PMatch: Probabilistic Subgraph Matching on Huge Social NetworksMatthias Broecheler
Users querying massive social networks or RDF databases are often not 100% certain about what they are looking for due to the complexity of the query or heterogeneity of the data. In this paper, we propose “probabilistic subgraph” (PS) queries over a graph/network database, which afford users great flexibility in specifying “approximately” what they are looking for. We formally define the probability that a substitution satisfies a PS-query with respect to a graph database. We then present the PMATCH algorithm to answer such queries and prove its correctness. Our experimental evaluation demonstrates that PMATCH is efficient and scales to massive social networks with over a billion edges.
Succinct Summarisation of Large Networks via Small Synthetic Representative G...Jérôme KUNEGIS
Talk by Jérôme Kunegis at BeNet'17 in Gent.
In this talk, Jérôme Kunegis presented ongoing work, see the abstract below.
Abstract: We describe a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of \emph{drawing} large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common \emph{hairball} look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the
problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.
Title: What Is the Difference between a Social and a Hyperlink Network? -- Ho...Jérôme KUNEGIS
Networks represent a type of dataset that is ubiquitous in many
disciplines and areas. Examples are social networks (ties between
people), communication networks, trophic networks ("who eats who"), the
World Wide Web, computer networks, lexical networks (connections between
words), transport networks, metabolic networks (e.g., interactions
between proteins), neural networks, animal networks, citation networks,
affiliation networks (of people in groups), software dependency
networks, and many more. In this talk, we present ongoing work on
answering the question "Can the type of network be detected from the
network structure alone?" For instance, given a completely unlabeled
network dataset consisting only of node and edges, can we detect whether
the data represents a social network or a hyperlink network? We present
machine learning and statistical approaches to answering questions of
this type. The presented results will make use of data in the KONECT
project, one of the largest repositories of network datasets, curated at
the University of Namur.
Measuring the Conflict in a Social Network with Friends and Foes: A Recent Al...Jérôme KUNEGIS
In this talk, Jérôme Kunegis will present recent results on the
measurement of conflict in signed social network. A signed social
network is a network in which both positive and negative ties are
present, for instance representing friendship and enmity, or trust and
distrust. Such networks have long been studied under the aspect of
balance theory, i.e., considering whether the individuals can be grouped
into two groups, such that the sign of all ties reflects the partition,
or equivalently in terms of the individual configuration of tryads. The
failure of such a structure to be present in a signed social network is
usually designated as conflict, and measuring the amount of conflict in
a given signed social network is an open problem. In this talk, a novel
measure of conflict is presented, based on algebraic graph theory, and
considering a previously known variant of the Laplacian matrix for
signed graphs. The talk will show both theoretical motivations for the
measure, as well as an evaluation of its utility at signed social
network analysis using multiple real-world signed social networks, based
on networks from the KONECT project. Jérôme Kunegis from the Center for
Complex Networks (naXys) at the University of Namur (Belgium) is the
founder and main lead of the KONECT project, a curated collection of
network datasets, algorithms and analyses, maintained at the University
of Namur.
A talk given in 2006 by Jérôme Kunegis about computer chess: from the beginning to the present, culminating with the match Kasparov – Deep Blue. Given in German at a seminar organised at the Technical University of Berlin Horst Zuse, computer scientist and son of computer pioneer Konrad Zuse.
Winning Science Slam by Jérôme Kunegis – First Prize at ICWSM 2016Jérôme KUNEGIS
These are the slides of the winning Science Slam presentation by Jérôme Kunegis that won the First Prize at the Science Slam of the International Conference on Weblogs and Social Media (ICWSM) in 2016.
Algebraic Graph-theoretic Measures of ConflictJérôme KUNEGIS
In this talk, I present recent results on the measurement of conflict in
signed social network. A signed social network is a network in which
both positive and negative ties are present, for instance representing
friendship and enmity, or trust and distrust. Such networks have long
been studied under the aspect of balance theory, i.e., considering
whether the individuals can be grouped into two groups, such that the
sign of all ties reflects the partition, or equivalently in terms of the
individual configuration of tryads. The failure of such a structure to
be present in a signed social network is usually designated as conflict,
and measuring the amount of conflict in a given signed social network is
an open problem. In this work, I present a novel measure of conflict,
based on algebraic graph theory, and considering a previously known
variant of the Laplacian matrix for signed graphs. The talk will show
both theoretical motivations for the measure, as well as an evaluation
of its utility at signed social network analysis using multiple
real-world signed social networks.
