21st Mediterranean Conference on
Control and Automation
MED’13
PhD Student Antigoni P. Anninou
Professor Peter P. Groumpos
27/6/2013
Laboratory for Automation and Robotics
Department of Electrical and Computer Engineering
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Outline
 Problem Formulation
 Fuzzy Cognitive Maps
 Non-Linear Hebbian Learning
 Decision Support System in Parkinson’s Disease
 Simulation Results
 Conclusions
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Aim
 Construction and training of a Fuzzy Cognitive Map
(FCM) in modeling a Decision Support System, to help
in diagnosis concerning the disease of Parkinson
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Fuzzy Cognitive Maps (FCM) (1/5)
Modeling method for describing
particular domains
Fyzzy-graph
structures
representing causal reasoning
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for
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Fuzzy Cognitive Maps (2/5)
 Nodes: Represent the system’s
concepts or variables
 Arrows: Interconnection between
nodes. Show the cause-effect
relationship between them.
 W: Interrelationship between two
nodes:



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W>0 positive causality
W<0 negative causality
W=0 no relationship
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Fuzzy Cognitive Maps (3/5)
 The value of each concept at every simulation step is
calculated,
computing
the
influence
of
the
interconnected concepts to the specific concept, by
applying the following calculation rule:
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Fuzzy Cognitive Maps (4/5)
 Ai(k+1) : the value of the concept Ci at the iteration step k+1
 Ai(k): the value of the concept Cj at the iteration step k
 Wij : the weight of interconnection from concept Ci to
concept Cj
 k1: the influence of the interconnected concepts in the
configuration of the new value of the concept Ai
 k2: the proportion of the contribution of the previous value
of the concept in the computation of the new value
 f : the sigmoid function
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Fuzzy Cognitive Maps (5/5)
Weaknesses
 Direct dependence of the initial knowledge of
experts
 Convergence to undesirable situations
Solution
 Training the FCM
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Non-Linear Hebbian Learning (NHL)
(1/2)
 Increase the effectiveness of FCMs and their
implementation in real problems
 Update weights associated only with edges that are
initially suggested by experts
 All concepts in FCM model are triggered at each
iteration step and change their values
 Output concepts → Desired Output Concepts
(DOCs)
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Non-Linear Hebbian Learning (2/2)
 Algorithm that modifies the weights:
h:learning parameter
g: weight reduction parameter
 Nodes are triggered simultaneously and interact in the
same iteration step, and their values updated through
this process of interaction
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Criteria
1st : Minimization of the objective function F
DOCi: the value of the output concept i as indicated in
each iteration
Ti: the mean target value of the concept DOCi
m: the number of the desired output nodes
2nd : Minimization of the variation of two subsequent values
of DOCs
F2 = | DOCi (k+1)- DOCi (k) |
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NHL Algorithm
 Read input state A0 and initial weight matrix W0
 Repeat for each iteration step k
- Calculate Ai according to (1)
- Update Wij(k) according to (3)
- Calculate the two criterion functions
 Repeat until the termination conditions are met
 Return the final weights Wfinal and concept values
in convergence region
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Schematic Representation of NHL
algorithm
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NHL Parameters
 The parameters arise from trials and experiments
0<h<0.1
0.9<g<1
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Decision Support System
Definition: Interactive computer – based support
system for making decisions in any complex
system, when individuals or a team of people are
trying to solve unstructured problems on an
uncertain environment
Aim: Reach acceptable and realistic decisions
Methodology: Exploitation of experts’ experience
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Why to model Decision Support
Systems with FCMs
 High amount of data and information from
interdisciplinary sources
 Information may be vague or missing
 Procedure is complex
 Many factors may be complementary,
contradictory or competitive
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Decision Making Support System in
Parkinson’s Disease (1/2)
Concepts:
 C1: Body Bradykinesia
 C2: Rigidity
 C3: Postural Instability
 C4: Movement of upper limbs
 C5: Gait
 C6: Tremor
 C7: Stage of Parkinson’s disease –five stages (output)
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Decision Making Support System
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The Fuzzy Cognitive Map Model
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Simulation Results
1st Scenario:
Suppose that the physician decided as initial values of the
inputs the following:
C1
Strong
C2
Strong
C3
Medium
C4
Medium
C5
Strong
C6
Very Strong
After COA defuzzyfication method the initial values for the
concepts would be:
A(0)=[0.75 0.75 0.5 0.5 0.75 1 1]
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Subsequent values of concepts till
convergence
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Output
 Without the learning algorithm
 Patient Stage 2
 NHL Algorithm
 Patient Stage 3
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nd
2
Scenario:
C1
Weak
C2
Weak
C3
Medium
C4
Medium
C5
Strong
C6
Zero
After COA defuzzyfication method the initial values for the
concepts would be:
A(0)=[0.75 0.75 0.5 0.5 0.75 1 1]
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Subsequent values of concepts till
convergence
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Output
 Without the learning algorithm
 Patient Stage 2
 NHL Algorithm
 Patient Stage 1
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Results
 Weight matrices influence the result
 Easy to use the proposed software tool
 Without the learning algorithm:




Few recursive steps (until 9 steps)
Fast diagnosis
Convergence to undesired equilibrium points
Demands training
 NHL Algorithm:
 Much more recursive steps
 Difficulty and many trials in order to find the right parameters h
and g
 Equilibrium points closer to the reality
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Conclusions (1/2)
 Modeling with this tool closely represents the way experts




perceive it
NHL algorithm offers more reasonable results according to
physicians
NHL algorithm needs more iteration steps in order to reach
an equilibrium point
By using FCM without a learning algorithm to train it, we
have a fast model that after a few iteration steps reaches an
equilibrium point
The suggested model is easily altered to incorporate other
diseases
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Conclusions (2/2)
 In most cases, FCMs are constructed manually, and,
thus, they cannot be applied when dealing with large
number of variables. In such cases, their development
could be significantly affected by the limited
knowledge and skills of the expert. Thus, it is essential
to use learning algorithms to accomplish this task
 Despite the early obtained encouraging results, we still
need the opinion of the physicians as to how useful
can this FCM modeling approach be to Parkinson’s
disease. Future collaboration and consultation with
physicians can help this effort
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Thank you for your attention
PhD Student Antigoni P. Anninou
Email: [email protected]
Professor Peter P. Groumpos
Email: [email protected]
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