Analyzing the performance of fuzzy cognitive maps with non-linear hebbian learning algorithm in predicting autistic disorder

Expert Systems with Applications 38 (2011) 1282–1292

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Analyzing the performance of fuzzy cognitive maps with non-linear hebbian learning algorithm in predicting autistic disorder Arthi Kannappan a,*, A. Tamilarasi b, E.I. Papageorgiou c a

MCA Department, Karpagam College of Engineering, Coimbatore 641 032, Tamil Nadu, India MCA Department, Kongu Engineering College, Perundurai, Erode, Tamil Nadu, India c Department of Informatics and Computer Technology, Technological Educational Institute of Lamia, 3rd km PEO Lamia–Athens, 35100 Lamia, Greece b

a r t i c l e

i n f o

Keywords: Autistic spectrum disorder Fuzzy cognitive maps Non-linear hebbian learning algorithm

a b s t r a c t The soft computing technique of fuzzy cognitive maps (FCM) for modeling and predicting autistic spectrum disorder has been proposed. The FCM models the behavior of a complex system and is used to develop new knowledge based system applications. FCM combines the robust properties of fuzzy logic and neural networks. To overwhelm the limitations and to improve the efficiency of FCM, a good learning method of unsupervised training could be applied. A decision system based on human knowledge and experience with a FCM trained using unsupervised non-linear hebbian learning algorithm is proposed here. Through this work the hebbian algorithm on non-linear units is used for training FCMs for the autistic disorder prediction problem. The investigated approach serves as a guide in determining the prognosis and in planning the appropriate therapies to special children. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Autism is a brain development disorder that first gives signs during infancy (or) childhood and generally follows a steady course without remission or relapse. Autism is characterized by widespread abnormalities of social interaction and communication and severely restricted interests and highly repetitive behavior (American Psychiatric Association, 2004). The main characteristics are impairments in social interaction, impairments in communication, restricted interests and repetitive behavior (Cohen & Donnellan, 1987). They also qualitatively differ in their use and understanding of non-verbal activities that influence the interaction with others such as eye contact, posture, facial expression and gestures. Persons with autism have a restricted range of interests, where as their thinking and behavior is rigid. In a recent study, a discriminant function analysis of the magnetic resonance imaging (MRI) of brain measures were used for the classification of autistic spectrum disorders (Akshoomoff et al., 2004). Numerous algorithms and methods have been proposed in order to achieve data classification and to improve its efficiency (Ishibuchi, Fujioka, & Tanaka, 1993; Papageorgiou, Papandrianos, Apostolopoulos, & Vassilakos, 2008a; Sabeti, Boostani, Katebi, & Price, 2007). A recent study proposes a new algorithm in predict-

* Corresponding author. E-mail addresses: [email protected] (Arthi Kannappan), angamuthu_ [email protected] (A. Tamilarasi), [email protected] (E.I. Papageorgiou). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.06.069

ing autistic disorder using neuro fuzzy model and hybrid model (Arthi & Tamilarasi, 2008, 2009a, 2009b). But the fuzzy cognitive map approach is a different technique from neural networks due to their properties and knowledge elicitation from experts (Papageorgiou, Stylios, & Groumpos, 2003b, 2007). It is an alternative approach to knowledge based techniques offering more semi-quantitative characteristics. The decision making problem of predicting autistic disorder is a complex process, because of the numerous elements/parameters (such as symptoms, signsmovements, etc.) involved in its operation, and a permanent attention is demanded. The knowledge of physicians according to the children’s signs and symptoms is the main point to succeed a diagnosis. In this study, the fuzzy cognitive mapping (FCM) approach is investigated to handle with the problem of autistic disorder prediction. The main topic of the presented effort is the representation of the cause-effect relationships within medical data by the application of the soft computing technique of fuzzy cognitive maps and the training of these relationships using an efficient unsupervised learning algorithm. FCM is a knowledgebased approach exploiting the main features of fuzzy logic and neural networks, and thus corresponding to an artificial cognitive network. It can handle efficiently with complex modeling problems to assess medical decision making tasks. In this proposed work, a new implementation approach on training fuzzy cognitive maps with non-linear hebbian learning is investigated and a clinical problem of ASD with real cases is examined to analyze the process and justify the results. Expert’s involvement is essential and obvious in this proposed model. Experts are the good assessors of this neurological disorder to promote the

