Augmented Fuzzy Cognitive Maps based on Case Based Reasoning for Decisions in Medical Informatics

1. Augmented Fuzzy Cognitive Maps based on Case Based Reasoning for Decisions in Medical Informatics Voula C. Georgopoulos1 & Chrysostomos D. Stylios2 1Technological Educational Institute of Patras, Greece 2Dept. of Computer Science, University of Ioannina, Greece

2. Outline • Introduction • FCMs for Decision Making • Augmenting FCMs using CBR • Algorithm for Augmented Competitive FCM using CBR • Example of a Medical Diagnostic System • Summary

3. Fuzzy Cognitive Maps • A Fuzzy Cognitive Map (FCM) is a soft computing tool that is based on Fuzzy Logic and Neural Network methodologies. • In a graphical illustration a FCM appears as a signed weighted graph with feedback that consists of nodes and weighted arcs. • Nodes of the graph stand for the concepts that are used to describe the behavior of the system being modeled. • Concepts are connected by signed and weighted arcs representing the causal relationships that exist between the concepts. Each concept represents a characteristic of the system; in general it can stand for events, actions, goals, values, trends of the system being modeled by the FCM.

4. Causal relationships between Concepts Between concepts, there are three possible types of causal relationships, which express the type of influence of one concept to the others. The weight of an interconnection, denoted by , for the arc from concept to concept , can be positive , which means that an increase in the value of concept leads to the increase of the value of concept , and a decrease in the value of concept leads to the decrease of the value of concept . Or there is negative causality which means that an increase in the value of concept leads to the decrease of the value of concept and vice versa. When, there is no relationship from concept to concept , then .

5. Determination of Concepts

6. FCM development • An FCM is a type of cognition network, developed by experts, using an interactive procedure of knowledge acquisition. • An expert defines the main concepts that represent the model of the system, based on his knowledge and experience on the operation of the system. • A concept can be a characteristic of the system, a state or a variable or input or an output of the system. • Moreover, he has observed which elements of the system influence other elements; and for the corresponding concepts he determines the negative, positive or zero effect of one concept on the others. • He describes each interconnection with a verbal value that represents the fuzzy degree of causality between concepts.

7. Many Experts • For better results in the development of the FCM and in order to create an advanced Fuzzy Cognitive Map, a group of experts is used. This methodology is more objective since all the experience and knowledge of the group of experts is taken into consideration. All experts are polled together and they determine the relevant factors, the main characteristics of the system and thus the concepts, which should be contained in the Fuzzy Cognitive Map. Then, they determine the structure and the interconnections of the network using fuzzy conditional statements. It is not necessary that all experts agree; FCMs can deal with multiple, perhaps even contradictory/conflicting data from experts, since explicit rules are not extracted as in rule-based Expert Systems.

8. Types of Concepts • In Decision-Making Systems the Fuzzy Cognitive Maps consist of two different types of concepts: • the n possible decision-concepts • the m factor-concepts. • The factor-concepts can be considered as inputs whereas the decision-concepts as outputs.

9. Case Based Reasoning • Situations where patient data presents a very rare configuration of symptoms where most of the nodes of the FCM would not be active, i.e, although the FCM-Model of a Medical DSS has been designed to include all possible symptoms and causative factors (nodes-concepts) and the relationship between them (weights) for some medical condition, in a particular situation very few symptoms are available and are taken into consideration. Thus, in such a diagnosis or prognosis model Decision Support FCM, the decision would be made only using a very small subset of the concepts of the entire system, leading to either an erroneous decision or difficulty in reaching stability since the weighting of the active nodes reflects only a small amount of the experts’ stored knowledge. • Using a CBR-augmented FCM Decision support system, in such situations, the DSS would draw upon cases that are maximally similar according to distance measures and would use the CBR subsystem to generate a sub-FCM emphasizing the nodes activated by the patient data and thus redistributing the causal weightings between the concept-nodes.

10. PATIENT DATA CBR FCM Diagnosis Augmented CFCM based on CBR

11. The most common techniques used in CBR diagnostic systems are based on nearest-neighbor retrieval since it is a simple approach that computes the similarity between stored cases and an input case based on weight features. The similarity of the problem (input case) to a case in the case-library for each case attribute is determined. This measure may be multiplied by a weighting factor.

12. Similarity Measure • The weighted sum of the similarity of all attributes provides a measure of the similarity of each case in the library to the input case, as given by: • where I is the input case; R the retrieved case; m the number of attributes in each case; i an individual attribute from 1 to m; f a similarity function for attribute i in cases I and R; and w the importance weighting of attribute i. This calculation is repeated for every case in the caselibrary to rank cases by similarity to the input. The normalization is used so that similarity values fall within a range of zero to one, where zero is totally dissimilar and one is an exact match.