PMatch: Probabilistic Subgraph Matching on Huge Social NetworksMatthias Broecheler
Users querying massive social networks or RDF databases are often not 100% certain about what they are looking for due to the complexity of the query or heterogeneity of the data. In this paper, we propose “probabilistic subgraph” (PS) queries over a graph/network database, which afford users great flexibility in specifying “approximately” what they are looking for. We formally define the probability that a substitution satisfies a PS-query with respect to a graph database. We then present the PMATCH algorithm to answer such queries and prove its correctness. Our experimental evaluation demonstrates that PMATCH is efficient and scales to massive social networks with over a billion edges.
Succinct Summarisation of Large Networks via Small Synthetic Representative G...Jérôme KUNEGIS
Talk by Jérôme Kunegis at BeNet'17 in Gent.
In this talk, Jérôme Kunegis presented ongoing work, see the abstract below.
Abstract: We describe a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of \emph{drawing} large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common \emph{hairball} look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the
problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.
Title: What Is the Difference between a Social and a Hyperlink Network? -- Ho...Jérôme KUNEGIS
Networks represent a type of dataset that is ubiquitous in many
disciplines and areas. Examples are social networks (ties between
people), communication networks, trophic networks ("who eats who"), the
World Wide Web, computer networks, lexical networks (connections between
words), transport networks, metabolic networks (e.g., interactions
between proteins), neural networks, animal networks, citation networks,
affiliation networks (of people in groups), software dependency
networks, and many more. In this talk, we present ongoing work on
answering the question "Can the type of network be detected from the
network structure alone?" For instance, given a completely unlabeled
network dataset consisting only of node and edges, can we detect whether
the data represents a social network or a hyperlink network? We present
machine learning and statistical approaches to answering questions of
this type. The presented results will make use of data in the KONECT
project, one of the largest repositories of network datasets, curated at
the University of Namur.
Measuring the Conflict in a Social Network with Friends and Foes: A Recent Al...Jérôme KUNEGIS
In this talk, Jérôme Kunegis will present recent results on the
measurement of conflict in signed social network. A signed social
network is a network in which both positive and negative ties are
present, for instance representing friendship and enmity, or trust and
distrust. Such networks have long been studied under the aspect of
balance theory, i.e., considering whether the individuals can be grouped
into two groups, such that the sign of all ties reflects the partition,
or equivalently in terms of the individual configuration of tryads. The
failure of such a structure to be present in a signed social network is
usually designated as conflict, and measuring the amount of conflict in
a given signed social network is an open problem. In this talk, a novel
measure of conflict is presented, based on algebraic graph theory, and
considering a previously known variant of the Laplacian matrix for
signed graphs. The talk will show both theoretical motivations for the
measure, as well as an evaluation of its utility at signed social
network analysis using multiple real-world signed social networks, based
on networks from the KONECT project. Jérôme Kunegis from the Center for
Complex Networks (naXys) at the University of Namur (Belgium) is the
founder and main lead of the KONECT project, a curated collection of
network datasets, algorithms and analyses, maintained at the University
of Namur.
A talk given in 2006 by Jérôme Kunegis about computer chess: from the beginning to the present, culminating with the match Kasparov – Deep Blue. Given in German at a seminar organised at the Technical University of Berlin Horst Zuse, computer scientist and son of computer pioneer Konrad Zuse.
Winning Science Slam by Jérôme Kunegis – First Prize at ICWSM 2016Jérôme KUNEGIS
These are the slides of the winning Science Slam presentation by Jérôme Kunegis that won the First Prize at the Science Slam of the International Conference on Weblogs and Social Media (ICWSM) in 2016.