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better performance of this framework. They can handle with the available experience and accumulated knowledge from experts. The easy of use and the low time requirement are important features of FCMs. Here, the main aim of this paper is to create a model that could predict the category of autism using the unsupervised non-linear hebbian learning algorithm for FCM tool. The overall structure of the decision making approach based on FCMs is investigated to help physicians, through the design of the knowledge representation and reasoning with FCM for the problem of autistic disorder prediction. Further, a number of different scenarios concentrated on autistic disorder individually for real clinical cases are examined to demonstrate the application of the proposed methodology and its functioning. The paper is organized into the following sections: the second section provides the main aspects to the fuzzy cognitive map theory and presents a description on the FCMs for medical decision making tasks. This is followed by the description of the problem of ASD, the reasons why the FCM approach was considered appropriate for modeling this particular domain and the stages in the development of the FCM model, constructing the resulting model for ASD. The fourth section provides a description on non-linear hebbian learning algorithm for training FCM for the specific problem of ASD. The next section provides its simulation analysis through a number of different scenarios and discussion of results. The conclusion is followed by exploring the potential of the FCM as a dynamic model in medicine for making decisions.

concepts that represent their relationships. The most important element in describing the system is the determination of which concept influences which other and with which degree. There are three possible types of causal relationships among concepts that express the type of influence from one concept to the others. The weight of the interconnection between concept Ci and concept Cj, denoted by Wij, could be positive Wij > 0 for positive causality or there is negative causality Wij < 0 or there is no relationship between concept Ci and concept Cj, thus Wij = 0. The causal knowledge of the dynamic behavior of the system is stored in the structure of the map and in the interconnections that summarize the correlation between cause and effect. Fig. 1 shows a fuzzy cognitive map designed to model some factor concepts, and decision output concepts in medical informatics, as well as their interactions. The main objective of building a fuzzy cognitive map around a problem is to be able to predict the outcome by letting the relevant issues interact with one another. These predictions can be used in a decision support system (DSS) for finding out whether a conclusion arrived at is consistent with the whole collection of stated causal assertions. At each step, the value Ai of a concept is calculated, computing the influence of the interconnected concepts to the specific concept according the following equation:

2 ðkþ1Þ

Ai

3

6 ðkÞ ¼ f6 4Ai þ

N X j–i j¼i

ðkÞ ðkÞ 7 Aj  wji 7 5

ð1Þ

2. Fuzzy cognitive maps in decision making or Fuzzy cognitive maps are diagrams used as causal representations between knowledge/data to represent events relations. They are modeling methods based on knowledge and experience for describing particular domains using concepts (variables, states, inputs, outputs) and the relationships between them (Kosko, 1986). FCM can describe any system using a model having signed causality (that indicates positive or negative relationship), strengths of the causal relationships (that take fuzzy values), and causal links that are dynamic (i.e., the effect of a change in one concept/node affects other nodes, which in turn may affect other nodes). The fuzzy part allows us to have degrees of causality, represented as links between the nodes of these diagrams, also known as concepts. This structure establishes the forward and backward propagation of causality, admitting the knowledge base to increase when concepts and links between them are increased. FCM is better than traditional rule-based reasoning since it uses stronger mathematical analysis. Fuzzy cognitive maps accommodate the knowledge-base building property (Papageorgiou et al., 2003b). It can handle with uncertainty and it is constructed by extracted knowledge in the form of fuzzy rules (Stylios & Groumpos, 2004). Researchers have used FCM’s for many tasks in several domains like disease diagnosis in the medical domain and fault management in distributed network environment (Ndousse & Okuda, 1996; Taber, 1991). The performance of FCM can be enhanced by incorporating the advantages of neural networks such as learning properties. Papageorgiou et al. had proposed efficient unsupervised learning algorithm for training the fuzzy cognitive maps (Papageorgiou et al., 2004; Papageorgiou, Parsopoulos, Stylios, Groumpos, & Vrahatis, 2005; Papageorgiou, Stylios, & Groumpos, 2003a, 2004). 2.1. Main aspects of fuzzy cognitive maps

  X ðk1Þ AðkÞ ¼ f Aðk1Þ þ A w ðkþ1Þ

where Ai k þ 1;

ðkÞ Ai

denotes the value of concept Ci at simulation step

denotes the value of concept Cj at simulation step k,

ðkÞ

wji is the weight of interconnection between concept Cj and concept Ci and f is the sigmoid threshold function which is calculated as f ðxÞ ¼ 1þe1kx where k is a positive constant which takes value as 1 or 5 and f(x) lies between 0 and 1. In this work we use m = 1, because this value showed best results in previous works (Miao & Liu, 2000). A concept is turned on or activated by making its vector element 1 or 1. New state vectors showing the effect of the activated concept are computed

C2

C1

C3

OUTC1 C8

C14 C18 OUTC2

FCM is used to model and simulate the behavior of any system. It consists of concepts (representing the main domain aspects such as variables, states, inputs, outputs) and of interconnections among

Fig. 1. A generic FCM model for medical decision making.

