Mining Attributed Networks Part 1 Introduction Rushed Kanawati, - - PDF document
Overview Complex Network Analysis Outlook Mining Attributed Networks Part 1 Introduction Rushed Kanawati, Martin Atzmueller A 3 , Universit e Sorbonne Paris Cit e, France CSAI, Tilburg University, Netherlands DSAA17, Tokyo 20
Overview Complex Network Analysis Outlook
Mining Attributed Networks
Part 1 – Introduction Rushed Kanawati, Martin Atzmueller
A3, Universit´ e Sorbonne Paris Cit´ e, France CSAI, Tilburg University, Netherlands DSAA’17, Tokyo – 20 October 2017
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Overview Complex Network Analysis Outlook
OUTLINE
1 Overview: Complex Networks 2 Complex Network Analysis 1 Centralities, Roles & Similarities 2 Community Detection 3 Link Prediction 3 Outlook: Alternative Network Models
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Overview Complex Network Analysis Outlook
COMPLEX NETWORKS
Definition Graphs abstracting, directly or indirectly, interactions in real-world systems. Basic topological features
I Low Density I Small Diameter I Scale-free I High Clustering Coefficient
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Overview Complex Network Analysis Outlook
SCALE-FREE
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Overview Complex Network Analysis Outlook
CLUSTERING COEFFICIENT
Definitions I Global version : 3⇥4
^
I Local on node v : # of links between neighbors of v # Potential links between neighbors of v ⌅ CC = 3⇥1
8
⌅ CCv=1 = 1
6
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Overview Complex Network Analysis Outlook
NOTATION
A graph G =< V, E ✓ V ⇥ V > I V: set of nodes (a.k.a. vertices, actors, sites) I E: set of edges (a.k.a. ties, links, bonds) Notations I AG Adjacency Matrix d : aij 6= 0 iff (vi, vj) 2 E, 0 otherwise. I n = |V| I m = |E|. Often m ⇠ n I Γ(v) : neighbors of node v. Γ(v) = {x 2 V : (x, v) 2 E}. I Node degree : d(v) =k Γ(v) k
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Overview Complex Network Analysis Outlook
COMPLEX NETWORKS : EXAMPLE I
Direct interactions
Density : 2−3 Diameter : 28 Clustering coeff.: 0.47
Greatest connected component of Wikipedia 7 / 45
Overview Complex Network Analysis Outlook
COMPLEX NETWORKS : EXAMPLE II
Indirect interactions
Density : 10−4 Diameter : 24 Clustering coeff.: 0.67
Co-authorship network - DBLP 1980-1984 (for authors active for more than 10 years) 8 / 45
Overview Complex Network Analysis Outlook
SIMILARITY GRAPHS
⌅ ✏-neighborhood graph : u, v are linked iff d(u, v) ✏ ⌅ k-nearest neighbor graph : each node is connected to k nearest nodes. ⌅ Relative neighborhood graph : u, v are linked iff d(u, v) maxx{d(v, x), d(u, x)}, 8x 6= u, v
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Overview Complex Network Analysis Outlook
SIMILARITY GRAPHS
Figure:RNG graph Figure: ✏-threshold graph Figure:Knn graph
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Overview Complex Network Analysis Outlook
COMPLEX NETWORKS 6= RANDOM GRAPHS
Erd¨
enyi model Rule : for n nodes, generate edges (i,j) randomly and independently with probability p ⌅ Low density ⌅ Small diameter ⌅ Clustering coefficient ⇠ p ⌅ not scale-free
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Overview Complex Network Analysis Outlook
COMPLEX NETWORKS 6= RANDOM GRAPHS
Small-world graphs ⌅ Low density ⌅ Small diameter ⌅ High clustering coefficient ⌅ not scale-free
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Overview Complex Network Analysis Outlook
COMPLEX NETWORKS 6= RANDOM GRAPHS
Preferential attachement Rule : New nodes prefer to connect to high degree nodes ⌅ Low density ⌅ Small diameter ⌅ Clustering coefficient ! 0 ⌅ Scale-free
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Overview Complex Network Analysis Outlook
COMPLEX NETWORK ANALYSIS
A lot of interesting results using a simple model: interacting nodes ⌅ Node related analysis tasks Centralities, Roles, Similarities ⌅ Community detection Local, disjoint, overlapping, hierarchical ⌅ Network evolution mining Link prediction
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Overview Complex Network Analysis Outlook
CENTRALITIES
Nodes centralities
Degree centrality example
I Importance and/or influence of a node I PageRank, HITS : web search results ranking I FolkRank: Tag recommendation I Betweenness, Closeness: Importance of actors in a social network I Viral maketing
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Overview Complex Network Analysis Outlook
ROLES
Node Roles
red nodes are star centers, blues are in-clique and others are peripherial
I Nodes having a similar structural behavior I Centers of stars, in cliques, peripheral nodes, . . . I Role query, Role outliers, Role dynamics, Role transfer, . . . I See Henderson et al. KDD 2012
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Overview Complex Network Analysis Outlook
NODE SIMILARITY
I A node is similar to itself I Neighborhood-based similarity: Two nodes are similar if they are connected to the same nodes. I Distance-based similarity: Two nodes are similar if they are connected by short paths. I Structural-similarity : Two nodes are similar if each one is similar to the neighbors of the other.
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Overview Complex Network Analysis Outlook
COMMUNITY DETECTION
Overview I Given a network/graph, find “modules” I Single network I Multiplex networks I Attributed networks I Community structures I Graph Clustering/disjoint communities I Hierarchical organization I Overlapping communities I Questions: I What is ”a community”? I What are ”good” communities? I How do we evaluate these?
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Overview Complex Network Analysis Outlook
COMMUNITY DETECTION
Definitions I A dense subgraph loosely coupled to other modules in the network I A community is a set of nodes seen as “one” by nodes outside of the community I A subgraph where almost all nodes are linked to other nodes in the community. I . . .
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Overview Complex Network Analysis Outlook
COMMUNITY DETECTION
Applications I Finding similar items (documents, users, queries, etc.) I Collaborative filtering I Network visualisation I Computation distribution I . . .
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Overview Complex Network Analysis Outlook
LOCAL COMMUNITY
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Overview Complex Network Analysis Outlook
LOCAL COMMUNITY
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Overview Complex Network Analysis Outlook
QUALITY FUNCTIONS : EXAMPLES I
Local modularity R [Cla05] R =
Bin Bin+Bout
Local modularity M [LWP08] M = Din
Dout
Local modularity L [CZG09] L = Lin
Lex where : Lin = P
i∈D
kΓ(i)\Dk kDk
, Lex =
P
i∈B
kΓ(i)\Sk kBk
And many many others . . . [YL12]
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Overview Complex Network Analysis Outlook
GLOBAL COMMUNITY DETECTION
I Communities can also be defined with respect to the whole graph I Graph has community structure, if its structure is different from a random graph I Random graph: Not expected to have community structure I Here: Any two vertices have the same probability to be adjacent I Define null model; use it for investigating if we can observe community structure in a graph
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Overview Complex Network Analysis Outlook
GLOBAL COMMUNITY DETECTION
Problem I Divide the set of nodes in a number of (overlapping) subsets such that induced subgraphs are dense and loosely coupled. Recommended readings I S. Fortunato. Community detection in graphs. Physics Reports, 2010, 486, 75-174 I L. Tang, H. Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010
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Overview Complex Network Analysis Outlook
COMMUNITIES DETECTION: METHODS
Classification I Group-based Nodes are grouped in function of shared topological features (ex. clique) I Network-based Clustering, Graph-cut, block-models, modularity optimization I Propagation-based Unstable approaches, good when used with ensemble clustering I Seed-centric from local community identification to global community detection I Descriptive Community Detection Identifies communities and description (for attributed network).
