a game theoretic framework for heterogenous information network clustering
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Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Game Theoretic Framework forHeterogeneous Information Network Clustering
Faris Alqadah
Johns Hopkins University
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Motivation
Heterogeneous Information Networks (HINs) are pervasivein applications ranging from bioinformatics to e-commerce.
Generalization of bi-clustering to pairwise relations asopposed to tensor spaces.
No unified definition of a HIN-cluster or algorithmicframework to mine them.
Address short coming of ‘pattern’-based approaches.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
HINs
Objects derived fromdistinct domains
Topology of the networkdetermined bypairwise-binary relationsamongst domains.
Graph representation of aHIN is a multi-partitegraph.
Clicking patterns, socialnetworks, gene networksfrom different experiments.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Related Work
Three major categories of work
Multi-way clustering [5, 4, 1, 2]: Directly extendbi-clustering or co-clustering. Mostly hard-clusters.
Information-network [10, 11]: Combine ranking andclustering using probabilty generating models, limited bynetwork-topology, hard clustering.
Pattern-based [3, 12, 7]: Formal Concept Analysis,overlapping clustering, too many clusters, parametersettings.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Multiple-edge HIN,competingcluster-influences.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Multiple-edge HIN,competingcluster-influences.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
For single-edge HIN,trade-off between numberof nodes in bipartite sets.
Multiple-edge HIN,competingcluster-influences.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
Multiple-edge HIN,competingcluster-influences.
An ‘ideal’ HIN-clustershould be an equilibriumpoint among all competingclustering influences.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Key Idea
Multiple-edge HIN,competingcluster-influences.
An ‘ideal’ HIN-clustershould be an equilibriumpoint among all competingclustering influences.
Nash equilibrium: No onecan do any betterassuming everyone elseretains the same strategy.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Notation
Context Kij = (Gi ,Gj , Iij), two sets and a relation.
A HIN Gn = (V,E) where V is a set of domains{G1, . . . ,Gn} and (Gi ,Gj) ∈ E iff ∃Kij
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Notation
Context Kij = (Gi ,Gj , Iij), two sets and a relation.
A HIN Gn = (V,E) where V is a set of domains{G1, . . . ,Gn} and (Gi ,Gj) ∈ E iff ∃Kij
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Concepts (maximal bicliques)
Common neighbors:
ψj(Ai) =
{
{gj ∈ Gj |gj Iijgi ∀gi ∈ Ai} if (Gi ,Gj) ∈ E,
∅ otherwise.
Concept or maximal bi-clique: (Ai ,Aj) such thatψj(Ai) = Aj and ψi(Aj) = Ai .
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Concepts (maximal bicliques)
Common neighbors:
ψj(Ai) =
{
{gj ∈ Gj |gj Iijgi ∀gi ∈ Ai} if (Gi ,Gj) ∈ E,
∅ otherwise.
Concept or maximal bi-clique: (Ai ,Aj) such thatψj(Ai) = Aj and ψi(Aj) = Ai .
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
FCA-based approaches
Generalize the notion of a concept (several definitions),and enumerate all such concepts.
Parameter settings not always intuitive.
Substantially different algorithm design for simple changein definition.
For suitably defined game, Nash equilibrium points capturemaximal bi-cliques.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Normal form game
A finite, n-player, normal form game, G, is a triple 〈N, (Mi), (ri )〉where
N = {1, . . . ,n} is the set of players
Mi = {m1i , . . . ,m
lii } is the set of moves available to player i
and li is the number of available moves for that player.
ri : M1 × · · · × Mn → R is the reward function for eachplayer i . It maps a profile of moves to a value.
Each player i selects a strategy from the set of all availablestrategies, Pi = {pi : Mi → [0,1]}
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Normal form game
A finite, n-player, normal form game, G, is a triple 〈N, (Mi), (ri )〉where
N = {1, . . . ,n} is the set of players
Mi = {m1i , . . . ,m
lii } is the set of moves available to player i
and li is the number of available moves for that player.
ri : M1 × · · · × Mn → R is the reward function for eachplayer i . It maps a profile of moves to a value.