Algebraic Graph-theoretic Measures of ConflictJérôme KUNEGIS
In this talk, I present recent results on the measurement of conflict in
signed social network. A signed social network is a network in which
both positive and negative ties are present, for instance representing
friendship and enmity, or trust and distrust. Such networks have long
been studied under the aspect of balance theory, i.e., considering
whether the individuals can be grouped into two groups, such that the
sign of all ties reflects the partition, or equivalently in terms of the
individual configuration of tryads. The failure of such a structure to
be present in a signed social network is usually designated as conflict,
and measuring the amount of conflict in a given signed social network is
an open problem. In this work, I present a novel measure of conflict,
based on algebraic graph theory, and considering a previously known
variant of the Laplacian matrix for signed graphs. The talk will show
both theoretical motivations for the measure, as well as an evaluation
of its utility at signed social network analysis using multiple
real-world signed social networks.
Publicity slides for the "Karriere-Lounge – INFORMATIK" event (in German), a job fair held during the INFORMATIK 2013 conference.
http://www.informatik2013.de/karrierelounge_de.html
What Is the Added Value of Negative Links in Online Social Networks?Jérôme KUNEGIS
We investigate the "negative link" feature of social networks that
allows users to tag other users as foes or as distrusted
in addition to the usual friend and trusted links. To
answer the question whether negative links have an added value for an
online social network, we investigate the machine learning problem of
predicting the negative links of such a network using only the positive
links as a basis, with the idea that if this problem can be solved with
high accuracy, then the "negative link" feature is redundant. In
doing so, we also present a general methodology for assessing the added
value of any new link type in online social networks. Our evaluation is
performed on two social networks that allow negative links: The
technology news website Slashdot and the product review site Epinions.
In experiments with these two datasets, we come to the conclusion that a
combination of centrality-based and proximity-based link prediction
functions can be used to predict the negative edges in the networks we
analyse. We explain this result by an application of the models of
preferential attachment and balance theory to our learning problem, and
show that the "negative link" feature has a small but measurable added
value for these social networks.
We present the Koblenz Network
Collection (KONECT), a project to collect
network datasets in the areas of web science, network science and
related areas, as well as provide tools for their analysis. In the cited
areas, a
surprisingly large number of very heterogeneous data can be modeled as
networks and consequently, a unified representation of networks can be used
to gain insight into many kinds of problems. Due to the emergence of the
World Wide Web in the last decades many such datasets are now openly available.
The KONECT project thus has the goal of
collecting many diverse network datasets from the Web, and providing a
way for their systematic study.
The main parts of KONECT are (1)~a collection of
over 160 network datasets, consisting of directed, undirected,
unipartite, bipartite, weighted, unweighted, signed and temporal
networks collected from the Web, (2)~a Matlab toolbox for network
analysis and (3)~a website giving a compact overview the various
computed statistics and plots. In this paper, we describe KONECT's
taxonomy of networks datasets, give an overview of the datasets
included, review the supported statistics and plots, and briefly discuss
KONECT's role in the area of web science and network science.
Preferential Attachment in Online Networks: Measurement and ExplanationsJérôme KUNEGIS
We perform an empirical study of the preferential attachment phenomenon
in temporal networks and show that on the Web, networks follow a
nonlinear preferential attachment model in which the exponent depends on
the type of network considered. The classical preferential attachment
model for networks by Barabási and Albert (1999) assumes a linear
relationship between the number of neighbors of a node in a network and
the probability of attachment. Although this assumption is widely made
in Web Science and related fields, the underlying linearity is rarely
measured. To fill this gap, this paper performs an empirical
longitudinal (time-based) study on forty-seven diverse Web network
datasets from seven network categories and including directed,
undirected and bipartite networks. We show that contrary to the usual
assumption, preferential attachment is nonlinear in the networks under
consideration. Furthermore, we observe that the deviation from
linearity is dependent on the type of network, giving sublinear
attachment in certain types of networks, and superlinear attachment in
others. Thus, we introduce the preferential attachment exponent $\beta$
as a novel numerical network measure that can be used to discriminate
different types of networks. We propose explanations for the behavior
of that network measure, based on the mechanisms that underly the growth
of the network in question.