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using method of successive substitution, i.e., by iteratively multiplying the previous state vector by the relational matrix using standard matrix multiplication Ak = Ak1 + Ak1  W. The iteration stops when a limit vector is reached, i.e., when Ak = Ak1 or when At  At1 6 e; where e is a residual, whose value depends on the application type (and in most applications is equal to 0.001). Eq. (1) includes the previous value of each concept, and so the FCM possesses memory capabilities and there is a smooth change after each simulation step. The forward inference process of FCM starts with a stimulus event vector. The event vector is inserted into the FCM. Multiplying the stimulus vector to the FCM matrix is the first in a series of such multiplications that eventually yields one of the following: A fixed point: if the FCM equilibrium state of a dynamical system is a unique state vector, the state vector remains unchanged for successive iterations, then it is called the fixed point. A limit cycle: if the FCM settles down with a state vector repeating in the form A1 ? A2 ?    ? Ai    ? A1 then this equilibrium is called a limit cycle. A chaotic attractor: the FCM state vector keeps changing at every iteration and repeating states are never found. The development and design of the appropriate fuzzy cognitive map for the description of a system requires the contribution of human knowledge. The experts develop fuzzy cognitive maps using an interactive procedure of presenting their knowledge on the operation and behavior of the system. Experts are asked to determine the concepts that best describe the model of the system, since they know which factors are the key principles and functions of the system operation and behavior, and they introduce a concept for each one. Experts have observed the operation and behavior of the system during its operation, since they are the operators and supervisors of the system, who control it using their experience and knowledge. They have stored in their mind the correlation among different characteristics, states, variables and events of the system and in this way they have encoded the dynamics of the system using fuzzy rules. The procedure described here is an approach that based in previous works for constructing FCMs (Papageorgiou, Stylios, & Groumpos, 2006; Papageorgiou et al., 2003a). When the FCM model has been developed, the NHL algorithm is applied to adjusting the weights of the FCM interconnections and modifying them according to the specific problem characteristics. The NHL algorithm adapts synchronously the non-zero weights of the FCM model using the unsupervised learning approach. The main advantage of the NHL algorithm is that it can modify the initial FCM causal links between the concepts in order to increase classification capabilities of the FCM. In this way the NHL algorithm increases the FCMs’ effectiveness, flexibility and robustness, and creates advanced FCMs with dynamic behavior and great modeling abilities (Papageorgiou, Papandrianos, Apostolopoulos, & Vassilakos, 2008b; Papageorgiou et al., 2005). 2.2. Fuzzy cognitive maps in medicine FCM is an efficient modeling method, which is based on human knowledge and experience. Fuzzy cognitive maps accommodate the knowledge-base building property. It can handle with uncertainty and it is constructed by extracted knowledge in the form of fuzzy rules (Stylios & Groumpos, 2004). Researchers have used FCM’s for many tasks in several domains like disease diagnosis in the medical domain and fault management in distributed network environment (Akshoomoff et al., 2004; Georgopoulos & Stylios, 2003a). In another study fuzzy cognitive maps have been used for differential diagnosis of specific language impairment

(Georgopoulos, Malandraki, & Stylios, 2003b). Papageorgiou et al. introduced a novel approach of fuzzy cognitive maps as the computational modeling method which tackles the complexity and allows the analysis and simulation of the clinical radiation procedure (Papageorgiou et al., 2003a). Smith et al. reported their work on enhanced risk assessment in a health care institution using cognitive fuzzy modeling which is a combination of fuzzy cognitive models and fuzzy rule-based techniques (Mitra & Hayashi, 2000; Smith & Eloff, 2000). 3. Autistic disorder problem description and construction of fuzzy cognitive map model Here, in this subsection, the ASD problem is described consisting of the 24 concepts presented in Table 1. Three experts like pediatrician, occupational therapist and special educator were used to determine the main concepts of the model as well as their interconnections among concepts. This process was completed through a questionnaire, which created for this process and proposed to the team of experts. The questionnaire is presented in Appendix A which is from the modified checklist for autism in toddlers (MCHAT), a questionnaire is prepared with 23 questions which are considered as core problematic areas of autism (Robins, Fein, Barton, & Green, 2001). The linguistic values which are obtained from the parents of the autistic infants and the weights are calculated by the experts individually as per concepts represented in Table 1. The concepts represent attributes, characteristics, qualities and states of the system. Here the FCM model is an abstract conceptual model depending on three experts like pediatrician, special educator and occupational therapist who decide about the input and output concepts (decision output concepts, DOC). The input concept represents the symptoms and signs of autistic spectrum disorder and can be depicted in Fig. 1. The input vector consist of various symptoms of autism which takes linguistic properties like (a) certainly not, (b) at times and (c) always as shown in Fig. 2 and for the output concept value as shown in Fig. 3. Also all the three experts’ suggestions and their intuitive knowledge is given in Appendix B.