Each player i selects a strategy from the set of all availablestrategies, Pi = {pi : Mi → [0,1]}
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Nash equilibrium and example
Nash equilibrium: A strategy profile in which no player has anincentive to unilaterally deviate [8, 6].
∀i ∈ N,pi ∈ Pi :
ri(p∗1, . . . ,p
∗i−1,pi , . . . ,p
∗n) ≤ ri(p
∗1, . . . ,p
∗n)
Player 2 chooses 0 Player 2 chooses 1 Player 2 chooses 2
Player 1 chooses 0 (0,0) (1,0) (2,-2)Player 1 chooses 1 (0,1) (1,1) ( 3,-2)Player 1 chooses 2 (-2,2) (-2,3) (2,2)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Nash equilibrium and example
Nash equilibrium: A strategy profile in which no player has anincentive to unilaterally deviate [8, 6].
∀i ∈ N,pi ∈ Pi :
ri(p∗1, . . . ,p
∗i−1,pi , . . . ,p
∗n) ≤ ri(p
∗1, . . . ,p
∗n)
Player 2 chooses 0 Player 2 chooses 1 Player 2 chooses 2
Player 1 chooses 0 (0,0) (1,0) (2,-2)Player 1 chooses 1 (0,1) (1,1) ( 3,-2)Player 1 chooses 2 (-2,2) (-2,3) (2,2)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Party planner game
Two party planners P1 and P2 plan a party by invitingguests from disjoint sets of clients G1 and G2.
Party planners receive compensation based on overallsatisfaction of clients.
Client satisfaction is a function of positive and negativeinteractions at the party
P1 and P2 do not cooperate, but are privy to each othersguest list at any point. Both wish to maximizecompensation.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Satisfaction Reward Function
Let (A1,A2) be a party. Define satisfaction of g1 ∈ A1 attendingparty (A1,A2) as
sat1(g1,A2) =|ψ2(g1) ∩ A2| − w ∗ |A2 \ ψ
2(g1)|
|A2|(1)
Overall reward to party planner i :
rsati (Ai ,Aj) =
∑
gi∈Ai
sati(gi ,Aj) (2)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Concepts as Nash equilibrium points
M1 M1,M2 M1,M2,M3 M1,M3 M2 M2,M3 M3G1 (1,1) (1,2) (1,3) (1,2) (1,1) (1,2) (1,1)
G1,G2 (2,1) (-1,-1) (-2,-3) (-1,-1) (-4,-2) (-4,-4) (-4,-2)G1,G2,G3 (3,1) (0,0) (-3,-3) (-3,-2) (-3,-1) (-6,-4) (-9,-3)
G1,G3 (2,1) (2,2) (0,0) (-1,-1) (2,1) (-1,-1) (-4,-2)G2 (1,1) (-2,-4) (-3,-9) (-2,-4) (-5,-5) (-5,-10) (-5,-5)
G2,G3 (2,1) (-1,-1) (-4,-6) (-4,-4) (-4,-2) (-7,-7) (-10,-5)G3 (1,1) (1,2) (-1,-3) (-2,-4) (1,1) (-2,-4) (-5,-5)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Concepts as Nash equilibrium points
Theorem
For any instance of the bi-clustering game Gbicluster in which rsati
is the selected reward function, there exists w∗, such that∀w ≥ w∗ if (A∗
1,A∗2) is a concept of K = (G1,G2, I12) then
(A∗1,A
∗2) is a Nash equilibrium point of Gbicluster .
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
HIN-clustering game
Extend bi-clustering game to n-party planners, n sets of guests.Guest interactions are determined by network topology.
Mining HIN-clusters is equivalent to findingNash-equilibrium points of the HIN-clustering game.