Online Dating Recommender Systems: The Split-complex Number ApproachJérôme KUNEGIS
A typical recommender setting is based on two kinds of relations:
similarity between users (or between objects) and the taste of users
towards certain objects. In environments such as online dating
websites, these two relations are difficult to separate, as the users
can be similar to each other, but also have preferences towards other
users, i.e., rate other users. In this paper, we present a novel and
unified way to model this duality of the relations by using
split-complex numbers, a number system related to the complex numbers
that is used in mathematics, physics and other fields. We show that
this unified representation is capable of modeling both notions of
relations between users in a joint expression and apply it for
recommending potential partners. In experiments with the Czech dating
website Libimseti.cz we show that our modeling approach leads to an
improvement over baseline recommendation methods in this scenario.
Fairness on the Web: Alternatives to the Power LawJérôme KUNEGIS
This paper presents several measures of fairness and inequality based on the degree
distribution in networks, as alternatives to the well-established power-law exponent.
Networks such as social networks, communication networks and the World
Wide Web itself are often characterized by their unequal distribution of
edges: Few nodes are attached to many edges, while many nodes are
attached to only few edges. The inequality of such network structures is
typically measured using the power-law exponent, stating that the number of
nodes with a given degree is proportional to that degree taken to a
certain exponent. However, this approach has several weaknesses, such
as its narrow applicability and expensive computational complexity.
Beyond the fact that power laws are by far not a
universal phenomenon on the Web, the power-law exponent has the
surprising property of being negatively correlated with the usual
notion of inequality, making it unintuitive as a fairness measure. As
alternatives, we propose several measures based on the Lorenz curve,
which is used in economics but rarely in networks study, and on the
information-theoretical concept of entropy. We show in experiments on a
large collection of online networks that these measures do not suffer under
the drawbacks of the power-law exponent.
KONECT Cloud – Large Scale Network Mining in the CloudJérôme KUNEGIS
In the Winter 2011/2012 run at the Future SOC Lab, we used the KONECT
framework (Koblenz Network Collection) to compute ten
different network statistics on a large collection of downsampled
versions of a large network dataset, with the goal of determining
whether sampling of a large network can be used to reduce the
computational effort needed to compute a network statistic. Preliminary
results show that this is indeed the case.
On the Spectral Evolution of Large Networks (PhD Thesis by Jérôme Kunegis)Jérôme KUNEGIS
In this thesis, I study the spectral characteristics of large dynamic networks and formulate the spectral evolution model. The spectral
evolution model applies to networks that evolve over time, and describes their spectral decompositions such as the eigenvalue and singular value
decomposition.
The spectral evolution model states that over time, the eigenvalues of a
network change while its eigenvectors stay approximately constant.
Bad News Travel Fast: A Content-based Analysis of Interestingness on TwitterJérôme KUNEGIS
On the microblogging site Twitter, users can forward any message they receive to all of their followers. This is called a retweet and is usually done when users find a message particularly interesting and worth sharing with others. Thus, retweets reflect what the Twitter community considers
interesting on a global scale, and can be used as a function of interestingness to generate a model to describe the
content-based characteristics of retweets. In this paper, we analyze a set of high- and
low-level content-based features on several large collections of Twitter messages.
We train a prediction model to forecast for a given tweet its likelihood of being
retweeted based on its contents. From the parameters learned by the model
we deduce what are the influential content features that contribute to the
likelihood of a retweet. As a result we obtain insights into what
makes a message on Twitter worth retweeting and, thus, interesting.
On the Scalability of Graph Kernels Applied to Collaborative RecommendersJérôme KUNEGIS
We study the scalability of several recent graph kernel-based collaborative recommendation algorithms.
We compare the performance of several graph kernel-based
recommendation algorithms, focusing on runtime and recommendation accuracy with respect to the reduced rank of the subspace. We inspect the exponential and Laplacian exponential kernels, the resistance distance kernel, the regularized Laplacian kernel, and the stochastic diffusion kernel. Furthermore, we introduce new variants of kernels based on the graph
Laplacian which, in contrast to existing kernels, also allow
negative edge weights and thus negative ratings. We perform an evaluation on the Netflix Prize rating corpus on prediction and recommendation tasks, showing that dimensionality reduction not only makes prediction faster, but sometimes also more accurate.