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Overview Complex Network Analysis Outlook
GROUP-BASED APPROACHES
Principle Search for special (dense) subgraphs: I k-clique I n-clique I -dense clique I K-core
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Overview Complex Network Analysis Outlook
GROUP-BASED APPROACHES
from Symeon Papadopoulos, Community Detection in Social Media, CERTH-ITI, 22 June 2011
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Overview Complex Network Analysis Outlook
QUASI-CLIQUE
Search for special (dense) subgraphs: I Generalize clique to dense subgraph I Different definitions (degree, density) I Subset of nodes is quasi-clique, if I Nodal degree: every node in induced subgraph is adjacent to at least (n - 1) other nodes in the subgraph I Edge density: Number of edges in subgraph is at least n(n - 1)/2 (with n : number of nodes in subgraph)
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Overview Complex Network Analysis Outlook
NETWORK-BASED APPROACHES
Clustering approaches I Apply classical clustering approaches using graph-based distance function I Different types of Graph-based distances: neighborhood-based, path-based (Random-walk) I Usually requires the number of clusters to discover
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Overview Complex Network Analysis Outlook
MODULARITY OPTIMIZATION APPROACHES
Modularity: a partition quality criteria Q(P) = 1 2m X
c2P
X
i,j2c
(Aij didj 2m ) (1)
Figure: Example : Q = 0.31
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Overview Complex Network Analysis Outlook
MODULARITY OPTIMIZATION APPROACHES
I Applying classical optimization algorithms (ex. Genetic algorithms [Piz12]). I Applying hierarchical clustering and select the level with Qmax (ex. Walktrap [PL06]) I Divisive approach : Girvan-Newman algorithm [GN02] I Greedy optimization : Louvain algorithm [BGL08] I . . .
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Overview Complex Network Analysis Outlook
MODULARITY OPTIMIZATION LIMITATIONS
Hypothesis The best partition of a graph is the one that maximizes the modularity. If a network has a community structure, then it is possible to find a precise partition with maximal modularity If a network has a community structure, then partitions inducing high modularity values are structurally similar. All three hypothesis do not hold [GdMC10, LF11].
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Overview Complex Network Analysis Outlook
PROPAGATION-BASED APPROACHES
Algorithm 1 Label propagation Require: G =< V, E > a connected graph,
1: Initialize each node with unique label lv 2: while Labels are not stable do 3:
for v 2 V do lv = arg max
l
|Γl(v)| /* random tie-breaking */
4:
end for
5: end while 6: return communities from labels
Γl(v) : set of neighbors having label l
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Overview Complex Network Analysis Outlook
LABEL PROPAGATION
Advantages I Complexity : O(m) I Highly parallel Disadvantages I No convergence guarantee, oscillation phenomena I Low robustness Different runs yield very different community structure due to randomness
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Overview Complex Network Analysis Outlook
SEED-CENTRIC ALGORITHMS
(KANAWATI, SCSM’2014)
Algorithm 2 General seed-centric community detection algorithm Require: G =< V, E > a connected graph,
1: C ; 2: S compute seeds(G) 3: for s 2 S do 4:
Cs compute local com(s,G)
5:
C C + Cs
6: end for 7: return compute community(C)
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Overview Complex Network Analysis Outlook
LINK PREDICTION
Link predction I Structural Find hidden/missing links in a network
I Temporal Predicting new links to appear at time tp based
Readings I M. Pujari et. al., Link prediction in complex networks, chapter 3, in Advanced methods for complex networks Analysis, N. Meghanthan (Editor), IGI publishing, 2016.
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Overview Complex Network Analysis Outlook
OUTLOOK: ALTERNATIVE NETWORK MODELS
Network science is mature enough to a move towards more complex, expressive models ⌅ K-partite networks
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Overview Complex Network Analysis Outlook
ALTERNATIVE NETWORK MODELS
Network science is mature enough to a move towards more complex, expressive models ⌅ K-partite networks ⌅ Dynamic networks
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Overview Complex Network Analysis Outlook
ALTERNATIVE NETWORK MODELS
Network science is mature enough to a move towards more complex, expressive models ⌅ K-partite networks ⌅ Dynamic networks ⌅ Heterogeneous networks ⌅ Multiplex networks
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Overview Complex Network Analysis Outlook
ALTERNATIVE NETWORK MODELS
Network science is mature enough to a move towards more complex, expressive models ⌅ K-partite networks ⌅ Dynamic networks ⌅ Heterogeneous networks ⌅ Multiplex networks ⌅ Attributed networks
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Overview Complex Network Analysis Outlook
ALTERNATIVE NETWORK MODELS
Network science is mature enough to a move towards more complex, expressive models ⌅ K-partite networks ⌅ Dynamic networks ⌅ Heterogeneous networks ⌅ Multiplex networks ⌅ Attributed networks Next: A powerful model : Multiplex Network
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Overview Complex Network Analysis Outlook
BIBLIOGRAPHY I
Vincent D Blondel, Jean-loup Guillaume, and Etienne Lefebvre, Fast unfolding of communities in large networks, Journal of Statistical Mechanics: Theory and Experiment 2008 (2008), P10008. Aaron Clauset, Finding local community structure in networks, Physical Review E (2005). Jiyang Chen, Osmar R. Za¨ ıane, and Randy Goebel, Local community identification in social networks, ASONAM, 2009,
Review E (2010), no. 81, 046106.
Andrea Lancichinetti and Santo Fortunato, Limits of modularity maximization in community detection, CoRR abs/1107.1 (2011). 43 / 45
Overview Complex Network Analysis Outlook
BIBLIOGRAPHY II
Feng Luo, James Zijun Wang, and Eric Promislow, Exploring local community structures in large networks, Web Intelligence and Agent Systems 6 (2008), no. 4, 387–400. Clara Pizzuti, A multiobjective genetic algorithm to find communities in complex networks, IEEE Trans. Evolutionary Computation 16 (2012), no. 3, 418–430. Pascal Pons and Matthieu Latapy, Computing communities in large networks using random walks, J. Graph Algorithms Appl. 10 (2006), no. 2, 191–218. Jaewon Yang and Jure Leskovec, Defining and evaluating network communities based on ground-truth, ICDM (Mohammed Javeed Zaki, Arno Siebes, Jeffrey Xu Yu, Bart Goethals, Geoffrey I. Webb, and Xindong Wu, eds.), IEEE Computer Society, 2012, pp. 745–754. 44 / 45
Overview Analysis Conclusion
Mining Attributed Networks
Part 2 – Analysis of Multiplex Networks Rushed Kanawati, Martin Atzmueller
A3, Universit´ e Sorbonne Paris Cit´ e, France CSAI, Tilburg University, Netherlands DSAA’17, Tokyo – 20 October 2017
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Overview Analysis Conclusion
OUTLINE
1 Multiplex networks: Overview & Definitions 2 Analysis of multiplex networks 1 Network Measures 2 Analysis tasks 3 Evaluation 3 Conclusions
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Overview Analysis Conclusion
MULTIPLEX NETWORK: DEFINITIONS
G =< V, E, C >
from [Mucha et. al., 2010]
I V set of nodes I E = {E1, . . . , Eα} : 8k 2 [1, α]Ek ✓ V ⇥ V I C Layer coupling links Coupling I Ordinal Coupling : Diagonal inter-layer links among consecutive layers. I Categorical Coupling : Diagonal inter-layer links between all pairs of layers. I Generalized coupling ? Ex. Decay functions
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Overview Analysis Conclusion
NOTATION
Notation
I A[k] Adjacency Matrix of slice k : a [k]
ij 6= 0 iff (vi, vj) 2 Ek, 0 otherwise.