Finding Nash-equilibrium is non-trivial [9].
Adapt simple strategy and key heuristic to enumerate theNash equilibrium points.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Strategy and heuristics
M1 M1,M2 M1,M2,M3 M1,M3 M2 M2,M3 M3G1 (1,1) (1,2) (1,3) (1,2) (1,1) (1,2) (1,1)
G1,G2 (2,1) (-1,-1) (-2,-3) (-1,-1) (-4,-2) (-4,-4) (-4,-2)G1,G2,G3 (3,1) (0,0) (-3,-3) (-3,-2) (-3,-1) (-6,-4) (-9,-3)
G1,G3 (2,1) (2,2) (0,0) (-1,-1) (2,1) (-1,-1) (-4,-2)G2 (1,1) (-2,-4) (-3,-9) (-2,-4) (-5,-5) (-5,-10) (-5,-5)
G2,G3 (2,1) (-1,-1) (-4,-6) (-4,-4) (-4,-2) (-7,-7) (-10,-5)G3 (1,1) (1,2) (-1,-3) (-2,-4) (1,1) (-2,-4) (-5,-5)
1 Mark all second components that are maximal in each row.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Strategy and heuristics
M1 M1,M2 M1,M2,M3 M1,M3 M2 M2,M3 M3G1 (1,1) (1,2) (1,3**) (1,2) (1,1) (1,2) (1,1)
G1,G2 (2,1**) (-1,-1) (-2,-3) (-1,-1) (-4,-2) (-4,-4) (-4,-2)G1,G2,G3 (3,1**) (0,0) (-3,-3) (-3,-2) (-3,-1) (-6,-4) (-9,-3)
G1,G3 (2,1) (2,2**) (0,0) (-1,-1) (2,1) (-1,-1) (-4,-2)G2 (1,1**) (-2,-4) (-3,-9) (-2,-4) (-5,-5) (-5,-10) (-5,-5)
G2,G3 (2,1**) (-1,-1) (-4,-6) (-4,-4) (-4,-2) (-7,-7) (-10,-5)G3 (1,1) (1,2**) (-1,-3) (-2,-4) (1,1) (-2,-4) (-5,-5)
1 Mark all second components that are maximal in each row.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Strategy and heuristics
M1 M1,M2 M1,M2,M3 M1,M3 M2 M2,M3 M3G1 (1,1) (1,2) (1**,3**) (1**,2) (1,1) (1**,2) (1**,1)
G1,G2 (2,1**) (-1,-1) (-2,-3) (-1,-1) (-4,-2) (-4,-4) (-4,-2)G1,G2,G3 (3**,1**) (0,0) (-3,-3) (-3,-2) (-3,-1) (-6,-4) (-9,-3)
G1,G3 (2,1) (2**,2**) (0,0) (-1,-1) (2**,1) (-1,-1) (-4,-2)G2 (1,1**) (-2,-4) (-3,-9) (-2,-4) (-5,-5) (-5,-10) (-5,-5)
G2,G3 (2,1**) (-1,-1) (-4,-6) (-4,-4) (-4,-2) (-7,-7) (-10,-5)G3 (1,1) (1,2**) (-1,-3) (-2,-4) (1,1) (-2,-4) (-5,-5)
1 Mark all second components that are maximal in each row.2 Mark all first components that are maximal in each column.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Strategy and heuristics
M1 M1,M2 M1,M2,M3 M1,M3 M2 M2,M3 M3G1 (1,1) (1,2) (1**,3**) (1**,2) (1,1) (1**,2) (1**,1)
G1,G2 (2,1**) (-1,-1) (-2,-3) (-1,-1) (-4,-2) (-4,-4) (-4,-2)G1,G2,G3 (3**,1**) (0,0) (-3,-3) (-3,-2) (-3,-1) (-6,-4) (-9,-3)
G1,G3 (2,1) (2**,2**) (0,0) (-1,-1) (2**,1) (-1,-1) (-4,-2)G2 (1,1**) (-2,-4) (-3,-9) (-2,-4) (-5,-5) (-5,-10) (-5,-5)
G2,G3 (2,1**) (-1,-1) (-4,-6) (-4,-4) (-4,-2) (-7,-7) (-10,-5)G3 (1,1) (1,2**) (-1,-3) (-2,-4) (1,1) (-2,-4) (-5,-5)
1 Mark all second components that are maximal in each row.2 Mark all first components that are maximal in each column.3 Any cell that has both components marked is a Nash
equilibrium.