Table 1 The concepts of the FCM model in predicting ASD. Concepts

Description

Type of the data

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18

Enjoy being swung Take an interest in other children Climbing on things Enjoy playing Pretend other things Pointing index finger Indication of interest Playing with small toys Bringing objects to parents Eye contact Oversensitive to noise Smile in response to parents face Imitate Response to the name Looking at a toy when pointing Walking Look at things you are looking at Unusual finger movements near his/her face Attract your attention Deafness Understanding what others say Stare at nothing Look at your face to check reaction Autism (High, Probable Autism and No autism)

Three Three Three Three Three Three Three Three Three Three Three Three Three Three Three Three Three Three

fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy

values values values values values values values values values values values values values values values values values values

Three Three Three Three Three Three

fuzzy fuzzy fuzzy fuzzy fuzzy fuzzy

values values values values values values

C19 C20 C21 C22 C23 OUTC1

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1 0.9 0.8

certainly no

0.7

at times always

0.6

4. Non-linear hebbian learning algorithm

0.5 0.4 0.3 0.2 0.1 0

0

10

20

30

40

50

60

70

80

90

100

Fig. 2. Membership function for the concept C1 (Enjoy being swung).

T(influence)

1 0.9 0.8

no influence

0.7

probable

0.6

definite

0.5 0.4 0.3 0.2 0.1 0

0

10

20

30

40

50

60

70

80

90

5. All the weights are gathered into a weight matrix (Wji)n  n, where n is the number of concepts can be represented as in the following Table 2 and an FCM model for predicting the autistic disorder with the calculated value of weights can be shown in Fig. 4

100

The Hebbian paradigm is perhaps the best-known unsupervised learning theory in connectionism (Papageorgiou et al., 2006). The non-linear hebbian learning algorithm focus in the domain of artificial neural network field and it embodies properties such as locality and the capability of being applicable to the basic weight-and-sum structure of neuron models. Papageorgiou et al., proposed a new method for characterizing brain tumors using unsupervised hebbian learning algorithm (Papageorgiou et al., 2008c). Since FCM have non-linear structure of their concepts, the non-linear hebbian learning is used to train FCM for prediction and classifying autistic disorder. Here in this algorithm, the learning rule for FCMs integrates a learning rate parameter gk, weight decay parameter c, and the input/output concepts. The value of each concept of FCM is updated through Eq. (1) whereas the value of weight is calculated using Eq. (2).When the NHL algorithm is applied, only the initial non-zero weights suggested by the experts are updated for each iteration step. All the other weights of weight matrix Wji remains zero which is their initial value. There is a proposed two termination condition for the NHL algorithm. The first termination condition is the minimization of function F1 which uses decision of concepts (DOC) as defined by experts and a target value Ti which represents a desired value (or) the mean value when DOC represents a concept. The second termination condition is the minimization of the variation between two subsequent values of DOC and helps to terminate the iterative process of the learning algorithm. The proposed algorithm can be written as follows.

Fig. 3. Membership function representing T (influence).

4.1. Algorithm of non-linear hebbian learning to predict the class of autism

3.1. Steps in constructing FCM s for autism disorder prediction 1. Every expert like psychologist, pediatricians, special educators describe each interconnections with linguistic fuzzy rule to assign the weight. The fuzzy rules for each interconnection can be calculated using the following IF a change B occurs in the value of concept Cj THEN a change D in the value of concept Ci is caused. Infer: The influence from Cj to Ci is E where B, D and E are fuzzy linguistic variables that experts use to describe the variance of concept values and the degree of influence from concept Cj to Ci. For example weight from C22 to OUTC1 and C18 to OUTC1 can be represented respectively as IF a small change occurs in the value of C22 THEN a small change is caused in the value of OUTC1. Infer: Influence of C22 to OUTC1 is low. IF a large change occurs in C18 THEN a large change in OUTC1 is high. Infer: Influence of C18 to OUTC1 is high. 2. The inferred fuzzy weights are combined using the SUM method as suggested by the three experts. 3. Using defuzzification method of centroid, weight is calculated as

R ul 0 ðuÞdu 0 u ¼ Ru B l 0 ðuÞdu u B

ð2Þ

4. All the linguistic weights u0 are transformed into a numerical weight wj which lies in the range [1, 1].

Algorithm: PredictAut () ðkÞ Step 1: Initialize the concepts Ai , weights wji for each interconnections given by the experts, the input values for 23 concepts, learning rate parameter gk = 0.001, weight decay parameter c = 0.98 and T imin 6 Ti 6 T imax , where i is the number of decision concepts (for this problem i = 1 to 3 due to three output concepts). Step 2: Each concept in the questionnaire is divided into factor concepts (k = 23) and define the decision output concepts (DOCs) like high autism (OUTC1), probable autism (OUTC2) and no autism (OUTC3) which are the outputs of the system. Step 3: Repeat steps 4–7 for each k value till the stopping condition is satisfied. Step 4: At each simulation step k, the value Ai of a concept is calculated using the following rule as in Eq. (1). Step 5: For the non-linear adaptation algorithm, the value of ðkÞ weight wji is calculated with learning rate parameter (gk) and the weight decay parameter (c) using the following mathematical form ðkÞ