I m[k] = |Ek|. Often, we have m ⇠ n I Neighbors of v in slice k: Γ(v)[k] = {x 2 V : (x, v) 2 Ek}. I All neighbors of v : Γ(v)tot = [s∈{1,...,α}Γ(v)[s] I Node degree in slice k: dk
v =k Γ(v)[k] k
I Total degree of node v: dtot
v
= ||Γtot(v)||
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Overview Analysis Conclusion
MULTIPLEX NETWORKS: RELATED TERMS
Recommended readings / S. Mikko Kivel¨ a et. al.. Multilayer Networks. arXiv:1309.7233, March 2014
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Overview Analysis Conclusion
POWER OF THE MULTIPLEX MODEL
Multi-relational networks European airports network
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Overview Analysis Conclusion
POWER OF MULTIPLEX MODEL
Dynamic networks Academic collaborations per year
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Overview Analysis Conclusion
POWER OF THE MULTIPLEX MODEL
Heterogeneous networks DBLP author-centred multiplex network
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Overview Analysis Conclusion
MULTIPLEX NETWORKS : MEASURES
⌅ Need of generalization of the usual measures : Degree Neighborhood Centralities Paths and distances Clustering coefficient . . . ⌅ New layer-oriented questions to answer : Which layers determine the centrality of a user Which layers are relevant to measure the similarity of two nodes How one layer influence the evolution
. . .
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Overview Analysis Conclusion
APPROACHES
1 Transformation into a monoplex centred problem
I Layer aggregation approaches. I Hypergraph transformation based approaches I Ensemble approaches
2 Generalization of monoplex oriented algorithms to multiplex networks
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Overview Analysis Conclusion
LAYER AGGREGATION
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Overview Analysis Conclusion
LAYER AGGREGATION
Aggregation functions
Aij = 8 < : 1 91 l α : A [l]
ij 6= 0
Aij =k {d : A[d]
ij
6= 0} k Aij = 1 α
α
X
k=1
wkA[k]
ij
Aij = sim(vi, vj)
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Overview Analysis Conclusion
K-UNIFORM HYPERGRAPH TRANSFORMATION
Principle I A k-uniform hypergraph is a hypergraph in which the cardinality
I Mapping a multiplex to a 3-uniform hypergraph H = (V, E) such that : V = V [ {1, . . . , α} (u, v, i) 2 E if 9l : A [l]
uv 6= 0, u, v 2 V, i 2 {1, . . . , α}
I Apply hypergraphs analysis approaches (Ex. tensor-based approaches)
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Overview Analysis Conclusion
MULTIPLEX: NODE NEIGHBORHOOD
Some options I Γmux(v) = [α
k=1Γk(v)
I Γmux(v) = \α
k=1Γk(v)
I Γmux(v) = {x 2 Γ(v)tot : sim(x, v) δ} δ 2 [0, 1] I Γmux(v) = {x 2 Γ(v)tot : Γ(v)tot\Γ(x)tot
Γ(v)tot[Γ(x)tot δ}
I . . .
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Overview Analysis Conclusion
PATHS, SHORTEST DISTANCE
Some options I Path in an aggregated network I daverage =
Pm
α=1 d(u,v)[α]
m
8u, v 2 V and (u, v) / 2 Ei. I path length(u, v) =< r1, r2, . . . , rα > where ri number of links in layer i I pathx(u, v) dominates pathy(u, v)9j : rx
j < ry j , 8k 6= j rx j ry j
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Overview Analysis Conclusion
WHAT ABOUT COMMUNITIES?
What is a dense subgraph in a multiplex network ?
[BCG11] 16 / 49
Overview Analysis Conclusion
COMMUNITY DETECTION IN MULTIPLEX NETWORKS
Approaches 1 Transformation into a monoplex community detection problem
I Layer aggregation approaches. I Multi-objective optimization approach. I Ensemble clustering approaches
2 Generalization of monoplex oriented algorithms to multiplex networks.
I Generalized-modularity optimization I Generalized info-map I Generalized walktrap I Seed-centric approaches
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Overview Analysis Conclusion
MULTI-OBJECTIVE OPTIMIZATION APPROACH [AP14]
1 Rank the set of α layers according to some importance criteria 2 C1 community(G[1]) 3 for i 2 [2, α] do: Ci optimize(community(G[i]), similarity(Ci1)) 4 return Cα
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING APPROACHES
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING APPROACHES
Ensemble Clustering [SG03] I CSPA: Cluster-based Similarity Partitioning Algorithm I HGPA: HyperGraph-Partitioning Algorithm I MCLA: Meta-Clustering Algorithm I . . .
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING: APPROACHES
CSPA: Cluster-based Similarity Partitioning Algorithm I Let K be the number of basic models, Ci(x) be the cluster in model i to which x belongs. I Define a similarity graph on objects : sim(v, u) =
K
P
i=1
δ(Ci(v),Ci(u)) K
I Cluster the obtained graph : Isolate connected components after prunning edges Apply community detection approach I Complexity : O(n2kr) : n # objects, k # of clusters, r# of clustering solutions
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Overview Analysis Conclusion
CSPA : EXAMPLE
from Seifi, M. Cœurs stables de communaut´ es dans les graphes de terrain. Th` ese de l’universit´ e Paris 6, 2012 22 / 49
Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION I
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION II
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION III
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION IV
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION V
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION VI
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Overview Analysis Conclusion
ENSEMBLE CLUSTERING : ILLUSTRATION VII
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MULTIPLEX MODULARITY
Generalized modularity [MRM+10] I Qmultiplex(P) = 1 2µ X
c2P
X
i,j2c k,l:1!α
@ @A[k]
ij λk
d[k]
i d[k] j
2m[k] 1 A δkl + δijCkl
ij
1 A I µ = P
j2V k,l:1!α
m[k] + Cl
jk
I Ckl
ij Inter slice coupling = 0 8i 6= j
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Overview Analysis Conclusion
SEED-CENTRIC ALGORITHMS [KAN14]
Algorithm 1 General seed-centric community detection algorithm Require: G =< V, E > a connected graph,
1: C ; 2: S compute seeds(G) 3: for s 2 S do 4:
Cs compute local com(s,G)
5:
C C + Cs
6: end for 7: return compute community(C)
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Overview Analysis Conclusion
THE LICOD ALGORITHM [YK14]
1 Compute a set of seeds that are likely to be leaders in their communities
Heuristic : nodes having higher degree centralities than their neighbors
2 Each node in the graph ranks seeds in function of its own preference
In function of increasing shortest path (length)
3 Iterate till convergence: Each node modifies its preference vector in function of neighbor’s preferences
Applying rank aggregation methods.
