the fifth international conference on network analysis net
Post on 28-May-2022
1 Views
Preview:
TRANSCRIPT
The Fifth International Conference on
Network Analysis NET 2015
May 18-20, 2015
Laboratory of Algorithms and Technologies for Networks Analysis
(LATNA),
National Research University Higher School of Economics, Nizhny
Novgorod, Russia
2 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Monday, May 18
Room 209 HSE, 136 Rodionova Str.
09:00-09:30 Registration
09:30-10:00 Panos M. Pardalos
The Fifth International Conference on Network Analysis NET 2015
10:00-10:50 Fedor Fomin
Graph Modification Problems: A modern perspective
10:50-11:10 Coffee Break
11:10-12:00 Konstantin Avratchenkov
Graph-based semi-supervised learning methods
12:00-13:00 Session 1
Liudmila Ostroumova Prokhorenkova
Global clustering coefficient in scale-free networks
Alexander Krot
Local clustering coefficient in preferential attachment graphs
Akmaljon Artikov
Factorization threshold models for scale-free networks generation
13:00-14:30 Lunch Break
14:30-15:20 Alexander Kononov
Energy-Efficient Scheduling problems
15:20-15:40 Coffee Break
15:40-16:40 Session 2
Dmitriy Malyshev
A complexity dichotomy and a new boundary class for the dominating set problem
Anna Pirova
Parallel algorithm of graph ordering for minimizing sparse Cholesky factor fill-in
The Fifth International Conference on Network Analysis 3
Margarita Pankratova
Hybrid methods for mapping a parallel program onto computing network
16:40-17:00 Coffee Break
17:00-18:00 Session 3
Andrey Murashov
The text network analysis: What does strategic documentation tell us about regional integration?
Alexander Semenov
Threshold selection for pseudo-bimodal networks of retweets via different metrics of network
centrality
Sergey Bastrakov
An Algorithm for Constraint/Generator Removal from Double Description of Polyhedra
4 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Tuesday, May 19
Room 209 HSE, 136 Rodionova Str.
09:30-10:20 Oleg Prokopyev
Finding maximum subgraphs with relatively large vertex connectivity
10:20-10:40 Coffee Break
10:40-11:30 Oleg Burdakov
A bi-criteria approach to solving huge hop-constrained Steiner tree problems
11:30-12:30 Session 4
Yury Maximov
Improved polynomial time approximation guarantees for well structured quadratic optimization
problems
Theodore Trafalis
Kernel methods in Natural Gas Storage Valuation
Dmitry Zhelonkin
Sentiment Analysis in Russian Social Networks
12:30-14:00 Lunch Break
14:00-14:50 Andrey Leonidov
Network effects in economics and finance
14:50-15:10 Coffee Break
15:10-16:10 Session 5
Mario R. Guarracino
On Laplacian regularization for generalized eigenvalue classifiers
Artem Ryblov
Network analysis of Mass spectroscopy medical data
Alexander Karsakov
Network analysis of methylation data for cancer diagnostics
16:10-16:30 Coffee Break
The Fifth International Conference on Network Analysis 5
16:30-17:30 Session 6
Alexandr Maximenko
Comparing Complexity of Combinatorial Polytopes
Dmitry Mokeev
König graphs for 4-path. Full description
Dmitry Gribanov
Integer programming in simplices
6 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Wednesday, May 20
Room 209 HSE, 136 Rodionova Str.
10:00-10:50 Andrey Raigorodskii
Small Subgraphs in Preferential Attachment Networks
10:50-11:10 Coffee Break
11:10-12:30 Session 7
Dima Kamzolov
Computationally efficient PageRank algorithm exploting graph sparsity
Irina Utkina
Branch and bound algorithm for cell formation problem
Alexander Gasnikov
Semi-Supervised PageRank Model Learning with Gradient-Free Optimization Methods
Alexander Gagloev
Sparsity and randomization based techniques in huge scale traffic matrix estimation problems
12:30-14:00 Lunch Break
14:00-14:50 Nelly Litvak
Ranking in large scale-free networks
14:50-15:10 Coffee Break
15:10-16:10 Session 8
Alexander Nikolaev
Bayesian Evidence Cascades and Seed-Initiated Marketing Campaigns in Social Networks
Petr Koldanov
Identification of concentration graph in Gaussian graphical model
Alexey Kazakov
Dynamics of the ensemble of inhibitory coupled neuron-like Rulkov map
The Fifth International Conference on Network Analysis 7
Graph Modification Problems: A modern perspective
Fedor Fomin
Bergen University, Norway and St Petersburg department of Steklov Mathematical
Institute
In network (or graph) modifications problem we have to modify (repair, improve, or
adjust) a network to satisfy specific required properties while keeping the cost of the
modification to the minimum. The commonly adapted mathematical model in the study
of network problems is the graph modification problem. This is a fundamental unifying
problem with a tremendous number of applications in various disciplines like machine
learning, networking, sociology, data mining, computational biology, computer vision,
and numerical analysis, and many others.