Learning Spectral Graph Transformations for Link PredictionJérôme KUNEGIS
We present a unified framework for learning link prediction and edge weight prediction functions in large networks, based on the transformation of a graph’s algebraic spectrum. Our approach generalizes several graph kernels and dimensionality reduction methods and provides a method to estimate their parameters efficiently. We show how
the parameters of these prediction functions can be learned by reducing the problem to a one-dimensional regression problem whose runtime only depends on the method’s reduced rank and that can be inspected visually. We derive variants that apply to undirected, weighted, unweighted, unipartite and bipartite graphs. We evaluate our method
experimentally using examples from social networks, collaborative filtering, trust networks, citation networks, authorship graphs and hyperlink networks.
The Slashdot Zoo: Mining a Social Network with Negative EdgesJérôme KUNEGIS
We analyse the corpus of user relationships of the Slashdot technology news site. The data was collected from the Slashdot Zoo feature where users of the website can tag other users as friends and foes, providing positive and negative endorsements. We adapt social network analysis techniques to the problem of negative edge weights. In particular, we consider signed variants of global network characteristics such as
the clustering coefficient, node-level characteristics such as centrality and popularity measures, and link-level characteristics such as distances and similarity measures. We evaluate
these measures on the task of identifying unpopular users,
as well as on the task of predicting the sign of links and show that the network exhibits multiplicative transitivity which allows algebraic methods based on matrix multiplication to
be used. We compare our methods to traditional methods which are only suitable for positively weighted edges.
Spectral Analysis of Signed Graphs for Clustering, Prediction and VisualizationJérôme KUNEGIS
We study the application of spectral clustering, prediction and
visualization methods to graphs with negatively weighted edges. We show
that several characteristic matrices of graphs can be extended to graphs
with positively and negatively weighted edges, giving signed spectral
clustering methods, signed graph kernels and network visualization
methods that apply to signed graphs. In particular, we review a signed
variant of the graph Laplacian. We derive our results by considering
random walks, graph clustering, graph drawing and electrical networks,
showing that they all result in the same formalism for handling
negatively weighted edges. We illustrate our methods using examples
from social networks with negative edges and bipartite rating graphs.
Network Growth and the Spectral Evolution ModelJérôme KUNEGIS
We introduce and study the spectral evolution model, which characterizes
the growth of large networks in terms of the eigenvalue decomposition of
their adjacency matrices: In large networks, changes over time result in
a change of a graph's spectrum, leaving the eigenvectors unchanged. We
validate this hypothesis for several large social, collaboration,
authorship, rating, citation, communication and tagging networks,
covering unipartite, bipartite, signed and unsigned graphs. Following
these observations, we introduce a link prediction algorithm based on
the extrapolation of a network's spectral evolution. This new link
prediction method generalizes several common graph kernels that can be
expressed as spectral transformations. In contrast to these graph
kernels, the spectral extrapolation algorithm does not make assumptions
about specific growth patterns beyond the spectral evolution model. We
thus show that it performs particularly well for networks with
irregular, but spectral, growth patterns.
Publicity slides for the "Karriere-Lounge – INFORMATIK" event (in German), a job fair held during the INFORMATIK 2013 conference.
http://www.informatik2013.de/karrierelounge_de.html
What Is the Added Value of Negative Links in Online Social Networks?Jérôme KUNEGIS
We investigate the "negative link" feature of social networks that
allows users to tag other users as foes or as distrusted
in addition to the usual friend and trusted links. To
answer the question whether negative links have an added value for an
online social network, we investigate the machine learning problem of
predicting the negative links of such a network using only the positive
links as a basis, with the idea that if this problem can be solved with
high accuracy, then the "negative link" feature is redundant. In
doing so, we also present a general methodology for assessing the added
value of any new link type in online social networks. Our evaluation is
performed on two social networks that allow negative links: The
technology news website Slashdot and the product review site Epinions.