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Overview Analysis Conclusion
MUXLICOD
Multiplex degree centrality [BNL13] dmultiplex
i
=
α
X
k=1
d[k]
i
d[tot]
i
log d[k]
i
d[tot]
i
! Multiplex shortest path SP(u, v)multiplex =
α
P
k=1
SP(u, v)[k] α Multiplex neighborhood Γmux(v) = {x 2 Γ(v)tot : Γ(v)tot \ Γ(x)tot Γ(v)tot [ Γ(x)tot δ}
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Overview Analysis Conclusion
RANK AGGREGATION
[PK12, DKNS01]
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Overview Analysis Conclusion
OTHER ALGORITHMS
1 Random walk based approach (Generalization of Walktrap [KM15] 2 Generalized infomap [DLAR15]
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Overview Analysis Conclusion
EVALUATION CRITERIA I
1 Multiplex modularity 2 Redundancy [BCG11] ρ(c) = X
(u,v)2 ¯ ¯ Pc
k {k : 9A[k]
uv 6= 0} k
α⇥ k Pc k ¯ ¯ P the set of couple (u, v) which are directly connected in at least two layers 3 Complementarity :γ(c) = Vc ⇥ εc ⇥ Hc
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Overview Analysis Conclusion
EVALUATION CRITERIA II
I Variety Vc : the proportion of occurrence of the community c across layers of the multiplex. Vc =
α
X
s=1
k9(i, j) 2 c/A[s]
ij 6= 0k
α 1 (1) I Exclusivity εc : number of pairs of nodes, in community c, that are connected exclusively in one layer. εc =
α
X
s=1
kPc,sk kPck (2)
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Overview Analysis Conclusion
EVALUATION CRITERIA III
I Homogeneity Hc : How uniform is the distribution of the number of edges, in the community c, per layer. Hc = ⇢ 1 if σc = 0 1
σc σmax
c
(3) with avgc =
α
X
s=1
kPc,sk α σc = v u u t
α
X
s=1
(kPc,sk avgc)2 α σmax
c
= r (max(k Pc,d k) min(k Pc,d k))2 2
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Overview Analysis Conclusion
DATASETS
Benchmark networks Lazzega Lawyer network #nodes 71 #layer 3
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Overview Analysis Conclusion
DATASETS
Dataset Physicians collaboration network #nodes 246 #layers 3
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Overview Analysis Conclusion
RESULTS: REDUNDANCY
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Overview Analysis Conclusion
RESULTS: COMPLEMENTARITY
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Overview Analysis Conclusion
RESULTS: MULTIPLEX MODULARITY
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Overview Analysis Conclusion
PARETO FRONT
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Overview Analysis Conclusion
LAZEGA DATASET: COMPARATIVE STUDY
Figure: NMI (lower triangular part) , adjusted Rand (upper triangular part).
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Overview Analysis Conclusion
CONCLUSIONS
I Multiplex networks provide a rich representation of real-world interaction systems I A lot of work to reformulate basic network concepts for multiplex settings, e.g. Roles, RandomWalk, PageRank, etc. I Community evaluation: still an open problem I Uncovered topics : Layer selection and compression, Co-evolution models, Dynamics on multiplex networks I Ideas under exploration: I Multiplex of multiplexes I Interactive Multiplex network visualisation. I Benchmarking of available tools
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Overview Analysis Conclusion
BIBLIOGRAPHY I
Alessia Amelio and Clara Pizzuti, Community detection in multidimensional networks, IEEE 26th International Conference on Tools with Artificial Intelligence, 2014, pp. 352–359. Michele Berlingerio, Michele Coscia, and Fosca Giannotti, Finding and characterizing communities in multidimensional networks, ASONAM, IEEE Computer Society, 2011, pp. 490–494. Federico Battiston, Vincenzo Nicosia, and Vito Latora, Metrics for the analysis of multiplex networks, CoRR abs/1308.3182 (2013). Cynthia Dwork, Ravi Kumar, Moni Naor, and D Sivakumar, Rank aggregation methods for the Web, WWW, 2001, pp. 613–622. Manlio De Domenico, Andrea Lancichinetti, Alex Arenas, and Martin Rosvall, Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems, Phys. Rev 5 (2015), 011027. 47 / 49
Overview Analysis Conclusion
BIBLIOGRAPHY II
Rushed Kanawati, Seed-centric approaches for community detection in complex networks, 6th international conference on Social Computing and Social Media (Crete, Greece) (Gabriele Meiselwitz, ed.), vol. LNCS 8531, Springer, June 2014, pp. 197–208. Zhana Kuncheva and Giovanni Montana, Community detection in multiplex networks using locally adaptive random walks, MANEM 2workshop - Proceedings of ASONAM 2015 (Paris), August 2015. Peter J Mucha, Thomas Richardson, Kevin Macon, Mason A Porter, and Jukka-Pekka Onnela, Community structure in time-dependent, multiscale, and multiplex networks, Science 328 (2010), no. 5980, 876–878. Manisha Pujari and Rushed Kanawati, Supervised rank aggregation approach for link prediction in complex networks, WWW (Companion Volume) (Alain Mille, Fabien L. Gandon, Jacques Misselis, Michael Rabinovich, and Steffen Staab, eds.), ACM, 2012, pp. 1189–1196.