In this talk we give an overview of recent results and techniques in parameterized
algorithms for graph modification problems.
8 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Graph-based semi-supervised learning methods
Konstantin Avratchenkov
INRIA, France
Semi-supervised learning methods constitute a category of machine learning methods
which use labelled points together with the similarity graph for classification of data
points into predefined classes. For each class a semi-supervised method provides a
classification function. The main idea of the semi-supervised methods is based on the
assumption that the classification function should change smoothly over the similarity
graph. This idea can be formulated as an optimization problem. Some particularly well
known semi-supervised learning methods are the Standard Laplacian (or transductive
learning) method and the Normalized Laplacian (or diffusion kernel) method. Different
semi-supervised learning methods have different kernels which reflect how the
underlying similarity graph influences the values of the classification functions. In the
present work, we analyse a general family of semi-supervised methods, explain the
differences between the methods and provide recommendations for the choice of the
kernel parameters and labelled points. In particular, it appears that it is preferable to
choose a method and a kernel based on the properties of the labelled points. Our
general framework gives particularly promising PageRank based method. We illustrate
our general theoretical conclusions with a typical benchmark example, clustered
preferential attachment model and two applications. One application is about
classification of Wikipedia pages and another application is about classification of
content in P2P networks. (This talk is based on the joint works with P. Goncalves, A.
Mishenin and M. Sokol)
The Fifth International Conference on Network Analysis 9
Energy-Efficient Scheduling problems
Alexander Kononov
Sobolev Institute of Mathematics, Novosibirsk
Scheduling problems has long been in the center of interest from the researchers in
Computer Science, Business Analytics, Operations Research and Engineering due to a
wide range of applications such as timetabling, transportation, air traffic control etc. The
classical scheduling problems usually try to optimize various performance metrics such
as schedule length (makespan), or number of jobs completed by their due date etc.,
subject to various capacity or resource constraints such as number of concurrent jobs
that a processor can handle or bandwidth constraints.
In today's world, energy is one of the most important resources and energy conservation
is a major concern today. It has been realized recently that energy is not just a regular
resource similar to processor capacity. We address one of the main mechanisms for
reducing the energy consumption in modern computer systems which is based on the
use of speed scalable processors. This relatively new technique saves energy by
utilizing the full speed/frequency spectrum of a processor and applying low speeds
whenever possible. The dependence of energy consumption on performance of the
system is highly non-linear and as a result new techniques to assign tasks to processors
and execute them in the optimal or near-optimal manner are required.
We are given a set of jobs, each one specified by its release date, its deadline and its
processing volume (work), and a single (or a set of) speed-scalable processor(s). We
adopt the standard model in speed-scaling in which if a processor runs at speed s then
the energy consumption is sα per time unit, where α> 1. Our goal is to find a schedule
respecting the release dates and the deadlines of the jobs so that the total energy
consumption is minimized.
Dynamic speed scaling leads to many interesting complicated scheduling problems. At
any time a scheduler has to decide not only which job to execute but also which speed
to use. Consequently, there has been considerable research interest in the design and
analysis of efficient scheduling algorithms. We survey recent research that has appeared
in the theoretical computer science literature on algorithmic problems related to off-line
energy-efficient scheduling problems.
10 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Finding maximum subgraphs with relatively large vertex connectivity
Oleg Prokopyev
University of Pittsburgh, USA
We consider a clique relaxation model based on the concept of relative vertex
connectivity. It extends the classical definition of a k-vertex-connected subgraph by
requiring that the minimum number of vertices whose removal results in a disconnected
(or a trivial) graph is proportional to the size of this subgraph, rather than fixed at k.
Consequently, we further generalize the proposed approach to require vertex-
connectivity of a subgraph to be some function f of its size. We discuss connections of
the proposed models with other clique relaxation ideas from the literature and
demonstrate that our generalized framework, referred to as f-vertex-connectivity,
encompasses other known vertex-connectivity-based models, such as s-bundle and k-
block. We study related computational complexity issues and show that finding
maximum subgraphs with relatively large vertex connectivity is NP-hard. An interesting
special case that extends the R-robust 2-club model recently introduced in the literature
is also considered. In terms of solution techniques, we first develop general linear mixed
integer programming (MIP) formulations. Then we describe an effective exact
algorithm that iteratively solves a series of simpler MIPs, along with some
enhancements, in order to obtain an optimal solution for the original problem. Finally,
we perform computational experiments on several classes of random and real-life
networks to demonstrate performance of the developed solution approaches and
illustrate some properties of the proposed clique relaxation models.
The Fifth International Conference on Network Analysis 11
A bi-criteria approach to solving huge hop-constrained Steiner tree
problems
Oleg Burdakov
Linkoping University, Sweden
We consider the directed Steiner tree problem (DSTP) with a constraint on the total
number of arcs (hops) in the tree. This problem is known to be NP-hard. Only heuristics
can be applied in the case of its instances whose size is beyond the capacity of the
existing exact algorithms. The hop-constrained DSTP is viewed as a bi-criteria problem
in which the tree cost and the number of hops are minimized. We derive optimality
conditions and use them for developing an approach aimed at approximately solving
hop-constrained DSTP. The approach can also be used for improving approximate
solutions produced by other heuristic algorithms or as a part of exact algorithms.