In experiments with these two datasets, we come to the conclusion that a
combination of centrality-based and proximity-based link prediction
functions can be used to predict the negative edges in the networks we
analyse. We explain this result by an application of the models of
preferential attachment and balance theory to our learning problem, and
show that the "negative link" feature has a small but measurable added
value for these social networks.
We present the Koblenz Network
Collection (KONECT), a project to collect
network datasets in the areas of web science, network science and
related areas, as well as provide tools for their analysis. In the cited
areas, a
surprisingly large number of very heterogeneous data can be modeled as
networks and consequently, a unified representation of networks can be used
to gain insight into many kinds of problems. Due to the emergence of the
World Wide Web in the last decades many such datasets are now openly available.
The KONECT project thus has the goal of
collecting many diverse network datasets from the Web, and providing a
way for their systematic study.
The main parts of KONECT are (1)~a collection of
over 160 network datasets, consisting of directed, undirected,
unipartite, bipartite, weighted, unweighted, signed and temporal
networks collected from the Web, (2)~a Matlab toolbox for network
analysis and (3)~a website giving a compact overview the various
computed statistics and plots. In this paper, we describe KONECT's
taxonomy of networks datasets, give an overview of the datasets
included, review the supported statistics and plots, and briefly discuss
KONECT's role in the area of web science and network science.
Preferential Attachment in Online Networks: Measurement and ExplanationsJérôme KUNEGIS
We perform an empirical study of the preferential attachment phenomenon
in temporal networks and show that on the Web, networks follow a
nonlinear preferential attachment model in which the exponent depends on
the type of network considered. The classical preferential attachment
model for networks by Barabási and Albert (1999) assumes a linear
relationship between the number of neighbors of a node in a network and
the probability of attachment. Although this assumption is widely made
in Web Science and related fields, the underlying linearity is rarely
measured. To fill this gap, this paper performs an empirical
longitudinal (time-based) study on forty-seven diverse Web network
datasets from seven network categories and including directed,
undirected and bipartite networks. We show that contrary to the usual
assumption, preferential attachment is nonlinear in the networks under
consideration. Furthermore, we observe that the deviation from
linearity is dependent on the type of network, giving sublinear
attachment in certain types of networks, and superlinear attachment in
others. Thus, we introduce the preferential attachment exponent $\beta$
as a novel numerical network measure that can be used to discriminate
different types of networks. We propose explanations for the behavior
of that network measure, based on the mechanisms that underly the growth
of the network in question.
Online Dating Recommender Systems: The Split-complex Number ApproachJérôme KUNEGIS
A typical recommender setting is based on two kinds of relations:
similarity between users (or between objects) and the taste of users
towards certain objects. In environments such as online dating
websites, these two relations are difficult to separate, as the users
can be similar to each other, but also have preferences towards other
users, i.e., rate other users. In this paper, we present a novel and
unified way to model this duality of the relations by using
split-complex numbers, a number system related to the complex numbers
that is used in mathematics, physics and other fields. We show that
this unified representation is capable of modeling both notions of
relations between users in a joint expression and apply it for
recommending potential partners. In experiments with the Czech dating
website Libimseti.cz we show that our modeling approach leads to an
improvement over baseline recommendation methods in this scenario.
Fairness on the Web: Alternatives to the Power LawJérôme KUNEGIS
This paper presents several measures of fairness and inequality based on the degree
distribution in networks, as alternatives to the well-established power-law exponent.
Networks such as social networks, communication networks and the World
Wide Web itself are often characterized by their unequal distribution of
edges: Few nodes are attached to many edges, while many nodes are
attached to only few edges. The inequality of such network structures is
typically measured using the power-law exponent, stating that the number of
nodes with a given degree is proportional to that degree taken to a
certain exponent. However, this approach has several weaknesses, such
as its narrow applicability and expensive computational complexity.
Beyond the fact that power laws are by far not a
universal phenomenon on the Web, the power-law exponent has the
surprising property of being negatively correlated with the usual
notion of inequality, making it unintuitive as a fairness measure. As
alternatives, we propose several measures based on the Lorenz curve,
which is used in economics but rarely in networks study, and on the
information-theoretical concept of entropy. We show in experiments on a
large collection of online networks that these measures do not suffer under
the drawbacks of the power-law exponent.