Machine Learning Research 3 (2003), 583–617. 48 / 49
Overview Analysis Conclusion
BIBLIOGRAPHY III
Zied Yakoubi and Rushed Kanawati, Licod: Leader-driven approaches for community detection, Vietnam Journal of Computer Science 1 (2014), no. 4, 241–256. 49 / 49
Université Sorbonne Paris Cité, France Tilburg University, Netherlands
DSAA 2017, Tokyo, 2017-10-20
Overview/Recap: Attributed Networks Compositional Subgroup Analysis Community Detection Link Prediction Summary
2
Set of atomic entities (actors)
Set of links/edges between nodes ("ties") Edges model pairwise relationships Edges: Directed or undirected Social network [Wassermann & Faust 1994]
Social structure capturing actor relations Actors, links given by dyadic ties between actors
Abstract object – independent of representation
3
Structural
Measure ties between actors (è links) Specific relation Make up connections in graph/network
Compositional
Measure actor attributes
Age Gender Ethnicity Affiliation …
Describe actors
4
Graph: edge attributes and/or node attributes
Structure: ties/links (of respective relations)
Attributes - additional information
Actor attributes (node labels) Link attributes (information about connections) Attribute vectors for actors and/or links … can be mapped from/to each other
Integration of heterogenous data (networks +
Enables simultaneous analysis of relational +
5
Examples
Citation Attributes
(Co-)Authors Affiliation Country Gender …
WWW
Links Content (BoW) …
(Newman 2003)
6
Subgroup
Subset of actors (and all their ties)
Define subgroups using specific criteria
Compositional – actor attributes Structural – using tie structures
Detection of cohesive subgroups &
Subgroup discovery è actor attributes … attributed graph è can combine both
7
Detect subgroups according to specific
Focus on actor attributes Describe actor subset using attributes
Often hypothesis-driven approaches: Test
In contrast: Subgroup discovery
Hypothesis-generating approach Exploratory data mining method Local exceptionality detection
8
Overview/Recap: Attributed Networks Compositional Subgroup Analysis Community Detection Link Prediction Summary
9
§ Task:
§ Examples:
§ "45% of all men aged between 35 and 45 have a high
§ "66% all all woman aged between 50 and 60 have a
Descriptive patterns for subgroup
Gender= Female Age = [50; 60] è Centrality = high {flickr, delicious}, {library, android}, {php, web} è Centrality = high
10
– Data as set of cases (records) in tabular form – Target concept (e.g. „high centrality“) – Quality function (interesting measure)
– Description, e.g., sex=female age= 50-60
– Size n, e.g., in 180 of 1000 cases – Deviation
11
n:Size of subgroup (number of cases) p: share of cases with target = true in the subgroup p0: share of cases with target = true in the total population a: weight size against deviation (parameter)
12
Heuristic: Beam Search Exhaustive Approaches:
Basic idea: Efficient data
SD-Map – based on FP-
SD-Map* – Utilizing
13
Optimistic Estimate
Optimistic Estimate:
Remove path starting at
14
Exceptional Model Mining
Identification of Patterns showing an "interesting behavior" for a certain
Mean test (e.g., influence factors for increased centrality) Linear regression (e.g., different centrality measures) Correlation Coefficient (e.g., factors for role analysis) Variance (e.g., degree, clustering coefficient, …) …
Algorithms:
Beam-Search
GP-Growth
Faster by multiple orders of magnitude compared to
standard methods
Fastest exhaustive algorithm so far
15
Overview/Recap: Attributed Networks Compositional Subgroup Analysis Community Detection Link Prediction Summary
16
Data sources
Structural variables (ties, links) Compositional variables
Actor attributes Represented as attribute vectors
Edge attributes
Each edge has an assigned label Multiplex graphs
17
Clustering edge-attributed graphs
Reduce/flatten to weighted graph
Derive weights according to number of edges where nodes are
directly connected [Berlingerio et al. 2011]
Standard graph clustering approaches can then be directly applied
Frequent-itemset based [Berlingerio et al. 2013] Subspace-oriented [Boden et al. 2012]
18
Non-uniform terminology
Social-attribute network Attribute augmented graph Feature-vector graph, vertex-labeled graph Attributed graph …
Different representations
19
Utilize structural + attribute information Different roles of a description
Methods "guiding"community detection using
"Dense structures" - connectivity But no "perfect" attribute homogeneity (purity)
Methods generating explicit descriptions, i.e.,
"Dense structures" – connectivity Concrete descriptions, e.g., conjunctive logical
20
Weight modification (edges) according to nodal
Abstraction into similarities between nodes
Specifically, distance-based community detection
Entropy-oriented methods
Model-based approaches [Xu et al. 2012, Yang et al.
21
Use attribute-based distance measure Community detection: Group nodes according to
Evaluate final partitioning using Modularity
22
For a partition, optimize entropy using
Integrate
23
In general: Model edge & attribute values
Use MDL to select clusters w.r.t. attribute
Data compression of connectivity
Lossless compression è MDL cost-function Resulting node groups
Homogeneous both in node & attribute matrix Nodes - similar connectivity & high attribute coherence
24
Community mining scenario
Discover "densely connected groups of nodes" Communities should have explicit description Community (evaluation) space: network/graph
Goal:
Often: Discover top-k communities Maximize some community
25
Social tagging system:
{work, flickr, delicious} {business, production, sales} {php, web, internet},
{work, flickr, delicious},
26
Cluster transformed node-attribute similarity
Mine frequent itemsets (binary attributes)
Combine dense subgraph mining + subspace
Apply correlated pattern mining Interleave community detection
Adapt local exceptionality detection (using
27
Twofold cluster O: Combine subspace-clustering &
O fulfills subspace property (maximal distance threshold
O fulfills quasi-clique property, according to nodal-
Induced subgraph of O is connected, and fulfills minimal
Quality function: Density ∙ Size ∙ #Dimensions Pruning using subspace & quasi-clique properties Includes Redundancy-optimization step (Overlapping
28
Structural correlation pattern mining (SCPM)
Correlation between node attribute set and dense
Quality measure: Comparison against null model
Size of the pattern Cohesion of the pattern (density of quasi-clique)
Compare against expected structural correlation of
29
Find communities with concise descriptions
Focus: Overlapping, diverse, descriptive
Language: Disjunctions of conjunctive
Two-stage approach
Greedy hill-climbing step: Generate candidates
Redescription generation: Induce description
Heuristic approach, due to large search
30
Starts with candidate communities
Domain knowledge Partial communities Start with single vertices (later being extended
ReMine algorithm for deriving patterns for
31
32
Basic Idea: Pattern Mining for Community
Mine patterns in description space (tags/topics)
Optimize quality measure in community space
Improve understandability of communities (explanation)
33
Goal: Identification/description of communities with
Input: Network/Graph + node properties (e.g., tags) Output: k-best community patterns
Description language: conjunctive expressions COMODO algorithm: Top-k pattern mining, based on
Discover k-best patterns Search space: Conjunctions/tags Apply standard community quality functions, e.g.,
34
Goal: Mine patterns describing such groups
Merge networks + descriptive features, e.g.,
Target both
Community structure (some evaluation function) & Community description (logical formula, e.g.,
35
Dataset of edges connecting two nodes
Described by intersection of labels of the two nodes Additionally: Store nodes, and respective degrees
Apply top-k method w/ optimistic-estimate pruning
Web Mining, Computer, Java Web Mining, Computer, JavaScript Web Mining, Computer
36
Problem: Exponential Search Space Optimistic Estimate: Upper bound for the
37
Overview/Recap: Attributed Networks Compositional Subgroup Analysis Community Detection Link Prediction Summary
38
Utilize both structure & attributive information
Relational data – Markov networks: Object labels +
Relations to statistical relational learning, e.g.