Specific label-correcting-type algorithms based on this approach will be presented, and
preliminary results of their performance on a set of test problems will be reported. The
test instances originate from 3D placement of unmanned aerial vehicles used for multi-
target surveillance. They are characterized by a relatively small number of terminal
nodes and a very large number of nodes and a huge number of arcs (above 108).
12 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Network effects in economics and finance
Andrey Leonidov
Theoretical Physics Department, P.N. Lebedev Phhysical Institute, Moscow Chair of
Discrete Mathematics, Moscow Institute of Physics and Technology Laboratory of
Social Analysis, Rissian Endowment for Education and Science
In the talk a review of network-related effects in economics and finance at the examples
of interbank input-output and international trade networks is given. We start with
discussing systemic risks in the interbank networks related to default contagion
propagation. After discussing main characteristics of interbank networks we discuss
probabilistic models of default contagion taking into account the bow-tie structure,
scale-free degree distributions and disassortativity of the corresponding oriented graph.
We continue with the role of topological characteristics of the input-output networks
underlying the dynamic macroeconomic multi-sector models of real business cycles, in
particular of Bonachich centrality. We conclude with considering topological properties
of international trade networks considered as oriented weighted graphs and studying the
spillover propagation of import demand shocks.
The Fifth International Conference on Network Analysis 13
Small Subgraphs in Preferential Attachment Networks
Andrey Raigorodskii
Yandex and Moscow State University, Moscow
Real-world networks such as web-graphs, social networks, biological networks, etc.
have many important characteristics including the degree distribution (which usually
follows a power law), the degree correlations, the diameter (which is usually small), the
robustness to random attacks on vertices and the vulnerability to attacks on hubs, and so
on. Also, a source of very important properties is given by counting small subgraphs in
the networks: the most well-known such property is "high clustering", but there are
many others. In our talk, we shall mainly concentrate on such properties.
On the other hand, many good and simple models of complex networks are provided by
the now classical principle of preferential attachment. So in the talk, we shall define
some of them and discuss the corresponding distributions of small subgraphs. We shall
give a survey of results including the most recent ones.
14 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Ranking in large scale-free networks
Nelly Litvak
University of Twente, Netherlands
Ranking algorithms are crucial for assessing the importance of a node in a network, and
have a wide range of applications, from clustering of networks to link prediction. An
example is the famous Google PageRank algorithm for ranking web pages. In this talk I
will discuss several topics related to the mathematical properties of ranking algorithms
in large networks.
One of the examples is the distribution of a family of rankings, which includes Google's
PageRank in random graphs. It has been observed empirically in many studies that the
distribution of the PageRank and In-degree in directed networks are closely related,
however, the literature did not provide any rigorous explanation for this phenomenon.
We make an important step further by obtaining a complete characterization of
PageRank distribution in a random graph created by a Directed Configuration Model.
Our results show remarkable accuracy when compared to the PageRank distribution on
the Wikipedia.
Next, I will discuss the problem of finding nodes with highest in-degrees when the
network is unknown. This is the case, for example, in the Twitter follower network, that
can be only accesses via the Twitter API. We propose Monte Carlo algorithms to find
most important nodes using only a very small number of API requests. These methods
are surprisingly efficient because of the high variability in the nodes’ degrees.
The Fifth International Conference on Network Analysis 15
Global clustering coefficient in scale-free networks
Liudmila Ostroumova Prokhorenkova
Yandex, Moscow
I will present a detailed analysis of the global clustering coefficient in scale-free graphs.
Many observed real-world networks of diverse nature have a power-law degree
distribution. Moreover, the observed degree distribution usually has an infinite variance.
Therefore, I will focus on such degree distributions.
There are two well-known definitions of the clustering coefficient of a graph: the global
and the average local clustering coefficients. There are several models proposed in the
literature for which the average local clustering coefficient tends to a positive constant
as a graph grows. On the other hand, there are no models of scale-free networks with an
infinite variance of the degree distribution and with an asymptotically constant global
clustering coefficient. Models with constant global clustering and finite variance were
also proposed. Therefore, in this talk I will focus only on the most interesting case and
analyze the global clustering coefficient for graphs with an infinite variance of the
degree distribution.
For unweighted graphs, I will show that the global clustering coefficient tends to zero
with high probability and I will also estimate the largest possible clustering coefficient
for such graphs. On the contrary, for weighted graphs, the constant global clustering
coefficient can be obtained even for the case of an infinite variance of the degree
distribution.
16 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Local clustering coefficient in preferential attachment graphs
Alexander Krot
Moscow Institute of Physics and Technology (MIPT), Moscow
In our study we analyze the local clustering coefficient for the PA-class of models (a
wide class of models was defined in terms of constraints that are sufficient for the study
of the degree distribution and the clustering coefficient.). We analyze the behavior of
C(d) which is the average local clustering for vertices of degree d.
