A Cognitive Heuristic model for Local Community Recognition

A Cognitive Heuristic model for Local
Community Recognition
A. Guazzini*
Department of Psychology, University of Florence
*: CSDC, Centre for the study of Complex Dynamics,
University of Florence, Italy

Contacts: andrea.guazzini@complexworld.net
emanuele.massaro@complexworld.net
franco.bagnoli@complexworld.net Webpage: http://www.complexworld.net/

Friday, June 8, 2012

A Cognitive Heuristic model of Local Community Recognition

Summary:

• The “ambiguous” concept of Community: just some Human examples
• The Cognitive Skills that make us smart and effective community detectors
• The Human Cognitive Heuristics: an operative deﬁnition
• A new operative framework for the modeling of Human Cognitive Heuristics:The
tri-partite model
• The challenge
• A minimal description of a cognitive inspired community recognizer
• Numerical simulations: the recipe
• Results
• A step forward
• Some Open Problems ....

AWASS 2012
Edinburg 10th-16th June



The “ambiguous” concept of Community: just some Human example
The concept of Human Community has been deﬁnitely
proved to be too wide and multidimensional to be easily
bound into a strict operative deﬁnition.

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The “ambiguous” concept of Community: just some Human example

The concept of Community appears
as Culture dependent and
determined by many socio
demographic factors

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The “ambiguous” concept of Community: the Clustering Spectrum
N°
of Communities
(K Individuals)

A better description for the Human communities
∼K
=
2 structure could be obtained considering the
Clustering Spectrum

∼ K
= 1
10

∼ K
= 4
10
Each Human Social Network can be
described in terms of density of
∼ K interactions among its members, so
= 8
10 designing a hierarchy of structures.

1
1 Normalized Weight Among Subjects (i.e. probability of interaction) 0

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The Human Social Skills: the perfect community recognizer

Humans have evolved their cognitive systems immersed
into an “Highly Social Environment”, developing
“Adapted” and sometimes Dedicated Neural Circuits
for facing with the Social Problems ... at least within the
Typical Sizes of the Human Communities.

Humans are: 15 5
effective Community Recognizer: usually they are very
“confident” about the communities they belong to and
very “confident” about the peculiarities that define Dunbar Theory 15
and distinguish such communities. (Categorization) Evolution has produced a
cognitive hierarchy of ecological
(typical) social structures.
effective Community Detectors: once trained cognition Such structures (Circles) can be
defined in terms of Emotional
50
appears as able to reveal an existing/known object Closeness among its members
(community) in an effective way, e.g. starting from few and revealed analyzing the
elements and consuming few time/resources frequencies of contact. 150

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A new operative framework for the modeling of Human Cognitive Heuristics:
The tri-partite model

Reaction time

Module I Flexibility
Unconscious knowledge
perceptive and attentive processes
Cognitive costs
Relevance Heuristic

Module II
Reasoning
Goal Heuristic
External Recognition Heuristic
Solve Heuristic
Data

Module III
Learning
Behavior
Evaluation Heuristic

The minimal structure of a Self
Awareness cognitive agent

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The Human Cognitive Heuristics: an operative deﬁnition

Using the theoretical tools of the Cognitive Neurosciences, Community Recognition/Deﬁnition and Community
Detection can be designed as the ability of the cognitive system to extract relevant information from the
environment, creating Prototypes (Mental Schemes) of Perceptive/knowledge Information Pattern

Prototype of Cognitive Heuristics

World Perception Gate Standard Neural
Cognitive Prototype Reasoning
Network Module (Mental Scheme-A)
I1 P1
w1,1
A1 Relevance/Coherence
Conscious Processing
Assessment
I2 P2 w.,2 A2 K1
w2,1
. Neuro . . K2
. Biology w2,n(K)
. wn(i),2 . .
of wn(a),2
. Encoding . w.,n(a) . Kn(K)
. Pn(i) An(a)
wn(i),n(a)
.
. k1 wn(k),n(a)
The Mental Scheme are
. k2 activated by the inputs and
. changes the representation of
IN Kn(k) the environment

Bounded Knowledge AWASS 2012 Bounded Knowledge
that integrates the Edinburg 10th-16th June that represents the
Input Input


“A Cognitive inspired Community Recognition Algorithm”

Considering an unknown dynamics network of relations, can be designed a Cognitive Agent that throughout
the “ecological interactions” with its neighbors, autonomously develops a representation/map of the existing
communities, or at least of its “position” along a given dimension?

5

15

50

150

Such algorithm should be intrinsically local and hence an optimal “Scalable Community Detection Algorithm”

AWASS 2012



The Simple Case
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AWASS 2012



The Simple Case
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AWASS 2012



The Simple Case

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The Simple Case

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The Simple Case !#$%%'()*#+(
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#M ij
j =1

AWASS 2012
! Edinburg 10th-16th June



The Simple Case
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Si =
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AWASS 2012



The Simple Case !#$#%'()%*#%!$
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The Simple Case

AWASS 2012



The Simple Case
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AWASS 2012



A more Complex Case
Fundamental
Developments

- Heterogeneous and dynamics parameters “m” and “alpha”.