ðk1Þ

wji ¼ c  wji

ðk1Þ

þ gk Ai

ðk1Þ

ðAj

ðk1Þ

 ðwji

ðk1Þ

Þwji

ðk1Þ

Ai

Þ

ð3Þ

Step 6: For each k, the weights are adjusted using the following equation ðk1Þ ðk1Þ Dwji ¼ gk Aiðk1Þ Aðk1Þ  wji ðAi Þ j

Step 7: Stopping condition: Either the condition 1 or 2 has to be satisfied to terminate the iterative process

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Table 2 Initial weight values Wji. Ci/ Cj

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.65 0 0

0.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.5 0 0.65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.65 0.65 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.65 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5 0 0 0 0 0 0 0

0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.65 O 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.8 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.65 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0.65 0 0 0 0 0 0 0 0 0 0.65 0 0 0 0 0

0.51 0.51 0.51 0.51 0.51 0.446 0.282 0.51 0.51 0.51 0.283 0.51 0.51 0.51 0.51 0.51 0.283 0.51 0.51 0.51 0.51 0.51 0.51 0

Fig. 4. FCM model for predicting the autistic disorder with the assigned numerical values of weights.

Condition 1 :

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u m uX Calculate F1 ¼ t ðDOC i  T i Þ2 i¼1

where m is the number of DOCs and Ti defines the target value which can be calculated as Ti = (T imin þ T imax )/2 where i = 1–3

   ðkþ1Þ ðkÞ  Condition 2 : Calculate F2 ¼ DOC i  DOC i  < e

where e takes a value of 0.001. Step 8: Stop the process with the resultant weight matrix. 5. Simulation results and discussion All the 23 concepts are considered as factor concepts by the experts as they are listed in Table 1 to design FCM model and each

concept represents three fuzzy values. In this problem, the concept C24 have been considered from the experts as decision output concept – DOC and could be categorized as Definite Autism (DA), Probable Autism (PA) and No Autism (NA) which takes a range of values such as 0.41 6 DA 6 1.00, 0.26 6 PA 6 0.40 and 0 6 NA 6 0.25, respectively. For this FCM model of the ASD problem, the values of concepts are changed synchronously in the same time units and referred as an iteration step. Eq. (1) can be applied to find the equilibrium final state after the creation of FCM. Initial concept values are given by the experts through intuition technique of their own innate intelligence and understanding by analyzing the different options of MCHAT questionnaire. For the first scenario, the following initial values of each one concept variable have been assigned, the first concept enjoy being swung (C1) has the value ‘‘Certainly not” (CN), the second concept (C2) has the value ‘‘No

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or Very little” (NVL), the third concept (C3) has the value ‘‘No, doesn’t do this” (ND), the concept (C4) has the value ‘‘Never” (NR), the concept (C5) has the value ‘‘No” (N), the concept (C6) has the value ‘‘Never” (NR), the concept (C7) has the value ”Never” (NR), the concept (C8) has the value ‘‘No, not at all” (NN), the concept (C9) has the value ”No, doesn’t do it” (ND), the concept (C10) has the value ‘‘No” (N), the concept (C11) has the value ‘‘I don’t think so” (IDT), the concept (C12) has the value ‘‘No” (N), the concept (C13) has the value ‘‘Does Not” (NS), the concept (C14) has the value ‘‘very little” (NV), the concept (C15) has the value ‘‘Seldom does this” (SD), the concept (C16) has the value ‘‘very little” (NV), the concept (C17) has the value ‘‘definitely not” (DN), the concept (C18) has the value ‘‘Yes, often and for rather long periods” (YO), the concept (C19) has the value ‘‘No” (N), the concept (C20) has the value ‘‘Yes” (Y), the concept (C21) has the value ‘‘Very little or No understanding‘‘ (VLNU), the concept (C22) has the value ‘‘Yes truly” (YT), the concept (C23) has the value ‘‘Does not look” (DNL). These Initial values of the concepts can be given as fuzzy sets as selecting the options for all the twenty three concepts in the Questionnaire. Then by the defuzzification process, the initial numerical values used for the simulation process are given in vector A0 = {0.30 0.55 0.60 0.65 0.20 0.69 0.73 0.77 0.86 0.10 0.57 0.40 0.50 0.62 0.60 0.71 0.90 0.15 0.25 0.45 0.49 0.34 0.62 0.51}. The input values and the initial weight matrix Wji of Table 2 are used in Eq. (1) to calculate the equilibrium region of the process when no learning algorithm is applied. After seven iteration steps, the FCM concept values do not change which indicates equilibrium region is reached as represented in Table 3. Here the experts have defined the accepted regions for high autism which lies between 0.81 and 1. It is observed that the concepts like C1, C3, C16 and C18 which has very high influence to the output of definite autism does not converge in the desired regions. So, the NHL algorithm is applied to fine-tuning FCM causal links by modifying the weight values. 5.1. Scenarios of training FCM tool for ASD Problem Three scenarios for training FCM model for ASD problem are considered in this proposed work. In the first scenario a real case of children with definite autism is investigated, where the initial values of concepts are represented as fuzzy membership values and trained to get new updated weight matrix and new concept values. This scenario is implemented with initial fuzzy membership values and initial weights of FCM where the NHL training algorithm is applied for ASD problem. The training process starts by applying the initial values of concepts to the vector A1 = {0.30 0.55 0.60 0.65