Heuristic: Every Nash equilibrium point is a superset of ann-concept.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
GHIN framework
Utilizing heuristic, exponential run time still possible.
Sacrifice completeness, but guarantee correctness
Attempt to form a Nash equilibrium point with each objectin the HIN.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
GHIN framework
1 For each object gi in the seed set attempt to formmaximally large n-partite clique in HIN.
2 Add objects from all domains to the clique while the rewardincreases.
3 Remove objects not in original clique from all domainswhile the reward increases.
4 If no change from step 2 and 3 Nash equilibrium found,else repeat 2 and 3.
5 Update the seed set by removing all objects in the cluster.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Shortcomings of satisfaction reward function
Satisfaction reward function simple, intuitive, and efficient.
If matrices in HIN have significantly different density levels,then bias occurs.
Use expected satisfaction instead.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Expected satisfaction
Assume all objects are independent.
For given party (A1, . . . ,An) expected number ofinteractions is number of success in |Aj | draws from finitepopulation of |Gj | objects
Expected number of success is hypergeometricallydistributed random variable.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Expected satisfaction
expij(gi ,Aj) =|Aj | ∗ |ψ
j(gi)|
|Gj |
varij(gi ,Aj) =|Aj | ∗ |ψ
j(gi)| ∗ (|Gj | − |Aj |) ∗ (|Gj | − |ψj (gi)|)
|Gj |2 ∗ (|Gj | − 1)
esat(gi ,Aj) =|ψj(gi) ∩ Aj | − expij(gi ,Aj)
√
varij(gi ,Aj)− w
esat(gi ,A−i) =∑
Aj⊆Gj ,(Gi ,Gj)∈E
esat(gi ,Gj)
resati (Ai ,A−i) =
∑
gi∈Ai
esat(gi ,A−i)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Expected satisfaction
expij(gi ,Aj) =|Aj | ∗ |ψ
j(gi)|
|Gj |
varij(gi ,Aj) =|Aj | ∗ |ψ
j(gi)| ∗ (|Gj | − |Aj |) ∗ (|Gj | − |ψj (gi)|)
|Gj |2 ∗ (|Gj | − 1)
esat(gi ,Aj) =|ψj(gi) ∩ Aj | − expij(gi ,Aj)
√
varij(gi ,Aj)− w
esat(gi ,A−i) =∑
Aj⊆Gj ,(Gi ,Gj)∈E
esat(gi ,Gj)
resati (Ai ,A−i) =
∑
gi∈Ai
esat(gi ,A−i)
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Tiring party goers
Incorporate ‘tiring’ factor to avoid too much overlap. Let c(gi)denote the number of clusters gi has appeared in upto thecurrent time-step, then let
t = f (c(gi))
wheref : N → (0,1]
and f is anti-monotonic. For example:
f (x) =1x2
f (x) =1ex
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Outline
1 IntroductionMotivation
2 PreliminariesHINs and FCAGame Theory
3 The Bi-clustering GameParty-Planners
4 FrameworkGHIN
5 Reward FunctionsExpected Satisfaction
6 Experimental ResultsReal world HINs
7 Conclusion
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
HINs and evaluation
HIN name Description Num domains Num classes Total num objectsMER Newsgroup, Middle East politics and Religion 3 2 24,783REC Newsgroup, recreation 3 2 26,225SCI Newsgroup, science 3 5 37,413PC Newsgroup, pc and software 3 5 35,186
PCR Newsgroup, politics and Christianity 3 2 24,485FOUR_AREAS DBLP subset of database, data mining, AI, and IR papers 4 4 70,517
Extrinsic evaluation, B3 recall and precision:
Prec(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|C(g) ∩ C(g′)|
Rcl(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|L(g) ∩ L(g′)|
B3Prec = Avgg [Avgg′,C(g)∩C(g′)6=∅[Prec(g,g′)]]
B3Rcl = Avgg [Avgg′,L(g)∩L(g′)6=∅[Rcl(g,g′)]]
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
HINs and evaluation
HIN name Description Num domains Num classes Total num objectsMER Newsgroup, Middle East politics and Religion 3 2 24,783REC Newsgroup, recreation 3 2 26,225SCI Newsgroup, science 3 5 37,413PC Newsgroup, pc and software 3 5 35,186
PCR Newsgroup, politics and Christianity 3 2 24,485FOUR_AREAS DBLP subset of database, data mining, AI, and IR papers 4 4 70,517
Extrinsic evaluation, B3 recall and precision:
Prec(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|C(g) ∩ C(g′)|
Rcl(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|L(g) ∩ L(g′)|
B3Prec = Avgg [Avgg′,C(g)∩C(g′)6=∅[Prec(g,g′)]]
B3Rcl = Avgg [Avgg′,L(g)∩L(g′)6=∅[Rcl(g,g′)]]
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
HINs and evaluation
HIN name Description Num domains Num classes Total num objectsMER Newsgroup, Middle East politics and Religion 3 2 24,783REC Newsgroup, recreation 3 2 26,225SCI Newsgroup, science 3 5 37,413PC Newsgroup, pc and software 3 5 35,186
PCR Newsgroup, politics and Christianity 3 2 24,485FOUR_AREAS DBLP subset of database, data mining, AI, and IR papers 4 4 70,517
Extrinsic evaluation, B3 recall and precision:
Prec(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|C(g) ∩ C(g′)|
Rcl(g,g′) =min(|C(g) ∩ C(g′)|, |L(g) ∩ L(g′)|)
|L(g) ∩ L(g′)|
B3Prec = Avgg [Avgg′,C(g)∩C(g′)6=∅[Prec(g,g′)]]
B3Rcl = Avgg [Avgg′,L(g)∩L(g′)6=∅[Rcl(g,g′)]]
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Results
HIN Algorithm F1 F0.5 F2
MER
GHIN expsat 0.627051 0.736396 0.622735GHIN sat 0.553790 0.649559 0.569664NetClus 0.3759 0.4512 0.322
MDC 0.3661 0.4533 0.3070
REC
GHIN expsat 0.544189 0.633362 0.508778GHIN sat 0.434367 0.485025 0.451840NetClus 0.2784 0.2870 0.2704
MDC 0.2845 0.2953 0.2746
SCI
GHIN expsat 0.484068 0.589704 0.530239GHIN sat 0.402306 0.481798 0.462886NetClus 0.2609 0.2583 0.2635
MDC 0.2532 0.2529 0.2535
PC
GHIN expsat 0.334827 0.520472 0.302943GHIN sat 0.306503 0.432229 0.345382NetClus 0.2254 0.2068 0.2477
MDC 0.2282 0.2116 0.2476
PCR
GHIN expsat 0.640894 0.793399 0.508778GHIN sat 0.541986 0.574588 0.530971NetClus 0.3642 0.4396 0.3109
MDC 0.3440 0.4268 0.2810
FOUR_AREAS
GHIN expsat 0.623117 0.598877 0.650079GHIN sat 0.5315 0.506687 0.5588NetClus 0.3612 0.36655 0.3560
MDC 0.5085 0.5162 0.5010
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Class distributions in clusters
Algorithm Class C1 C2 C3 C4
GHIN expsat
DB 0.0601266 0.93633 0.0133188 0.0512748DM 0.028481 0.0363608 0.0106007 0.850142IR 0.882911 0.0204432 0.133188 0.0339943AI 0.028481 0.00686642 0.842892 0.0645892
NetClus
DB 0.0553833 0.450802 0.500074 0.0955971DM 0.163934 0.15815 0.128535 0.304584IR 0.179553 0.0512035 0.242707 0.112786AI 0.60113 0.339844 0.128684 0.487033
MDC
DB 0.186681 0.232455 0.803727 0.000000DM 0.261844 0.000000 0.128592 0.161790IR 0.003183 0.278748 0.000000 0.75888AI 0.548292 0.488797 0.067680 0.079323