This talk is the continuation of (https://events.yandex.ru/lib/talks/1919/) with NEW
results about local clustering coefficient.
The Fifth International Conference on Network Analysis 17
Factorization threshold models for scale-free networks generation
Akmaljon Artikov, Yana Kashinskaya, Aleksandr Dorodnykh
Moscow Institute of Physics and Technology (MIPT), Moscow
Egor Samosvat
Yandex, Moscow
Many real networks such as the World Wide Web, financial, biological, citation, social
networks have a power-law degree distribution. Networks with this feature are also
called scale-free. Several models for producing scale-free networks have been obtained
and the most of them are based on the preferential attachment approach. This method
forces old vertices of higher degree to gain edges added to a network more rapidly in a
“rich-get-richer” manner. We will offer the model with another scale-free property
explanation.
Let us define our model for a scale-free networks generation. The model has n vertices
denoted by vi (1 ≤ i ≤ n). We assume that a network is embedded in a d-dimensional
Euclidean space and vertices’ coordinate vectors xi are random variables which are
uniformly and independently distributed over the surface of the Sd-1
sphere. In addition,
each vertex has a weight wi (all the weights are i.i.d. random variables with the preset
density function). An edge between vertices vi and vJ is drawn if and only if
(xi, xj) ∙ wi ∙ wj ≥ θ, (1)
where θ is a fixed threshold for the existence of an edge between a pair of vertices.
Models with a preset threshold for the edge existence are usually called threshold
models. Threshold models were actively investigated recently and have shown good
results in a scale-free networks generation [1], [2]. Actually, coordinates of vertices can
be considered as a latent vector of features that brings us to the matrix factorization
approach which has been successfully used in the link prediction problem [3].Having
combined these approaches we got generative factorization threshold model for the
complex networks.
The overview of our results is the following. First, we will tune the threshold θ in order
to obtain a sparse graph. Then we will show that our model produces scale-free
networks with the fixed power-law exponent if vertices’ weights are distributed
according to the Pareto distribution. Moreover, we will generalize our model to generate
oriented networks with a tunable power-law exponents.
Finally, we will demonstrate our results using computer simulation.
[1] Naoki Masuda, Hiroyoshi Miwa, and Norio Konno. Geographical threshold graphs with small-world and scale-free
properties. Physical Review E,71(3):036108, 2005.
[2] Yukio Hayashi. A review of recent studies of geographical scale-free networks. IPSJ Digital Courier, 2:155–164,
2006.
[3] Aditya Krishna Menon and Charles Elkan. Link prediction via matrix factorization. In Machine Learning and
Knowledge Discovery in Databases, pages 437–452. Springer, 2011.
18 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
A complexity dichotomy and a new boundary class for the dominating
set problem
Dmitriy Malyshev
Laboratory of Algorithms and Technologies for Networks Analysis (LATNA),
National Research University Higher School of Economics, Nizhny Novgorod
We study the computational complexity of the dominating set problem for hereditary
graph classes, i.e., classes of simple graphs closed under isomorphism and deletion of
vertices. Every hereditary class can be defined by a set of its forbidden induced
subgraphs. There are numerous open cases for the complexity of the problem even for
hereditary classes with small forbidden structures. We completely determine the
complexity of the problem for classes defined by forbidding a five-vertex path and any
set of fragments with at most five vertices.
The notion of a boundary class is a helpful tool for analyzing the computational
complexity of graph problems in the family of hereditary classes. Three boundary
classes were known for the dominating set problem prior to this study. We present a
new boundary class for it.
The Fifth International Conference on Network Analysis 19
Parallel algorithm of graph ordering for minimizing sparse Cholesky
factor fill-in
Anna Pirova
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
This work deals with the NP-complete problem of finding an ordering of graph vertices
that minimizes the fill-in of the Cholesky factor of the sparse matrix associated with the
graph. For this purpose, heuristic approaches based on graph algorithms are applied.
Nested dissection algorithm is one of such approaches commonly used due to its
potential for parallel processing. In this talk we address the problem of parallelization of
the multilevel nested dissection scheme for shared memory systems. The existing
libraries for parallel graph ordering have MPI-based implementations, nevertheless they
do not take into account the architectural features of the modern multicore systems. Our
work considers a new parallel ordering algorithm for shared-memory systems. Parallel
processing is done in a task-based fashion. We present and analyze two ways of
implementing the algorithm. The first approach employs a concurrent queue to store
subgraphs that can be ordered separately while the second one uses OpenMP 3.0 task
parallelism relying on the dynamic load balancing implemented in the OpenMP
runtime. The modified multilevel nested dissection algorithm from the recently
presented MORSy library is used for the ordering. Experimental results on the
symmetric positive definite matrices from the University of Florida Sparse Matrix
Collection prove the competiveness of our implementation on shared memory systems
to the widely used ParMetis library both in terms of the Cholesky factor fill-in and
performance. In our experiments parallel version of MORSy outperforms ParMetis on 8
matrices out of 14 with close quality of the resulting ordering.