- Introduction of a Typical Time Scales (e.g. Circadian Rhythm) in
correspondance of which the State Vector is reset.

- Introduction of a Bounded Long Term Knowledge Vector

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A more Complex Case
The Agent
Random Memory Random Learning
Parameter Parameter

Short Term (Unconscious)
“Bounded” Knowledge
mi ∈ (0, 1) αi ∈ (1, ∞) Long Term (Conscious)
“Bounded” Knowledge

S1 K1,1 K1,2 ... K1,n(s)
S2 K2,1 . . . . . .
. .
. .
. .
Sn(S) Kn(K),1 . . Kn(K),n(s)
State Bounded Vector Si(t) Knowledge Bounded Vector Ki(t)
where n(s) is a ﬁnite constant where n(K) is a ﬁnite constant

N Agent Estimated Entropy Agent Cognitive Dissonance
N

Ei =
t
Sij log(Sij )
t t
Di,j =
t t t
|Si,k − Sj,k |
j=1 k=1

AWASS 2012



A more Complex Case

The Environment

Connectivity Matrix Connectivity Matrix

10
Relevant Features
10

20
N = 90 20

30 30

40 Large Comm (BC)= 1 (90) 40

50
Medium Comm (MC) = 5 (18) 50

60 60

70 Small Comm (SC) = 10 (9) 70

80 80

90
P(Lij)=PA with PA(BC) PA(MC) PA(SC)
90
10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90

Unweighted Network
(Adjacency Matrix) Three different
“Typical Sizes”

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A more Complex Case
The Recipe

1- Discovery Phase
Information Spreading/Gathering phase and State Vector (Unconscious Knowledge) Updating

2- Cognitive Dissonance Phase
Evaluation of Ego-side Information Entropy and Cognitive Dissonance (with neighbors)

3- Reasoning Phase
Evolution/Modiﬁcation of the parameters whenever the discovery phase is “mute”

4- Inference Phase
Synchronized Reset of all the State Vector and Extrapolation of the ﬁrst K relevant
“approximation” of the network (state vectors), by the exploitation of the Ego Entropy.

AWASS 2012



A more Complex Case
The Recipe
1- Discovery Phase
Information Spreading/Gathering phase and State Vector (Unconscious Knowledge) Updating

Gathering SubPhase Learning SubPhase

t αt
(Qi,j ) i
t+1
Si,j = k(i) t αt
k=1 (Qi,k ) i
k(i)

Qt = mt Si + (1 − mt )
i i
t
i
t
Sk
k=1 Expansion of biggest component and reduction of smallest
component by renormalization.

Where S is the state vector, k(i) is the
number of neighbors of the agent i, and mti
the memory of agent i at time t

AWASS 2012



A more Complex Case
The Recipe
2- Cognitive Dissonance Phase
Evaluation of Ego-side Information Entropy and Cognitive Dissonance (with neighbors)

N Agent Estimated Entropy Agent Cognitive Dissonance
N

t
Ei = Sij log(Sij )
t t
Di,j =
t t t
|Si,k − Sj,k |
j=1 k=1

AWASS 2012



A more Complex Case
The Recipe
3- Reasoning Phase
Evolution/Modiﬁcation of the parameters whenever the discovery phase is “mute” and detection of the
change of sign in the second derivative of the entropy (Eti)

IF Just a “stupid/smart” rule
k(i) k(i) ds=0.1;
T
t−1 t
k=1 Di,k
Then
k=1 Di,k m(1,i)=m(1,i)*abs((randn*ds)+1);
|(Ei +
t−1
)| − |(Ei +
t
)| if m(1,i)1, m(1,i)=1; end;
t=t∗
k(i) k(i)
if m(1,i)0, m(1,i)=0.01; end;
FOR T − t∗ ∆t∗ alpha(1,i) = 1.5*abs((randn*ds)+1);
alpha(1,alpha(1,i)1)=1;

When the sign of the second derivative of the Agent
Entropy changes, the node temporary registers respectively:
- The state Vector
- The value of the ﬁrst derivative of Entropy
- The absolute Value of the Entropy
- The Cognitive Dissonance

Time
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A more Complex Case
The Recipe
4- Inference Phase
Synchronized Reset of all the State Vectors and Extrapolation of the ﬁrsts K relevant “approximation” of the
network (state vectors), by the exploitation of the Ego Entropy.

Sample coming from a
“typical” discovery period
(in humans the day)

Knowledge Time

Bounded Rationality
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A more Complex Case
Preliminary Results

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A more Complex Case Subject i (i=3) Long
Preliminary Results Term bounded
Memory

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A step forward: Some open problems

- Scalability of the algorithm with the System Size (N)

- Validation of the Dunbar Theory about the existence of typical sizes
of the human communities, due to their cognitive limits (i.e. Bounded
Rationality) and the environmental constraints (i.e. Network Topology)

- Multidimensional (i.e. more ecological) State Vector

- Rewiring, Pruning and human heuristics for the Network
Management.

AWASS 2012


A Cognitive Heuristic model for Local Community Recognition

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