Markov Logic Networks,
e.g., [Richardson & Domingos 2006]
Probabilistic Soft Logic,
e.g., [Kimmig et al. 2012, Bach et al. 2013]
Combine logic and probabilities - formulate "rules“ on
attribute domains for inferring links
Or: As before, transform to a simple "base"
39
How to model relationships between
for link prediction/link formation/label prediction generating a network
Utilize generative graph models:
Attributed graph model (AGM)
Multiplicative attributed graph model
Importance of attributes, structural inference
40
Overview/Recap: Attributed Networks Compositional Subgroup Analysis Community Detection Link Prediction Summary
41
Subgroup analysis & community detection
Compositional Structural + compositional Providing explicit descriptions
Both can be combined for obtaining descriptive
Different approaches/techniques, select
Outlook: Hybrid (multiplex, attributed) network
42
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Applications Tools Conclusions
Mining Attributed Networks
Part 4 – Applications, Tools & Conclusions Rushed Kanawati, Martin Atzmueller
A3, Universit´ e Sorbonne Paris Cit´ e, France CSAI, Tilburg University, Netherlands DSAA’17, Tokyo – 20 October 2017
1 / 53
Applications Tools Conclusions
OUTLINE
1 Applications Recommender systems, Cluster ensemble selection Explanation-aware recommendation 2 Tools Multiplex analysis Compositional analysis Attributed network analysis 3 Conclusions Summary Hybrid Approaches Further Directions & Outlook
2 / 53
Applications Tools Conclusions
APPLICATIONS
1 Film recommendation 2 Tag recommendation 3 Collaboration recommendation 4 Ensemble clustering selection
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Applications Tools Conclusions
FILM RECOMMENDATION
Film rating matrix = bipartite graph
4 / 53
Applications Tools Conclusions
FILM RECOMMENDATION
5 / 53
Applications Tools Conclusions
FILM RECOMMENDATION
6 / 53
Applications Tools Conclusions
FILM RECOMMENDATION : MULTIPLEX NETWORK
Figure: MovieLens 100k multiplex (Projection by users) Figure: MovieLens 100k multiplex (Projection by movies)
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Applications Tools Conclusions
FILM RECOMMENDATION : RESULTS
Simple approach Recommend the statistical mode value of links linking clusters of target user to the cluster of target films
MAE RMSE Precision Recall F1-measure GTM 0.9441 1.2549 0.2185 0.2207 0.2195
0.9293 1.2562 0.25587 0.2094 0.2303 muxlicod 0.9635 1.2773 0.2274 0.2134 0.2202 LA louvain 0.8352 1.1509 0.3113 0.2521 0.2779 LA walktrap 0.8216 1.1155 0.2642 0.2233 0.2420 PA louvain 0.8713 1.1917 0.2532 0.2032 0.2245 PA walktrap 0.8801 1.2023 0.2705 0.2011 0.2283 Table: Result of the proposed recommendation system with each algorithm in MovieLens 100k dataset (PA : Partition Aggregation, LA : Layer Aggregation
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Applications Tools Conclusions
APPLICATION II: TAG RECOMMENDER (TLTR)
Figure: TLTR model
9 / 53
Applications Tools Conclusions
FOLKSONOMY GRAPHS
Figure: Tripartite graph projection into three bipartite graphs
10 / 53
Applications Tools Conclusions
MULTIPLEX NETWORK CONSTRUCTION
Figure: Tag multiplex network: Steps of transformation
11 / 53
Applications Tools Conclusions
EXPERIMENTS: BIBSONOMY DATASET
# Users # Tags # Resources # Edges 116 412 361 24297
Table: Bibsonomy dataset
Networks slices Nodes Edges Density User User-Resource 116 901 0,135 User-Tag 116 985 0,147 Tag Tag-Resource 412 2496 0,0294 Tag-User 412 1956 0,0231 Resource Resource-Tag 361 2814 0,0433 Resource-User 361 1685 0,0259
Table: Multiplex networks of Bibsonomy
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Applications Tools Conclusions
TAG RECOMMENDATION: RESULTS
Graphs #Nodes #Edges #Users #Tags #Resources G 889 24297 116 412 361 Gc (Mux-Licod) 434 1677 97 154 183 compression in % 51, 18 93, 1 16, 37 62, 62 49, 30 Gc (GenLouvain) 16 79 4 6 6 compression in % 98, 2 99, 67 96, 55 98, 54 98, 33 Gc (LA (Licod)) 91 46 13 40 38 compression in % 89, 76 99, 81 88, 79 90, 29 89, 47 Gc (LA (Louvain)) 9 27 3 3 3 compression in % 98, 98 99, 88 97, 41 99, 27 99, 16 Gc (EC (Licod)) 151 993 3 89 59 compression in % 83, 08 95, 91 97, 41 78, 39 83, 65 Gc (EC (Louvain)) 25 187 8 11 6 compression in % 97, 18 78, 96 93, 10 97, 33 98, 3313 / 53
Applications Tools Conclusions
TAG RECOMMENDATION: RESULTS
Figure: Comparative study of different tag recommendation approaches in terms of precision with kt = 1
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Applications Tools Conclusions
TAG RECOMMENDATION: RESULTS
Figure: Comparative study of different tag recommendation approaches in terms of precision with kt = 2
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Applications Tools Conclusions
TAG RECOMMENDATION: RESULTS
Figure: Comparative study of different tag recommendation approaches in terms of precision with kt = 3
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Applications Tools Conclusions
TAG RECOMMENDATION: RESULTS
Figure: Comparative study of different tag recommendation approaches in terms of precision with kt = 4
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Applications Tools Conclusions
DISCUSSION
I Multiplex approaches outperform layer aggregation and EC approaches on benchmark networks I Layer aggregation approaches do well for film recommendation! I EC approaches rank first for Tag recommendation! I Problem: What is the Validity of topological community quality indexes?
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Applications Tools Conclusions
APPLICATION III: SCIENTIFIC COLLABORATION
RECOMMENDER
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Applications Tools Conclusions
LINK PREDICTION: SUPERVISED APPROACH
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Applications Tools Conclusions
EXPERIMENTS: DBLP
Years Properties Co-Author Co-Venue Co-Citation 1970-1973 Nodes 91 91 91 Edges 116 1256 171 1972-1975 Nodes 221 221 221 Edges 319 5098 706 1974-1977 Nodes 323 323 323 Edges 451 9831 993
Table: Basic statistics about the 3-layer DBLP multiplex networks
Years # Positive # Negatives Train/Test Labeling 1970-1973 1974-1975 16 1810 1972-1975 1976-1977 49 12141 1974-1977 1978-1979 93 26223
Table: # examples extracted from co-authorship layer (number of unconnected nodes in
connected components)
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Applications Tools Conclusions
LINK PREDICTION: RESULTS
Learning:1970-1973 Learning:1972-1975 Attributes Test:1972-1975 Test:1974-1977 F-measure AUC F-measure AUC Setdirect 0.0357 0.5263 0.0168 0.4955 Setdirect+indirect 0.0256 0.5372 0.0150 0.5132 Setdirect+multiplex 0.0592 0.5374 0.0122 0.5108 Setall 0.0153 0.5361 0.0171 0.5555 Setmultiplex 0.0374 0.5181 0.0185 0.5485
Table: Comparative link prediction results applying decision tree algorithm using different types of attributs
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Applications Tools Conclusions
APPLICATION IV: ENSEMBLE CLUSTERING SELECTION
Motivation The quality of a consensus clustering depends on both the quality and diversity of input base clusterings [FL08, AF09, NCC13, ADIA15]. Problem definition I Let Π = {π1, . . . , πn} be a set of base partitions I ES(Π) = Π∗ ⊂ Π : Q(EC(Π∗)) > Q(EC(Π)) I Q : Quality of the consensus clustering
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Applications Tools Conclusions
DIVERSITY
Clustering Similarity measures I Purity I Rand/ARI I NMI (Normlized mutual information) I IV (Information variation) [Mei03] I . . .
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Applications Tools Conclusions
QUALITY
Cluster internal quality indexes [AR14] I Silhouette index, I Calinski-Harabasz index I Davis-Bouldin index I Dunn index I . . . Network-oriented indexes I Modularity I Average conductance I Average local Modularities : L, M, R [Kan15] I See also [YL12] I . . .