0.20 0.69 0.73 0.77 0.86 0.10 0.57 0.40 0.50 0.62 0.60 0.71 0.90 0.15 0.25 0.45 0.49 0.34 0.62 0.51} which represent the case of definite autism and the initial weight matrix Wji is used. Due to the NHL training process, only the non-zero weights are updated at each iteration step and all the other weights remain zero. For the proposed study, the learning rate parameter gk takes value as 0.001 and weight decay parameter c takes value as 0.98 after trial and experiments (Papageorgiou et al., 2006). The proposed NHL algorithm continues until the two termination conditions are satisfied. Here the first termination condition reaches 0.10 and second condition value reaches a value which is less than the error tolerance level of 0.001. The training comes to an end after 21 iteration steps and the resultant weight matrix W 1ji can be represented as in Table 4. The updated concept values are given in A1 = {0.69 0.66 0.74 1.0 0.70 0.81 0.67 0.66 1.00 1.00 0.65 0.60 0.55 0.69 0.73 0.77 0.86 0.57 0.62 0.71 0.73 0.66 0.78 0.73} which gives the result of definite autism as specified by the experts and converges to the desired region. The second scenario that describes a case with probable autism is implemented with initial fuzzy membership values and initial weights of FCM where the NHL training algorithm is applied for ASD problem. The training process starts by applying the initial values of concepts to the vector A2 = {0.17 0.30 0.32 0.43 0.20 0.10 0.01 0.32 0.41 0.13 0.15 0.44 0.28 0.5 0.64 0.15 0.25 0.30 0.29 0.27 0.31 0.40 0.42 0.41}, where each one of the initial values of concepts represent the following states for the scenario of probable autism. The first concept C1 takes a value ‘‘at times” (AT),the second concept C2 takes a value ‘‘Yes, sometimes” (YS), the third concept C3 takes a value ‘‘Very rarely few steps only” (VR), the concept C4 takes a value ‘‘Rarely” (RY), the concept C5 takes a value ‘‘Slightly true” (ST), the concept C6 takes a value ‘‘Rarely” (RY), the concept C7 takes a value ‘‘Rarely” (RY), the concept C8 takes a value ‘‘Sometimes” (SS), the concept C9 takes a value ‘‘have for himself” (HH), the concept C10 takes a value ‘‘Sometimes” (SS), the concept C11 takes a value ‘‘Rarely” (RY), the concept C12 takes a value ‘‘Sometimes” (SS), the concept C13 takes a value ‘‘Once a while” (OW), the concept C14 takes a value ‘‘Yes, sometimes” (YS), the concept C15 takes a value ‘‘Once in a while” (OIW), the concept C16 takes a value ‘‘with others help” (WO), the concept C17 takes a value ‘‘Yes, sometimes” (YS), the concept C18 takes a value ‘‘Very rarely” (VR), the concept C19 takes a value ‘‘Slightly true” (ST), the concept C20 takes a value ‘‘Not sure” (NS), C21 takes a value ‘‘Rarely understands” (RU), the concept C22 takes a value ‘‘Sometimes” (SS),the concept 23 takes a value ‘‘Yes, slightly true” (YST). The training continues till it satisfies both termination conditions of NHL algorithm and updated weights W 2ji can be represented as in Table 5.

