21st Mediterranean Conference on Control and Automation Non Linear Hebbian Learning Techniques and Fuzzy Cognitive Maps in Modeling the Parkinson’s Disease PhD Student Antigoni P. Anninou Professor Peter P. Groumpos Laboratory for Automation and Robotics Department of Electrical and Computer Engineering 27/6/2013

Outline Problem Formulation Fuzzy Cognitive Maps Non-Linear Hebbian Learning Decision Support System in Parkinson’s Disease Simulation Results Conclusions 27/6/2013

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 27/6/2013

Fuzzy Cognitive Maps (FCM) (1/5) Modeling method for describing particular domains Fyzzy-graph structures for representing causal reasoning 27/6/2013

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: W>0 positive causality W<0 negative causality W=0 no relationship 27/6/2013

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: 27/6/2013

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 27/6/2013

Fuzzy Cognitive Maps (5/5) Weaknesses Direct dependence of the initial knowledge of experts Convergence to undesirable situations Solution Training the FCM 27/6/2013

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) 27/6/2013

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 27/6/2013

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) | 27/6/2013

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 27/6/2013

Schematic Representation of NHL algorithm 27/6/2013

NHL Parameters The parameters arise from trials and experiments 0.9<g<1 27/6/2013

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 27/6/2013

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 27/6/2013

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) 27/6/2013

Decision Making Support System 27/6/2013

The Fuzzy Cognitive Map Model 27/6/2013

Simulation Results 1st Scenario: Suppose that the physician decided as initial values of the inputs the following: C1 Strong C2 C3 Medium C4 C5 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] 27/6/2013

Subsequent values of concepts till convergence 27/6/2013

Output Without the learning algorithm NHL Algorithm Patient Stage 2 27/6/2013

2nd Scenario: C1 Weak C2 C3 Medium C4 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] 27/6/2013

Subsequent values of concepts till convergence 27/6/2013

Output Without the learning algorithm NHL Algorithm Patient Stage 2 27/6/2013

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 27/6/2013

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 27/6/2013

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 27/6/2013

Thank you for your attention PhD Student Antigoni P. Anninou Email: anninou@ece.upatras.gr Professor Peter P. Groumpos Email: groumpos@ece.upatras.gr 27/6/2013