13. Competitive Fuzzy Cognitive Map • The output nodes of a FCM used in decision-making, in many cases, must "compete" against each other in order for only one of them to dominate and be considered the correct decision. • In order to achieve this "competition“, the interaction of each of these nodes with the others should have a very high negative weight (even -1). This implies that the higher the value of a given node, this should lead to a lowering of the value of competing nodes, i.e. strong inhibition.

14. Algorithm • Set values Ai of nodes according to values of the factors involved in the decision process. These values are described using the fuzzy degrees none, very-very low, very low, low, medium, high, very high, and very-very high.. • The fuzzy connection weights between the factor-concepts and the decision-concepts are converted to initial values, which for the current research are between 0 and 1 using defuzzification. These are then placed in matrix W of size (n+m) x (n+m). The values in the first n columns correspond to the weighted connections from all the concepts towards the n decision-concepts, the values in the remaining m columns correspond to the weighted connections from all the concepts towards the factor-concepts. Also included in this matrix are the inhibition weight values for competition between output decision-concepts. • Use update rule: Anew=Aold*W.

15. Algorithm (cont.) • Pass the elements of Anew,through a sigmoid nonlinearity to ensure values of concepts between 0 and 1. The unipolar sigmoid is given by: where l determines the steepness of the continuous function . • Repeat steps until equilibrium has been reached and the values of the concepts no longer change • The procedure stops and the final values of the decision-concepts are found, the maximum of which is the chosen decision.

16. Algorithm (cont.) • In the decision process there are some factors that are considered most important for each particular decision. A logical majority rule operation is applied to the total of all critical factors involved in the decision. This means that if the majority of these critical factors is not activated when inputs are provided to the CFCM Decision System, then the CBR is called upon. The input values are then compared to the cases stored in the CBR and the case with the highest similarity is used to change the weights of the CFCM for the particular scenario leading to a more reliable decision. It should be noted that this step is actually performed before the first time the update rule is applied.

18. Example from Speech Pathology • Differential Diagnosis of Specific Language Impairment from Dyslexia and Autism. • SLI is a significant disorder of spoken language ability that is not accompanied by mental retardation, frank neurological damage or hearing impairment. Children with SLI face a wide variety of problems both on language and cognitive levels. • Dyslexia, or otherwise, specific or developmental dyslexia, constitutes a disorder of children that appears as a difficulty in the acquisition of reading ability, despite their mental abilities, the adequate school training or the positive social environment. • Autism is a developmental disorder and pathologically it is defined as an interruption or a regression at a premature level of a person’s development. The main idea in autism is the impaired or limited relation that exists between the autistic person and its environment

19. Why FCMs? • The major advantage of fuzzy cognitive maps is that they can handle even incomplete, competing or conflicting information. This is very important in decision-making systems for speech pathology because frequently important information may: • be missing (e.g. it may not be possible to conduct certain tests) • be unreliable; they may be a result of unreliable measurement techniques • be vague or conflicting; there may be more than one logical ways to interpret them • be difficult to integrate with other information.

20. Concepts for Medical Decision-Making FCM • The three disorder concepts correspond to the three disorders that are studied in the current differential diagnosis model: specific language impairment, dyslexia and autism. • The factor-concepts are symptoms and cause factors to the disorder concepts, and they are considered as measurements that can determine the result of the diagnosis. The factors-concepts are divided into language factors and non-language factors.

21. Qualitative Connection Between Factor- and Disorder-Concepts

22. Qualitative Connection Between Factor- and Disorder-Concepts (cont.)

24. CFCM for Differential Diagnosis of SLI

25. CFCM results for Different Cases

26. Example Clinical Cases Stored in Fuzzy CBR used to Augment FCM

27. Example • As an example we consider a input case that has the only the following factor weights based on the patient’s history and test results with nonzero values: Reduced Lexical Abilities: very-very high, Echolalia: very high, Reduced Ability of Verbal Language Comprehension: very-very high, Impaired Sociability: very-very high, Impaired Mobility: very-very high, Attention Distraction: very high. • CFCM: • SLI= 0.9023 Dyslexia=0.8475 Autism=0.9796 • CBR Augmented CFCM: • SLI= 0.8007 Dyslexia=0.6450 Autism=0.9924

28. Summary • The advantage of CBR-Augmented CFCMs lies in the ability to represent rare occurrences of medical conditions/symptoms, which may not be adequately represented in an CFCM due to its design methodology, which is dependent on human experts and learning algorithms. • The CBR-Augmented Competitive Fuzzy Cognitive Map is capable on its own to perform a comparison and lead to a decision based on expert opinions (structure of CFCM) and previous cases (CBR).