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

Webpage: http://www.complexworld.net/

Contacts: [email protected] [email protected]

[email protected]

Friday, June 8, 2012

http://www.complexworld.net/








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 2012Edinburg 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.




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

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

demographic factors




The “ambiguous” concept of Community: the Clustering Spectrum

A better description for the Human communities structure could be obtained considering the

Clustering Spectrum

N° of Communities

(K Individuals)

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

∼=K

2

∼=K

101

∼=K

104

∼=K

108

Each Human Social Network can be described in terms of density of

interactions among its members, so designing a hierarchy of structures.

11 0




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.

� 5

� 15

� 15

� 50

� 150

Dunbar Theory Evolution has produced a

cognitive hierarchy of ecological (typical) social structures.

Such structures (Circles) can be defined in terms of Emotional Closeness among its members

and revealed analyzing the frequencies of contact.

Humans are:effective Community Recognizer: usually they are very “confident” about the communities they belong to and

very “confident” about the peculiarities that define and distinguish such communities. (Categorization)

effective Community Detectors: once trained cognition appears as able to reveal an existing/known object

(community) in an effective way, e.g. starting from few elements and consuming few time/resources




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

The minimal structure of a Self Awareness cognitive agent

Module IUnconscious knowledge

perceptive and attentive processes

Relevance Heuristic

Module IIReasoning

Goal HeuristicRecognition Heuristic

Solve Heuristic

Module IIILearning

Evaluation Heuristic

Reaction time

Flexibility

Cognitive costs

External Data

Behavior




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

Perception GateWorld Reasoning

I1I2.

.

.

.

.

.

.

IN

P1

P2

.

.

.

Pn(i)

k1

k2

.Kn(k)

Neuro Biology

of Encoding

A1

A2

.

.

.

An(a)

w1,1

w.,2

w.,n(a)

wn(i),n(a)

wn(i),2

Standard Neural Network Module

wn(k),n(a)

Cognitive Prototype(Mental Scheme-A)

Bounded Knowledge that integrates the

Input

K1

K2

.

Kn(K)

w2,1

w2,n(K)

wn(a),2

Relevance/Coherence Assessment

The Mental Scheme are activated by the inputs and

changes the representation of the environment

Conscious Processing

Bounded Knowledge that represents the

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”



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The Simple Case




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Cogni

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The Simple Case




The Simple Case




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The Simple Case




A more Complex CaseFundamental 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




A more Complex Case The Agent

Short Term (Unconscious) “Bounded” Knowledge

S1

S2

.

.

.

Sn(S)

State Bounded Vector Si(t)where n(s) is a finite constant

Agent Estimated Entropy

Eti =

N�

j=1

Stij log(St

ij) Dti,j =

N�

k=1

|Sti,k − St

j,k|

Agent Cognitive Dissonance

Long Term (Conscious) “Bounded” Knowledge

K1,1 K1,2 ... K1,n(s)

K2,1 . . . . . .

.

.

.

Kn(K),1 . . Kn(K),n(s)

Knowledge Bounded Vector Ki(t)where n(K) is a finite constant

Random Memory Parameter

αi ∈ (1,∞)

Random Learning Parameter

mi ∈ (0, 1)




A more Complex Case

The Environment

Connectivity Matrix

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

Three different “Typical Sizes”

Connectivity Matrix

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

Unweighted Network (Adjacency Matrix)

Relevant Features

N = 90

Large Comm (BC)= 1 (90)

Medium Comm (MC) = 5 (18)

Small Comm (SC) = 10 (9)

P(Lij)=PA with PA(BC)< PA(MC)< PA(SC)




A more Complex Case

The Recipe

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

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

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

4- Inference PhaseSynchronized 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.




A more Complex Case

The Recipe

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

Gathering SubPhase

Where S is the state vector, k(i) is the number of neighbors of the agent i, and mt

i

the memory of agent i at time t

Learning SubPhase

Expansion of biggest component and reduction of smallest component by renormalization.

Qti = mt

iSti + (1−mt

i)k(i)�

k=1

Stk

St+1i,j =

(Qti,j)αt

i

�k(i)k=1(Q

ti,k)αt

i




A more Complex Case

The Recipe2- Cognitive Dissonance PhaseEvaluation of Ego-side Information Entropy and Cognitive Dissonance (with neighbors)

Agent Estimated Entropy

Eti =

N�

j=1

Stij log(St

ij) Dti,j =

N�

k=1

|Sti,k − St

j,k|

Agent Cognitive Dissonance




A more Complex Case The Recipe3- Reasoning PhaseEvolution/Modification of the parameters whenever the discovery phase is “mute” and detection of the change of sign in the second derivative of the entropy (Et

i)

IF

FOR T − t∗ > ∆t∗

T�

t=t∗

|(Et−1i +

�k(i)k=1 Dt−1

i,k

k(i))|− |(Et

i +�k(i)

k=1 Dti,k

k(i))| < � Then

ds=0.1; m(1,i)=m(1,i)*abs((randn*ds)+1);

if m(1,i)>1, m(1,i)=1; end; if m(1,i)<0, m(1,i)=0.01; end; alpha(1,i) = 1.5*abs((randn*ds)+1); alpha(1,alpha(1,i)<1)=1;

Just a “stupid/smart” rule

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




A more Complex Case

The Recipe4- Inference PhaseSynchronized 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.

TimeKnowledge

Bounded Rationality

Sample coming from a “typical” discovery period

(in humans the day)




A more Complex Case

Preliminary Results




A more Complex CasePreliminary Results Subject i (i=3) Long

Term bounded Memory




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.



A Cognitive Heuristic model for Local Community Recognition

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