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Sample Clusters
Terms Authors Conferencesdata Surajit Chaudhuri VLDB
database Divesh Srivastava SIGMODqueries H. V. Jagadish ICDE
databases Jeffrey F. Naughton PODSquerys Michael J. Carey EDBT
xml Raghu Ramakrishnan
mining Jiawei Han KDDlearning Christos Faloutsos PAKDD
data Wei Wang ICDMfrequent Heikki Mannila SDM
association Srinivasan Parthasarathy PKDDpatterns Ke Wang ICML
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Applying GHIN to EMAP data
E-MAP (epistatic miniarray porfiles) query and target genes
Genetic interaction score indicates whether strain ishealthier or sicker than expected (positive or negative)
Negative network derived by using scores ≤ −2.5
Find Nash points, and use functional enrichment: Do wefind small functional classes?
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Applying GHIN to EMAP data
−0.01 0 0.01 0.02 0.03 0.04 0.05 0.060
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fra
ctio
n of
pat
tern
s en
riche
d
P−value threshold
Functional enrichment by large classes (31−500)
Exp sat tiringSat
−0.01 0 0.01 0.02 0.03 0.04 0.05 0.060
0.1
0.2
0.3
0.4
0.5
0.6
0.7
P−value threshold
Fra
ctio
n of
pat
tern
s en
riche
d
Functional enrichment by small classes
Exp sat tiringSat
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Clusters exclusively annotated by small functional classes:
YBR078W ECM33YIL034C CAP2YIL159W BNR1YKL007W CAP1YMR054W STV1YMR058W FET3YMR089C YTA12
YFL031W HAC1YHR079C IRE1YJL095W BCK1YCL048W SPS22YIL073C SPO22YJL155C FBP26YLR267W BOP2
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Parameter study
Effect of w on extrinsic clustering quality.
0 2 4 6 8 10 12−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
w
F1
scor
e
merrecpcrpcscifour
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
0.6
0.7
w
F0.
5 sc
ore
merrecpcrpcscifour
0 2 4 6 8 10 12−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
w
F2
scor
e
merrecpcrpcscifour
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Parameter study
Effect of w on algorithm operation.
0 2 4 6 8 10 125
10
15
20
25
30
w
Ave
rage
num
iter
atio
ns to
find
Nas
h
merrecpcrpcscifour
0 2 4 6 8 10 120
0.5
1
1.5
2
2.5x 10
4
w
Tot
al n
umbe
r of
iter
atio
ns
mer
rec
pcr
pc
sci
four
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900
1000
w
Num
ber
clus
ters
mer
rec
pcr
pc
sci
four
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Conclusion
Novel framework for defining and enumeratingHIN-clusters.
First (as far as I know) connection between Informationnetwork clustering and game theory.
Initial experimental results show promise.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
Ongoing and future work
Development of reward functions, (information theortic,spectral?).
Clustering in biological data, do we find smaller functionalclasses compared to other bi-clustering methods?
Extension of framework to weighted HINs.
More algorithmic development.
Compare algorithms with actual Nash solver.
Introduction Preliminaries The Bi-clustering Game Framework Reward Functions Experimental Results Conclusion
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