20 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Hybrid methods for mapping a parallel program onto computing
network
Margarita Pankratova
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
We study the architecture depending graph decomposition problem that is the problem
of decomposition and mapping a parallel program onto a multiprocessor system.
We propose the mathematical model of this problem. Weighted graph represents a
parallel program. The nodes represent the parallel parts of program, the edges represent
the data communications between these parts. Weighted hyper graph represents a
computing system. The nodes represent the processors of system, the hyper edges
represent the physical links between processors. We offer an algorithm for transforming
a hyper graph model to a matrix model of computing system. The size of the graph of
parallel program is usually much more than the number of processors of computing
system, so we need to decompose this graph taking into the account balance restrictions.
The goal of this problem is to assign the decomposed graph to the processors and to
minimize the common cost of communications.
This problem is known to be NP-hard, the size of program graphs is about 106-109
nodes. We propose two hybrid algorithms for solving this problem.
The first algorithm we propose is based on recursive bisection scheme. We offer to use
iterated multilevel algorithm for graph bisection and spectral algorithm for matrix
bisection. The proposed recursive algorithm can be used for decomposing the original
problem to a number of problems with reduced size or for finding a solution of original
problem.
The second algorithm we propose is based on reduction the original problem to the
quadratic assignment problem by k-decomposition of the program graph. This algorithm
consists of 3 steps. The first step is decomposition the program graph. The second step
is solving the quadratic assignment problem, and the third step is restoration of solution
and the local optimization.
We have implemented the proposed algorithms and examined them on test benchmarks.
The Fifth International Conference on Network Analysis 21
The text network analysis: What does strategic documentation tell us
about regional integration?
Andrey Murashov
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
Values and attitude towards the regional integration process of the Russian political elite
are considered as an indication of what regional integration (RI) tends to be and how it
evolves over time. Our paper suggests how to systematically grasp and integrate elite’s
values and attitude into the analysis of RI by means of text network analysis (TNA).
Data to analyze is regional strategies of socio-economic development as a central and
most capacious source of information about political elite’s views on RI. From
methodological perspective we apply an approach which com-bines two methods -
comparative text-mining and graph analysis – “text network analysis”.
The TNA allows us to visualize the meanings and agendas present within political
manifests. We build a network of terms based on their co-occurrence in the same text
segments (paragraphs) extracted from the documents. There is an edge between two
terms if they appear in the same text segments. The weight of an edge is its frequency.
Such a net-work (or conceptual map) visualizes logical associations between concepts
presented in the political manifests.
The TNA is performed with R, specifically, with packages {igraph} (plots the graphs),
{tm} (provides functions for text mining) and {topicmodels} (classifies a corpus into
topics).
First we review general graph statistics followed by analysis of the networks’ content.
Upon removing most rare and random terms (concepts) from the networks we try to
detect communities in the graph (with the fast greedy algorithm). We also remove major
articulation points so that the layout of networks is rearrange and new concepts and
links between them are revealed. Topics modeling is used to estimate the similarity
between documents.
We found the TNA to be a valuable method for extracting elite’s attitude towards
regional integration process from public strategic documentation.
22 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Threshold selection for pseudo-bimodal networks of retweets via
different metrics of network centrality
Alexander Semenov
International Laboratory for Applied Network Research, National Research University
Higher School of Economics, Moscow
We present a novel approach to cluster users of Twitter and characterize their
preferences based on graph features of communication networks extracted from their
tweets. We show that network clustering on Twitter can be observed more distinctively
on unimodal projections of artificially created bimodal networks, where the most
popular users in the networks, constructed from the @retweet relationship are
considered as nodes of the second mode. The theoretical assumption behind this
approach is that the central users in this network can be considered as “power-users”
and other users retweet behavior towards them differs from their retweets of each-other.
For this purpose, we select a subset of top n users based on their centrality value and
iteratively assign them to be the second mode in our pseudo-bimodal networks, adding
one user on each step in the descending order of their centrality scores. After that for
each step we create two projections of the obtained pseudo-bimodal network: one for
“top” users and one for “bottom”. As a result we get unimodal networks with more
distinct clusters structure for each class of users which allows us to show indirect
connections among users from both classes. We developed our approach on a dataset
gathered during the Russian protest meetings on 24th of December, 2011 and tested it
with different centrality measures: Degree, Closeness, Betweennes, PageRank,
Eigenvector, Katz’, Bonacich’s Alpha and Power centralities and Klinenberg’s hub and
authority scores. For each measure we calculate the optimal threshold for the number of
top nodes to be converted to the second mode in the pseudo-bimodal network, which
maximizes modularity of graphs in both projections. We found out that PageRank gives
the best results and discuss the issues with performance of our approach and its further
applications.