Table 3 values of concepts at each step of FCM interaction. C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

0.3 0.57 0.639 0.655 0.658 0.659 0.659

0.55 0.58 0.576 0.546 0.531 0.526 0.525

0.6 0.69 0.759 0.781 0.787 0.788 0.788

0.65 0.66 0.659 0.659 0.659 0.659 0.659

0.2 0.63 0.723 0.741 0.745 0.745 0.745

0.69 0.67 0.662 0.66 0.659 0.659 0.659

0.73 0.82 0.83 0.831 0.831 0.83 0.83

0.77 0.75 0.746 0.746 0.746 0.746 0.746

0.86 0.7 0.67 0.66 0.66 0.66 0.66

0.1 0.57 0.607 0.668 0.688 0.69 0.69

0.57 0.64 0.655 0.658 0.659 0.659 0.659

0.4 0.598 0.645 0.656 0.658 0.659 0.659

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

COUT

0.5 0.62 0.65 0.657 0.659 0.659 0.659

0.62 0.72 0.713 0.761 0.778 0.783 0.783

0.6 0.74 0.756 0.759 0.759 0.759 0.759

0.71 0.6 0.563 0.546 0.539 0.536 0.535

0.9 0.78 0.779 0.781 0.781 0.781 0.781

0.15 0.67 0.76 0.77 0.77 0.77 0.77

0.25 0.56 0.636 0.654 0.658 0.659 0.659

0.45 0.5 0.497 0.507 0.505 0.506 0.505

0.49 0.29 0.68 0.76 0.78 0.78 0.78

0.34 0.42 0.603 0.646 0.656 0.658 0.659

0.62 0.21 0.737 0.83 0.844 0.846 0.846

0.51 0.998 0.999 1 1 1 1

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Table 4 Resultant weight matrix of the First scenario of NHL algorithm. Ci/Cj

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0

0.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.70 0 0.42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.83 0.55 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0 0 0

0 0 0.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 O 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.42 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.67 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0.69 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0

0.48 0.42 0.42 0.25 0.40 0.42 0.42 0.42 0.55 0.55 0.42 0.82 0.42 0.42 0.55 0.42 0.4 0.42 0.4 0.4 0.4 0.55 0.20 0

Table 5 Resultant weight matrix of the Second scenario of NHL Algorithm. Ci/Cj

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.496 0 0

0.62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.39 0 0.51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.49 0.50 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.51 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.39 0 0 0 0 0 0 0

0 0 0.38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.50 O 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.62 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.61 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.50 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0.50 0 0 0 0 0 0 0 0 0 0.51 0 0 0 0 0

0.39 0.39 0.39 0.40 0.40 0.35 0.23 0.40 0.39 0.39 0.22 0.39 0.39 0.39 0.39 0.40 0.22 0.39 0.40 0.39 0.40 0.39 0.39 0

Updated concept values are represented in vector A2 = {0.20 0.35 0.36 0.41 0.35 0.11 0.04 0.36 0.17 0.15 0.18 0.42 0.18 0.32 0.42 0.31 0.36 0.31 0.22 0.21 0.27 0.43 0.37 0.37} which results in probable autism and lies in the desired region 0.26 6 PA 6 0.40 as specified by the experts. In the third scenario, the NHL algorithm is implemented to the FCM tool for an initial set of random concept values which calculates DOCs and verifies the convergence of the FCM model. Here the algorithm is trained using the random concept values of A3 = {0.56 0.72 0.53 0.64 0.75 0.66 0.87 0.76 0.95 0.45 0.76 0.52 0.73 0.44 0.75 0.67 0.57 0.48 0.49 0.40 0.41 0.42 0.43 0.87} and the same initial weight matrix of W 3ji . The training continues till it satisfies both termination conditions of NHL algorithm. Updated

concept values A3 = {0.685 0.742 0.831 1 1 1 1 0.659 1 0.813 1 0.661 0.661 0.659 0 0.659 0.659 0.659 0.658 1 0.659 1 1 0.659} and W 3ji as in Table 6. From the calculated concept values, we can see that the value of DOC = 0.659, which means that a definite autism exists according to the initial determined fuzzy regions. Comparing the resultant weight matrix for the second scenario, with the initial weight matrix, as it has been assigned by experts, it is clear that most of the weight values have changed significantly. This is presumable especially for random values of initial concepts. Nearly 40 datasets have been collected for classification of three different categories like 23 as definite autism, 13 as Probable autism and 4 as no autism children. These 40 datasets are gathered as in Appendix C. The training of datasets starts with the initial

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Arthi Kannappan et al. / Expert Systems with Applications 38 (2011) 1282–1292 Table 6 Resultant weight matrix of the third scenario of NHL algorithm. Ci/Cj

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0

0.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.70 0 0.42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.83 0.55 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0 0 0

0 0 0.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 O 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.42 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.67 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0.69 0 0 0 0 0 0 0 0 0 0.55 0 0 0 0 0

0.48 0.42 0.42 0.25 0.40 0.42 0.42 0.42 0.55 0.55 0.42 0.82 0.42 0.42 0.55 0.42 0.4 0.42 0.4 0.4 0.4 0.55 0.20 0

Table 7 Classification results from NHL algorithm.