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Applications Tools Conclusions
ENSEMBLE SELECTION APPROACHES : LIMITATIONS
I Existing approaches are defined for attribute/value datasets with metric distances I Use of one quality/diversity measure. I Requires the number of clusters to select as input. I . . . Proposed approach: contributions I Designed for both networks and attribute/value datasets I Use of an ensemble of quality/diversity measures. I The number of selected base clustering is automatically computed.
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Applications Tools Conclusions
ENSEMBLE SELECTION APPROACH
The idea ⌅ Cluster the set of base clusterings using an ensemble of similarity measures Apply a multiplex community detection algorithm to a multiplex network whose nodes are the set of base clusterings and whose layers are defined by a set of proximity graphs, each defined according a to a given similarity measure ⌅ From each cluster select the node (i.e clustering) that is ranked first according to an ensemble of quality measures. Apply ensemble ranking algorithms
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Applications Tools Conclusions
ENSEMBLE SELECTION APPROACH
Algorithm 1 Graph-based cluster ensemble selection algorithm Require: Π = {π1, . . . , πr} a set of base clusterings Require: S = {S1, . . . , Sn} A set of partition similarity functions Require: Q = {Q1, . . . , Qm} A set of partition quality functions
1: Π∗ ← ∅ 2: MUX ← Multiplex(Π) 3: for all Si ∈ S do 4:
MUX.add layer(proximity graph(Π, Si))
5: end for 6: C = {c1, . . . , ck} ← community detection(MUX) 7: for all c ∈ C do 8:
ˆ π ← ensemble Ranking(c, Q)
9:
Π∗ ← Π∗ ∪ {ˆ π}
10: end for 11: return Π∗
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Applications Tools Conclusions
THE PROPOSED APPROACH
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Applications Tools Conclusions
THE PROPOSED APPROACH
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Applications Tools Conclusions
THE PROPOSED APPROACH
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Applications Tools Conclusions
ENSEMBLE RANKING
Problem I Let L be a set of elements to rank by n rankers I Let σi be the rank provided by ranker i I Goal: Compute a consensus ranking of L. Deja Vu: Social choice algorithms, but . . . I Small number of voters and big number of candidates I Algorithmic efficiency is required Algorithms I Borda I Kemeny approaches (commuting Condorcet winner if it exists)
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Applications Tools Conclusions
EXPERIMENT ON SMALL NETWORKS WITH KNOWN
GROUND TRUTH PARTITIONS
I Generation of 20 base clusterings applying a standard Label propagation algorithm I Proximity graphs : RNG I S = { NMI, ARI, VI } Q = { modularity, Local modularities L, M, R }
Table: Evaluation of the proposed graph-based ensemble selection Dataset Approach NMI ARI Zachary Ensemble clustering without selection 0.57 0.46 Ensemble clustering with selection 0.77 0.69 US Politics Ensemble clustering without selection 0.55 0.68 Ensemble clustering with selection 0.68 0.67 Dolphins Ensemble clustering without selection 0.55 0.39 Ensemble clustering with selection 0.58 0.59
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Applications Tools Conclusions
EXPERIMENT II : DBLP CO-AUTHORSHIP NETWORK
I Co-authorship network 1970-1977 (GCC) : |V| = 643, |m| = 886 I Generation of 10, 100 base clusterings I Proximity graphs : RNG I S = { NMI, ARI, VI } I Q = { modularity, Local modularities L, M, R }
Table: Evaluation of the proposed graph-based ensemble selection # base clusterings 10 Nodes Compression without selection 18,3% Nodes Compression with selection 20,9% Edge compression without selection 17,2% Edge compression with selection 17,6% Modularity without selection 0.3734 Modularity with selection 0.43756
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Applications Tools Conclusions
EXPERIMENT II : DBLP CO-AUTHORSHIP NETWORK
Table: Evaluation of the proposed graph-based ensemble selection # base clusterings 100 Nodes Compression without selection 35,1% Nodes Compression with selection 40,3% Edge compression without selection 36,2% Edge compression with selection 38,3% Modularity without selection 0.4031 Modularity with selection 0.4665
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Applications Tools Conclusions
MULTIPLEX ANALYSIS TOOLS
I muxviz : http://muxviz.net I Muna : http://lipn.fr/muna I Pymnet http://people.maths.ox.ac.uk/kivela/mln_library/
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Applications Tools Conclusions
MUXVIZ
I R package I Main features : ⌅ Visualization ⌅ Layer compression methods ⌅ Basic metrics ⌅ Community detection : Modularity-based, infomap I Input : text file per layer + one file for the general structure.
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Applications Tools Conclusions
MUNA
I Available for R and Python I Built on top of igraph I Extended set of multiplex network edition functions (similar to igraph) I Basic metrics : degree, neighborhood I Extended set of community detection approaches I Topological community evaluation indexes. I Limitations : I No visualisation support I Simple categorical coupling only.
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Applications Tools Conclusions
PYMNET
I Pure Python + integration with networkX package. I Can handle general multilayer networks I Rule based generation and lazy-evaluation of coupling edges I Various network analysis methods, transformations, reading and writing networks, network models etc. I Visualization support
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Applications Tools Conclusions
PYMNET: VISUALISATION EXAMPLE
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Applications Tools Conclusions
ATTRIBUTED NETWORK ANALYSIS TOOLS
I rsubgroup http://rsubgroup.org I VIKAMINE [AL12] http://vikamine.org I COMODO [AM11, ADM16] http://vikamine.org I DCM [PBvL14] http://patternsthatmatter.org/software.php#dcm I GAMER [GFBS13] http://dme.rwth-aachen.de/de/gamer
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Applications Tools Conclusions
RSUBGROUP
Open Source: http://rsubgroup.org I R-Package for subgroup discovery I Support for detecting compositional subgroups I Can be utilized for dyadic analysis (on attributed graphs) I Support for ARFF, CSV files I Simple interface to subgroup discovery functionality I Wrapper to Java-based (efficient) implementations I Based on Open Source VIKAMINE system
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Applications Tools Conclusions
VIKAMINE [AL12]
Open Source: http://vikamine.org I Visual, Interactive and Knowledge-intensive Analysis and semantic MINing Environment I Open Source Java implementation I Efficient automatic discovery & community detection algorithms I Seamless integration of visualization methods I Effective visualizations for ad-hoc analysis I Ad-hoc formalization, utilization, and extension of background knowledge I Works also on big data (Map/Reduce)
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Applications Tools Conclusions