The Fifth International Conference on Network Analysis 23
An Algorithm for Constraint/Generator Removal from Double
Sergey Bastrakov
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
A convex polyhedron in general dimension can be represented in two ways: as a set of
solutions to a system of linear inequalities (facet representation) and as a convex-conical
hull of a set of vectors (vertex representation). Facet and vertex representations together
form the double description of a polyhedron. We consider a problem of removing
elements from one of the representations (constrains or generators) given irreducible
double description of the original polyhedron. Namely, the problem is to compute the
vertex representation of a polyhedron defined by a subsystem of inequalities or facet
representation of a polyhedron generated by a subset of vectors. One of the applications
of the problem is automatic analysis, verification and optimization of software.
The naive approach is to directly solve the dual description problem for the resulting
polyhedron, neglecting the information of the double description of the original
polyhedron. However, this information can be used to construct a more efficient
algorithm, particularly when the number of removed elements is low. In 2014 Amato,
Scozzari & Zaffanella presented a new algorithm of this kind, called incremental.
We present a new algorithm. Similar to the incremental algorithm we construct a set of
facets adjacent to the facets being removed, but instead of solving the dual description
problem for this subset we find intersection points between those facets and a set of
specially constructed rays. The rays are continuations of edges of a polyhedron with
exactly one vertice lying on a removed facet. The complexity of the proposed algorithm
for removing one constraint is a product of squared sizes of the facet and vertex
representations of the original polyhedron. Computational experiments show that the
proposed algorithm outperforms the incremental algorithm by factor of 1.2 to 2x on
most test problems used by Amato, Scozzari & Zaffanella.
24 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Improved polynomial time approximation guarantees for well
structured quadratic optimization problems
Yury Maximov
The Institute for Information Transmission Problems Russian Academy of Sciences,
National Research University Higher School of Economics, Moscow
Semidefinite programming arises as a relaxation for a wide variety of combinatorial
optimization problems. For most of them it is tight in the class of polynomial algorithms
under the unique games conjecture. Nevertheless, for well structured quadratic
programming problems, approximation guarantees can be significantly improved even
is the problem itself is still NP-hard. In this talk, we introduce a new approach to
overcome semidefinite programming approximation barrier by introducing a low
complexity pattern into a semidefinite dual and combining semidefinite programming
with the dynamic programming techniques to solve the problem. We provide some new
approximation guarantees as well as numerical experiments for practical problems
(max-cut, max-k-cut, correlation clustering). Some applications to coding theory and
network optimization are also mentioned. The talk is based on the joint research with
Yu. Nesterov.
The Fifth International Conference on Network Analysis 25
Kernel methods in Natural Gas Storage Valuation
Theodore B. Trafalis, Alexander M. Malyscheff
School of Industrial and Systems Engineering, University of Oklahoma, USA
The valuation of natural gas storage contracts has recently received significant attention
in the energy management community. Least-Squares Monte Carlo (LSMC) represents
one approach to value such contracts. We apply kernel-based machine learning
techniques to derive the regression function required in the LSMC method.
26 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Sentiment Analysis in Russian Social Networks
Dmitry Zhelonkin
National Research University Higher School of Economics, Nizhny Novgorod
The present research focuses on investigating question of sentiment analysis in Russian
social networks based on opinion mining by machine learning techniques. As a network
node we consider one marked message. Set of such texts form network. One of the main
features of the present work is considering of texts sentiment or tone not in terms of
linguistics in the conventional sense but in the way of mental perception or tonality of
the document which is understood by a person in light of the events during some period.
Another novelty of the research is new feature creation method using delta-TFIDF for
accelerating learning process. The result of the work is a program application of the
prototyped algorithm aimed at working with big data which can evaluate general mood
in social network in the framework of some topic.
The Fifth International Conference on Network Analysis 27
On Laplacian regularization for generalized eigenvalue classifiers
Mario R. Guarracino, Mara Sangiovanni
High Performance Computing and Networking Institute, National Research Council,
Naples - Italy
Marco Viola, Gerardo Toraldo
Department of Mathematics and Applications, University of Naples “Federico II”,
Naples – Italy
Generalized Eigenvalue Classifiers are a class of supervised learning techniques derived
from Support Vector Machines. In this talk we describe some recent progresses
regarding the regularization of the classifiers in case of problems with more features
than samples (p>>n). We motivate the adoption of a novel regularization term that takes
into account the network structure of the training data and describe the advantages. We
provide some comparisons in terms of classification accuracy with other de facto
standard methods on real world datasets.
28 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Network analysis of Mass spectroscopy medical data
Artem Ryblov
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
The amount of available medical data is dramatically increasing: in the last 10 minutes
we generated more data than from prehistoric times until 2003! There is the same
situation with proteomic data, and we need to develop new methods to analyse it. There
are many well-established ways to predict risk of disease by doing analysis of
proteomic biomarkers, but recent investigations have shown that observed biomarkers
do not cover the whole set of disease data. In this situation it is very promising to
discover and analyse network biomarkers, which take into account the changes in the
topology of interrelations between different parameters. Many well established methods
translated from graph analysis can be then utilized but what to do if links between
parameters are unknown? Recently developed parenclitic networks analysis is very
useful for this set-up. Our method is based on the classical approach utilizing search of
the best model by multivariate logistic regression, but instead of doing regression on the
original data we preprocess the data by building the parenclitic network and analysing
its topology.