KONECT Cloud – Large Scale Network Mining in the CloudJérôme KUNEGIS
In the Winter 2011/2012 run at the Future SOC Lab, we used the KONECT
framework (Koblenz Network Collection) to compute ten
different network statistics on a large collection of downsampled
versions of a large network dataset, with the goal of determining
whether sampling of a large network can be used to reduce the
computational effort needed to compute a network statistic. Preliminary
results show that this is indeed the case.
On the Spectral Evolution of Large Networks (PhD Thesis by Jérôme Kunegis)Jérôme KUNEGIS
In this thesis, I study the spectral characteristics of large dynamic networks and formulate the spectral evolution model. The spectral
evolution model applies to networks that evolve over time, and describes their spectral decompositions such as the eigenvalue and singular value
decomposition.
The spectral evolution model states that over time, the eigenvalues of a
network change while its eigenvectors stay approximately constant.
Bad News Travel Fast: A Content-based Analysis of Interestingness on TwitterJérôme KUNEGIS
On the microblogging site Twitter, users can forward any message they receive to all of their followers. This is called a retweet and is usually done when users find a message particularly interesting and worth sharing with others. Thus, retweets reflect what the Twitter community considers
interesting on a global scale, and can be used as a function of interestingness to generate a model to describe the
content-based characteristics of retweets. In this paper, we analyze a set of high- and
low-level content-based features on several large collections of Twitter messages.
We train a prediction model to forecast for a given tweet its likelihood of being
retweeted based on its contents. From the parameters learned by the model
we deduce what are the influential content features that contribute to the
likelihood of a retweet. As a result we obtain insights into what
makes a message on Twitter worth retweeting and, thus, interesting.
On the Scalability of Graph Kernels Applied to Collaborative RecommendersJérôme KUNEGIS
We study the scalability of several recent graph kernel-based collaborative recommendation algorithms.
We compare the performance of several graph kernel-based
recommendation algorithms, focusing on runtime and recommendation accuracy with respect to the reduced rank of the subspace. We inspect the exponential and Laplacian exponential kernels, the resistance distance kernel, the regularized Laplacian kernel, and the stochastic diffusion kernel. Furthermore, we introduce new variants of kernels based on the graph
Laplacian which, in contrast to existing kernels, also allow
negative edge weights and thus negative ratings. We perform an evaluation on the Netflix Prize rating corpus on prediction and recommendation tasks, showing that dimensionality reduction not only makes prediction faster, but sometimes also more accurate.
Learning Spectral Graph Transformations for Link PredictionJérôme KUNEGIS
We present a unified framework for learning link prediction and edge weight prediction functions in large networks, based on the transformation of a graph’s algebraic spectrum. Our approach generalizes several graph kernels and dimensionality reduction methods and provides a method to estimate their parameters efficiently. We show how
the parameters of these prediction functions can be learned by reducing the problem to a one-dimensional regression problem whose runtime only depends on the method’s reduced rank and that can be inspected visually. We derive variants that apply to undirected, weighted, unweighted, unipartite and bipartite graphs. We evaluate our method
experimentally using examples from social networks, collaborative filtering, trust networks, citation networks, authorship graphs and hyperlink networks.
The Slashdot Zoo: Mining a Social Network with Negative EdgesJérôme KUNEGIS
We analyse the corpus of user relationships of the Slashdot technology news site. The data was collected from the Slashdot Zoo feature where users of the website can tag other users as friends and foes, providing positive and negative endorsements. We adapt social network analysis techniques to the problem of negative edge weights. In particular, we consider signed variants of global network characteristics such as
the clustering coefficient, node-level characteristics such as centrality and popularity measures, and link-level characteristics such as distances and similarity measures. We evaluate
these measures on the task of identifying unpopular users,
as well as on the task of predicting the sign of links and show that the network exhibits multiplicative transitivity which allows algebraic methods based on matrix multiplication to
be used. We compare our methods to traditional methods which are only suitable for positively weighted edges.