COMODO [AM11, ADM16]
Open Source: Available as plugin to VIKAMINE system vikamine.org I Description-oriented approach for community detection on attributed networks I Open Source Java implementation I Algorithm based on subgroup discovery I Top-k pattern mining I Concise descriptions (conjunctions of features/descriptors) I Efficient search & pruning techniques
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Applications Tools Conclusions
SUMMARY
I Powerful applications supported using multiplex and attributed network analysis. I New tools for multiplex mining : Muna [FK15], muxviz[DPA14], Pymnet I New tools for mining attributed networks: I Attributed graph clustering, e.g., GAMER [GFBS13] http://dme.rwth-aachen.de/de/gamer I Description-oriented community detection: VIKAMINE, COMODO [AL12, AM11, ADM16] (www.vikamine.org) I Compositional subgroup analysis: VIKAMINE & rsubgroup (rsubgroup.org)
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Applications Tools Conclusions
HYBRID APPROACHES
I Hybrid: combinations of attributed, multiplex, dynamic,
I Emerging research direction, combination of different techniques I Recent research directions regarding hybrid approaches, e.g., I subspace clustering [BGHS17] for edge attributed multi-graphs I Clustering attributed multi-graphs [PPD17] I Modeling and comparing graph-based hypotheses on attributed multiplex networks [ASK16, ASKA17] I Bayesian model fitting on edge formation in attributed multi-graphs [ENLSS17] I Exceptional model mining (Bayesian modeling) in attributed multiplex networks, cf. [Atz16]
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Applications Tools Conclusions
FURTHER DIRECTIONS & OUTLOOK
I Challenges modeling heterogeneous data, e.g. in ubiquitous and social environments, e. g., [ABK+14] I Necessary: Efficient methods and tools for the mining of such data I Mining complex networks from different perspectives & dimensions I Integration of attributed multiplex networks & temporal information I Explanation-aware methods, providing transparent modeling, mining & explanations, e. g., [RBSLB07, ARB10]
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Applications Tools Conclusions
BIBLIOGRAPHY I
Martin Atzmueller, Martin Becker, Mark Kibanov, Christoph Scholz, Stephan Doerfel, Andreas Hotho, Bjoern-Elmar Macek, Folke Mitzlaff, Juergen Mueller, and Gerd Stumme, Ubicon and its Applications for Ubiquitous Social Computing, New Review of Hypermedia and Multimedia 20 (2014), no. 1, 53–77. Ebrahim Akbari, Halina Mohamed Dahlan, Roliana Ibrahim, and Hosein Alizadeh, Hierarchical cluster ensemble selection, Engineering Applications of Artificial Intelligence 39 (2015), 146–156. Martin Atzmueller, Stephan Doerfel, and Folke Mitzlaff, Description-Oriented Community Detection using Exhaustive Subgroup Discovery, Information Sciences 329 (2016), 965–984. Javad Azimi and Xiaoli Fern, Adaptive cluster ensemble selection, IJCAI (Craig Boutilier, ed.), 2009, pp. 992–997. Martin Atzmueller and Florian Lemmerich, VIKAMINE - Open-Source Subgroup Discovery, Pattern Mining, and Analytics,
Discovery in Databases (Heidelberg, Germany), Springer Verlag, 2012. 48 / 53
Applications Tools Conclusions
BIBLIOGRAPHY II
Martin Atzmueller and Folke Mitzlaff, Efficient Descriptive Community Mining, Proc. 24th International FLAIRS Conference (Palo Alto, CA, USA), AAAI Press, 2011, pp. 459 – 464. Charu C. Aggarwal and Chandan K. Reddy (eds.), Data clustering: Algorithms and applications, CRC Press, 2014. Martin Atzmueller and Thomas Roth-Berghofer, The Mining and Analysis Continuum of Explaining Uncovered, Proc. 30th SGAI International Conference on Artificial Intelligence (AI-2010), 2010. Martin Atzmueller, Andreas Schmidt, and Mark Kibanov, DASHTrails: An Approach for Modeling and Analysis of Distribution-Adapted Sequential Hypotheses and Trails, Proc. WWW 2016 (Companion), IW3C2 / ACM, 2016. Martin Atzmueller, Andreas Schmidt, Benjamin Kloepper, and David Arnu, HypGraphs: An Approach for Analysis and Assessment of Graph-Based and Sequential Hypotheses, New Frontiers in Mining Complex Patterns. Postproceedings NFMCP 2016 (Heidelberg, Germany), LNAI, springer, 2017. 49 / 53
Applications Tools Conclusions
BIBLIOGRAPHY III
Martin Atzmueller, Detecting Community Patterns Capturing Exceptional Link Trails, Proc. IEEE/ACM ASONAM (Boston, MA, USA), IEEE Press, 2016. Brigitte Boden, Stephan G¨ unnemann, Holger Hoffmann, and Thomas Seidl, Mimag: mining coherent subgraphs in multi-layer graphs with edge labels, Knowledge and Information Systems 50 (2017), no. 2, 417–446. Manlio De Domenico, Mason A. Porter, and Alex Arenas, Multilayer analysis and visualization of networks, J. Complex Netw. (2014) 10 (2014). Lisette Esp´ ın-Noboa, Florian Lemmerich, Markus Strohmaier, and Philipp Singer, Janus: A hypothesis-driven bayesian approach for understanding edge formation in attributed multigraphs, Applied Network Science 2 (2017), no. 1, 16. Issam Falih and Rushed Kanawati, Muna: A multiplex network analysis library, The 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (Paris), August 2015, pp. 757–760. 50 / 53
Applications Tools Conclusions
BIBLIOGRAPHY IV
Xiaoli Z. Fern and Wei Lin, Cluster ensemble selection, Statistical Analysis and Data Mining 1 (2008), no. 3, 128–141. Stephan G¨ unnemann, Ines F¨ arber, Brigitte Boden, and Thomas Seidl, GAMer: A Synthesis of Subspace Clustering and Dense Subgraph Mining, Knowledge and Information Systems (KAIS), Springer, 2013. Rushed Kanawati, Empirical evaluation of applying ensemble methods to ego-centered community identification in complex networks, Neurocomputing 150, B (2015), 417–427. Marina Meila, Comparing clusterings by the variation of information, COLT (Bernhard Sch¨
eds.), Lecture Notes in Computer Science, vol. 2777, Springer, 2003, pp. 173–187. Murilo Coelho Naldi, Andr´ e C. P. L. F. Carvalho, and Ricardo J. G. B. Campello, Cluster ensemble selection based on relative validity indexes, Data Min. Knowl. Discov. 27 (2013), no. 2, 259–289. 51 / 53
Applications Tools Conclusions
BIBLIOGRAPHY V
Simon Pool, Francesco Bonchi, and Matthijs van Leeuwen, Description-driven community detection, ACM TIST 5 (2014),
Andreas Papadopoulos, George Pallis, and Marios D Dikaiakos, Weighted clustering of attributed multi-graphs, Computing 99 (2017), no. 9, 813–840. Thomas Roth-Berghofer, Stefan Schulz, David Leake, and Daniel Bahls, Explanation-Aware Computing, AI Magazine 28 (2007), no. 4. Christoph Scholz, Martin Atzmueller, Alain Barrat, Ciro Cattuto, and Gerd Stumme, New Insights and Methods For Predicting Face-To-Face Contacts, Proc. 7th Intl. AAAI Conference on Weblogs and Social Media (Palo Alto, CA, USA) (Emre Kiciman, Nicole B. Ellison, Bernie Hogan, Paul Resnick, and Ian Soboroff, eds.), AAAI Press, 2013. 52 / 53
Applications Tools Conclusions
BIBLIOGRAPHY VI
Jaewon Yang and Jure Leskovec, Defining and evaluating network communities based on ground-truth, ICDM (Mohammed Javeed Zaki, Arno Siebes, Jeffrey Xu Yu, Bart Goethals, Geoffrey I. Webb, and Xindong Wu, eds.), IEEE Computer Society, 2012, pp. 745–754. 53 / 53