The Fifth International Conference on Network Analysis 29
Network analysis of methylation data for cancer diagnostics
Alexander Karsakov
Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod
At the present time DNA methylation patterns are established as having fundamental
role in the development of cancer diseases. Actually it is well known that methylation
values of specific genes are different between normal and cancer cells. In this work we
used mathematical theory of complex networks analysis to investigate some of features
of methylation regulation. Information obtained from patients with various kinds of
oncology diseases is represented as networks. Nodes in the network represent a specific
gene, while edges connecting them show an abnormal relation between their
methylation levels or other measures. The analysis of network topology allows us to
detect which topological indices are associated with the cancer development. Moreover,
networks of control and oncology subjects are different and there are numerical metrics
that can be used to distinguish and then perform classification of them. After analyzing
data of 12 cancer diseases I got accuracy rate of classification comparable with using
classical machine learning algorithms. In addition, a described approach allows
discovering important functional relationship between specific genes. Knowledge of
significant genes and their relationships can significantly help biologists and clinicians
to study possible ways of cancer treatment. Beyond the results obtained in the study of
this specific disease, the proposed algorithm may be used for analysis any other clinical
data, where the relationships between different features are more important than their
values.
30 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Comparing Complexity of Combinatorial Polytopes
Alexandr Maximenko
P.G. Demidov Yaroslavl State University, Yaroslavl
We consider 0-1 polytopes associated with NP-hard problems. It is known that the face
lattice of such a polytope reflects the structure of the feasible solutions set of the
appropriate discrete optimization problem. Therefore we can measure complexity of a
problem in terms of combinatorial characteristics of its polytope. The simplest examples
of such characteristics are the number of vertices, the number of facets and the
dimension of a polytope. More interesting are the diameter of the graph, its clique
number and the extension complexity of a polytope. In this talk we compare complexity
of combinatorial polytopes associated with well known NP-hard problems: boolean
quadratic programming, graph coloring, knapsack problem, travelling salesman problem
and many others. In particular, we show that boolean quadratic polytopes are faces of
mentioned polytopes. Hence, in this sense they contain no extra details in comparison
with other polytopes associated with NP-hard problems.
The Fifth International Conference on Network Analysis 31
König graphs for 4-path. Full description.
Dmitry Mokeev
Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), National
Research University Higher School of Economics, Nizhny Novgorod
Let F be a class of graphs. A König graph for F is a graph in which every induced
subgraph has the property that minimum carginality of a set of vertices meeting every
induced F-subgraph of G equals a maximum number of vertex-disjoint induced F-
subgraphs in G.
The aim of this work is to characterize König graphs for set consisting from one simple
path with 4 vertices (4-path). There are two approaches to description of this class. One
of them is constructive: we show how to construct a graph of given class by operations
of edge subdivision and replacement of vertices and terminal paths with cographs. In
another approach we look for a standard description of hereditary class by forbidden
subgraphs.
32 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Integer programming in simplices
Dmitry Gribanov
Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), National
Research University Higher School of Economics, Nizhny Novgorod
We investigate integer programming problems on polyhedrons that restricted to be
simplices. Note that deciding whether a simplex contains an integer point is trivially
NP-complete, since the set of feasible solutions of the knapsack problem is a simplex.
So the integer programming in simplex becomes NP-hard problem. Papadimitriou
(1981) showed, using dynamic programming, that if the n-dimensional polyhedron is
induced by system of inequalities with fixed number of rows and bounded elements,
then the integer programming problem can be solved in polynomial time. Thus one can
show, that the integer programming problem in simplex can be solved in polynomial
time, if the maximum absolute value of the system sub-determinants is fixed. We
developed an algorithm for integer programming, based on the unimodular cone
decomposition procedure, that can find all vertices of integer hull of the simplex. Our
algorithm has polynomial complexity in previous assumptions and not depends
exponentially from the right part coefficients of the system. Also we show how to make
some generalisations of this approach using more general class of polytopes.
Finally we show existence of the much more efficient algorithm, if the width of a
simplex is large enough. Unfortunately the computation of the width of a simplex is NP-
hard due to Andras Sebo (1999).
The Fifth International Conference on Network Analysis 33
Computationally efficient PageRank algorithm exploting graph sparsity
Dmitry Kamzolov
Moscow Institute of Physics and Technology (MIPT), Moscow
In this work, we explore various mechanisms ranking web sites in terms of their
computational efficiency. Many Internet sites and links between them represented as a
weighted graph whose vertices correspond to the sites, and the edges correspond to the
links between sites. Rapid growth of the Internet motivates the creation of new efficient
algorithms. The main problem in the ranking problem is a huge number of sites that we
need ranking. The method, that works in linear time on the number of sites in the space
of dimension 108 and more, is computational expensive and inefficient. In this work, we
consider an algorithm based on the sparsity ideas for ranking web-pages. The key idea
of the method is using of component-wise descent with 1-norm for sparse matrix. In
contrast to the gradient descent it increases the number of steps of the algorithm, but
each step is done in a small number of arithmetic operations. Using this idea we can
solve a large class of ranking problems in logarithmic time with respect to the number
of sites. We also provide a computational experiment that check theoretical estimates of
the time of the algorithm. It is shown that the theoretical estimate of the number of steps
matches to the experiment.
