart local moving algorithm for large-scale modularity-based community detection
We introduce a new algorithm for modularity-based community detection in
large networks. The algorithm, which we refer to as a smart local moving
algorithm, takes advantage of a well-known local moving heuristic that is also
used by other algorithms. Compared with these other algorithms, our proposed
algorithm uses the local moving heuristic in a more sophisticated way. Based on
an analysis of a diverse set of networks, we show that our smart local moving
algorithm identifies community structures with higher modularity values than
other algorithms for large-scale modularity optimization, among which the
popular 'Louvain algorithm' introduced by Blondel et al. (2008). The
computational efficiency of our algorithm makes it possible to perform
community detection in networks with tens of millions of nodes and hundreds of
millions of edges. Our smart local moving algorithm also performs well in small
and medium-sized networks. In short computing times, it identifies community
structures with modularity values equally high as, or almost as high as, the
highest values reported in the literature, and sometimes even higher than the
highest values found in the literature
What is the Minimal Systemic Risk in Financial Exposure Networks?
Management of systemic risk in financial markets is traditionally associated
with setting (higher) capital requirements for market participants. There are
indications that while equity ratios have been increased massively since the
financial crisis, systemic risk levels might not have lowered, but even
increased. It has been shown that systemic risk is to a large extent related to
the underlying network topology of financial exposures. A natural question
arising is how much systemic risk can be eliminated by optimally rearranging
these networks and without increasing capital requirements. Overlapping
portfolios with minimized systemic risk which provide the same market
functionality as empirical ones have been studied by [pichler2018]. Here we
propose a similar method for direct exposure networks, and apply it to
cross-sectional interbank loan networks, consisting of 10 quarterly
observations of the Austrian interbank market. We show that the suggested
framework rearranges the network topology, such that systemic risk is reduced
by a factor of approximately 3.5, and leaves the relevant economic features of
the optimized network and its agents unchanged. The presented optimization
procedure is not intended to actually re-configure interbank markets, but to
demonstrate the huge potential for systemic risk management through rearranging
exposure networks, in contrast to increasing capital requirements that were
shown to have only marginal effects on systemic risk [poledna2017]. Ways to
actually incentivize a self-organized formation toward optimal network
configurations were introduced in [thurner2013] and [poledna2016]. For
regulatory policies concerning financial market stability the knowledge of
minimal systemic risk for a given economic environment can serve as a benchmark
for monitoring actual systemic risk in markets.Comment: 25 page
Online unit clustering in higher dimensions
We revisit the online Unit Clustering and Unit Covering problems in higher
dimensions: Given a set of points in a metric space, that arrive one by
one, Unit Clustering asks to partition the points into the minimum number of
clusters (subsets) of diameter at most one; while Unit Covering asks to cover
all points by the minimum number of balls of unit radius. In this paper, we
work in using the norm.
We show that the competitive ratio of any online algorithm (deterministic or
randomized) for Unit Clustering must depend on the dimension . We also give
a randomized online algorithm with competitive ratio for Unit
Clustering}of integer points (i.e., points in , , under norm). We show that the competitive ratio of
any deterministic online algorithm for Unit Covering is at least . This
ratio is the best possible, as it can be attained by a simple deterministic
algorithm that assigns points to a predefined set of unit cubes. We complement
these results with some additional lower bounds for related problems in higher
dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA
2017
Multi-objective model for optimizing railway infrastructure asset renewal
Trabalho inspirado num problema real da empresa Infraestruturas de Portugal, EP.A multi-objective model for managing railway infrastructure asset renewal is presented. The model aims to optimize three objectives, while respecting operational constraints: levelling investment throughout multiple years, minimizing total cost and minimizing work start postponements. Its output is an optimized intervention schedule. The model is based on a case study from a Portuguese infrastructure management company, which specified the objectives and constraints, and reflects management practice on railway infrastructure. The results show that investment levelling greatly influences the other objectives and that total cost fluctuations may range from insignificant to important, depending on the condition of the infrastructure. The results structure is argued to be general and suggests a practical methodology for analysing trade-offs and selecting a solution for implementation.info:eu-repo/semantics/publishedVersio
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
This paper proposes scalable and fast algorithms for solving the Robust PCA
problem, namely recovering a low-rank matrix with an unknown fraction of its
entries being arbitrarily corrupted. This problem arises in many applications,
such as image processing, web data ranking, and bioinformatic data analysis. It
was recently shown that under surprisingly broad conditions, the Robust PCA
problem can be exactly solved via convex optimization that minimizes a
combination of the nuclear norm and the -norm . In this paper, we apply
the method of augmented Lagrange multipliers (ALM) to solve this convex
program. As the objective function is non-smooth, we show how to extend the
classical analysis of ALM to such new objective functions and prove the
optimality of the proposed algorithms and characterize their convergence rate.
Empirically, the proposed new algorithms can be more than five times faster
than the previous state-of-the-art algorithms for Robust PCA, such as the
accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms
achieve higher precision, yet being less storage/memory demanding. We also show
that the ALM technique can be used to solve the (related but somewhat simpler)
matrix completion problem and obtain rather promising results too. We further
prove the necessary and sufficient condition for the inexact ALM to converge
globally. Matlab code of all algorithms discussed are available at
http://perception.csl.illinois.edu/matrix-rank/home.htmlComment: Please cite "Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized
Alternating Direction Method with Adaptive Penalty for Low Rank
Representation, NIPS 2011." (available at arXiv:1109.0367) instead for a more
general method called Linearized Alternating Direction Method This manuscript
first appeared as University of Illinois at Urbana-Champaign technical report
#UILU-ENG-09-2215 in October 2009 Zhouchen Lin, Risheng Liu, and Zhixun Su,
Linearized Alternating Direction Method with Adaptive Penalty for Low Rank
Representation, NIPS 2011. (available at http://arxiv.org/abs/1109.0367
- …