Spectral Analysis of Signed Graphs for Clustering, Prediction and VisualizationJérôme KUNEGIS
We study the application of spectral clustering, prediction and
visualization methods to graphs with negatively weighted edges. We show
that several characteristic matrices of graphs can be extended to graphs
with positively and negatively weighted edges, giving signed spectral
clustering methods, signed graph kernels and network visualization
methods that apply to signed graphs. In particular, we review a signed
variant of the graph Laplacian. We derive our results by considering
random walks, graph clustering, graph drawing and electrical networks,
showing that they all result in the same formalism for handling
negatively weighted edges. We illustrate our methods using examples
from social networks with negative edges and bipartite rating graphs.
Network Growth and the Spectral Evolution ModelJérôme KUNEGIS
We introduce and study the spectral evolution model, which characterizes
the growth of large networks in terms of the eigenvalue decomposition of
their adjacency matrices: In large networks, changes over time result in
a change of a graph's spectrum, leaving the eigenvectors unchanged. We
validate this hypothesis for several large social, collaboration,
authorship, rating, citation, communication and tagging networks,
covering unipartite, bipartite, signed and unsigned graphs. Following
these observations, we introduce a link prediction algorithm based on
the extrapolation of a network's spectral evolution. This new link
prediction method generalizes several common graph kernels that can be
expressed as spectral transformations. In contrast to these graph
kernels, the spectral extrapolation algorithm does not make assumptions
about specific growth patterns beyond the spectral evolution model. We
thus show that it performs particularly well for networks with
irregular, but spectral, growth patterns.
Osisko Development - Investor Presentation - June 24
Predicting Directed Links using Nondiagonal Matrix Decompositions
1. Web Science & Technologies
University of Koblenz ▪ Landau, Germany
Predicting Directed Links using
Nondiagonal Matrix Decompositions
Jérôme Kunegis & Jörg Fliege
Int. Conf. on Data Mining 2012
5. Computing Ak When A is Symmetric
Eigenvalue decomposition: A=UΛU T
Ak = (U Λ UT) (U Λ UT) . . . (U Λ UT)
k T
=UΛ U
Problem: A is asymmetric
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 5
6. Asymmetric Eigenvalue Decomposition
When A is diagonalizable: A=UΛU −1
Problem:
A is not
diagonalizable Advogato
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 6
7. Singular Value Decomposition
T
A=UΛV
k T
UΣ V
T T T
=UΣV VΣU ...UΣV
T
=AA ...A
Problem: This does not
equal Ak
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 7
8. DEDICOM
T
Solution: A=UXU
“DEDICOM – Decomposition into Directed Components”
X= Not diagonal
Advogato
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 8
9. Computation of Ak with DEDICOM
A =UX Uk k T
k
A is easy to compute
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 9
10. Finding a DEDICOM
Singular value decomposition:
T
A = U(Σ V U ) U T
Problem: Not computed to full rank
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 10
11. DEDICOM Algorithms
Using singular value decomposition A = U Σ VT
LEFT A = U (Σ VT U) UT
RIGHT A = V (VT U Σ) VT
CLO A = Q X QT
U Σ UT + V Σ VT = Q Λ QT (eigenvalue decomp.)
X = QT A Q
ITER Iterative algorithm
(Harshman 1978) (Kliers et al. 1990)
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 11
12. Approximation of eA = I + A + ½A² + ⅙A³ + . . .
Approximating A Approximating eA
Advogato trust
Advogato trust
DEDICOM algorithms
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 12
14. References
Predicting directed links using nondiagonal matrix decompositions
Jérôme Kunegis & Jörg Fliege
Int. Conf. on Data Mining, 2012
Models for analysis of asymmetrical relationships among n objects or stimuli
Richard A. Harshman
Contributions to economic analysis 187, 185–204, 1990
A generalization of Takane's algorithm for DEDICOM
Henk A. Kliers, Jos M. ten Berge, Yoshio Takane & Jan de Leeuw
Psychometrika 55(1), 151–158, 1990
Jérôme Kunegis & Jörg Fliege Predicting Directed Links using Nondiagonal Matrix Decompositions
kunegis@uni-koblenz.de ICDM 2012 14