34 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Semi-Supervised PageRank Model Learning with Gradient-Free
Optimization Methods
Alexander Gasnikov
Moscow Institute of Physics and Technology (MIPT), The Institute for Information
Transmission Problems Russian Academy of Sciences, Moscow
In our work we consider a problem of web page relevance to a search query. We are
working in the framework called Semi-Supervised PageRank which can account for
some properties which are not considered by classical approaches such as PageRank and
BrowseRank algorithms. We introduce a graphical parametric model for web pages
ranking. The goal is to identify the unknown parameters using the information about
page relevance to a number of queries given by some experts (assessors). The resulting
problem is formulated as an optimization one. Due to hidden huge dimension of the last
problem we use random gradient-free methods with oracle error to solve it. We prove
the convergence theorem and give the number of arithmetic operations which is needed
to solve it with a given accuracy.
The Fifth International Conference on Network Analysis 35
Sparsity and randomization based techniques in huge scale traffic
matrix estimation problems
Alexander Gagloev, Nazar Buzun, Yuriy Dorn, Alexander Gasnikov, Andrey
Golov, Aydar Gubaydullin, Yury Maximov, Mikhail Mendel
Moscow Institute of Physics and Technology (MIPT), Moscow
The problem is to recover the unknown Traffic Matrix, which is a high dimensional ill-
posed inverse problem. The typical dimension of the problems we are dealing with is
106 - 10
8. To solve this we propose to reduce the problem to a linearly constrained
quadratic convex optimization problem. The main goal of the work is to compare the
properties of different optimization techniques depending on the problem structure. We
focus on gradient type methods such as gradient descent, stochastic gradient descent and
componentwise descent in primal and dual spaces. We show that some special
properties of the incidence matrix (column sparsity, row sparsity) allows to improve
convergence guarantees for the algorithms above. Finally, we provide some numerical
experiments on real and synthetic data.
36 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Bayesian Evidence Cascades and Seed-Initiated Marketing Campaigns
in Social Networks
Alexander Nikolaev
University at Buffalo, the State University of New York
The influence maximization problem, as defined in social network science, lies in
finding a set of seeds that can initiate a diffusion-driven cascade in an optimal way. We
explore flexible, time-dependent seed activation solutions for long-term
intervention/campaign planning on networks. We model influence propagation as
parallel Bayesian evidence cascades. The investigations with the model shed light on
the phenomena of belief reinforcement and viral spread of innovations, rumors,
opinions, etc., in social networks.
The NP-Hard problem of selecting a set of influential nodes to generate a maximal
cascade of "positive" subjective evidence (in support of a hypothesis claim preferred by
the decision-maker), is solved as a mixed-integer program.
The Fifth International Conference on Network Analysis 37
Identification of concentration graph in Gaussian graphical model
Petr Koldanov, Alexander Koldanov, Panos Pardalos
Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), National
Research University Higher School of Economics, Nizhny Novgorod
Concentration graph is an important structure in Gaussian graphical models. Problem of
identification of concentration graph from observation attract a growing attention last
decade.
This problem is interesting from theoretical point of view and from practical
applications as well. Different identification procedures were studied in the literature.
A few results are known about optimality of considered procedures. In this talk we will
prove optimality of multiple testing identification procedure based on simultaneous
inference of optimal two-decision tests.
38 May 18th - May 20
th 2015, Nizhny Novgorod, Russia
Dynamics of the ensemble of inhibitory coupled neuron-like Rulkov
maps
Alexey Kazakov, Tatiana Levanova
Lobachevsky State University of Nizhny Novgorod, National Research University
Higher School of Economics, Nizhny Novgorod
We study three neuron-like Rulkov maps [1-3] with mutual inhibitory couplings. In
order to receive more biological relevant description of couplings we consider main
features of real biological inhibitory couplings, such as dependence of postsynaptic
element activity level on presynaptic element activity level and inertia of couplings.
Constructed in such a way model is discrete and so it is very easy to numerical analysis.
We study numerically (using NN HSE cluster) different dynamical regimes that can be
obtained in this ensemble by governing coupling parameters, including chaotic regime,
and bifurcation transition from one regime to another.
[1] N.F. Rulkov, Phys. Rev. E 65 041922 (2002)
[2] A.L. Shilnikov, N.F. Rulkov, Bifurcations and Chaos 13(11), (2003)
[3] A.L. Shilnikov, N.F. Rulkov, Physics Letters A 328, 177 (2004)
top related