DA PA NA

DA

PA

NA

20/23 2/13 –

3/23 10/13 1/4

– 1/13 3/4

DA – definite autism, PA – probable autism, NA – no autism.

concept values, initial weight matrix values and then trained using non-linear hebbian learning algorithm to calculate the final concept values for classification. The training ends with the iteration values (k) as 21, condition 1 as 0.07446 and condition 2 value as 0.00701. The resultant concept values can be represented as {0.70 0.74 0.81 0.70 0.71 1 1 1 0.67 0.70 0.63 0.63 0.64 0.64 0 0.65 0.68 0.66 0.67 1 0.67 1 0.68 0.66} which results in definite autism. Using the learning algorithm for the proposed FCM tool, 20 records from 23 datasets gives a result of definite autism and 3 records as probable autism, 10 from 13 records gives a result probable autism, 2 as definite and 1 as no autism, 3 from 4 records gives a result of no autism and 1 as probable autism. The classification results can be represented as in Table 7. Classification accuracy can be calculated as

Accuracy Percentage ¼ ð20=23 þ 10=13 þ 3=4Þ=3 ¼ 79:9%

ð4Þ

6. Conclusion The knowledge-based approach used in this work focuses on the soft computing technique of fuzzy cognitive maps with NHL training algorithm for the estimation of medical outcomes and resource utilization. In the presented research, we have proposed the FCM learning approach for the process of predicting the autistic disorder. The presented solution has been raised by some of the requirements imposed by the targeted application: the causal association of symptoms and signs of autistic spectrum disorder that seem to be crucial for the right medical diagnosis. We have also sketched in this paper the exemplary problem of medical diagnosis and its simulation using the proposed solution.

The main objective of this work was to present a method based on fuzzy cognitive mapping technique to develop an expert system for predicting the autistic disorder. Modeling with this tool (FCM) represents closely to the way experts perceive it. Therefore, the suggested model is easily understandable and each parameter has a perceivable meaning. The suggested model can be easily altered to incorporate new phenomena, and if the behavior in the model is different from the real world and from what is expected, it is always easy to find which factor should be used to analyze. Acknowledgements Authors would like to thank the Dr. A. Thejavathi, pediatrician and Ms. Sudha, Occupational therapist, Coimbatore for their kind support in collection of datasets. Appendix A Name:

Age:

Gender:

1. Does your child enjoy being swung, bounced on your knee etc.? (a) Certainly not (CN) (b) At times (c) Always (AL) (AT) 2. Does your child take an interest in other children? (a) Yes, Quite a lot (b) Yes, (c) No or Very little (YQ) sometimes (NVL) (YS) 3. Does Your child like climbing on things such as upstairs? (a) Yes, often (YO) (b) No, (c) Very rarely few doesn’t do steps only (VR) this (ND) 4. Does your child enjoy playing peek-a-boo/hide-andseek? (a) Never (NR) (b) Rarely (c) Usually does (continued on next page)

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Appendix A (continued) Name:

Appendix A (continued) Age:

Gender:

(RY)

(UD)

Name:

Age:

Gender:

(YO)

5. Does your child ever pretend, for example, to talk on the phone or take care of dolls or Pretend other things? (a) No (N) (b) Yes (Y) (c) Slightly true (ST)

19. Does your child try to attract your attention to his/her own activity? (a) Yes (Y) (b) No (N) (c) Slightly true (ST)

6. Does Your child ever use his/her index finger to point, to ask for something? (a) Never (NR) (b) certainly (c) Rarely (RY) (CY)

20. Have you ever wondered if your child is deaf? (a) Yes (Y) (b) Definitely (c) not sure (NS) not deaf (DND)

7. Does your child ever use his/her index finger to point, to indicate interest in something? (a) Never (NR) (b) certainly (c) Rarely (RY) (CY)

21. Does your child understand what people say? (a) Yes, understands (b) Rarely (c) Very little or no very well (YUV) understands understanding (RU) (VLNU)

8. Can your child play properly with small toys (eg car or bricks) without just mouthing? (a) Usually does (UD) (b) No, not at (c) Sometimes (SS) all (NN)

22. Does your child sometimes stare at nothing or wander with no purpose? (c) Yes truly (YT) (a) No, I don’t think (b) so (NID) sometimes (SS)

9. Does your child ever bring objects over to you (parents) to show you something? (a) No, doesn’t do it (b) have for (c) Does it (DI) (ND) himself (HH) 10. Does your child look you in the eye for more than a second or two? (a) No (N) (b) Yes (Y) (c) Sometimes (SS) 11. Does your child ever seem oversensitive to noise? (e.g. Plugging ears)? (a) I don’t think so (b) Rarely (c) Usually does (IDT) (RY) (UD) 12. Does your child smile in response to your face or your smile? (a) No (N) (b) Yes (Y) (c) Sometimes (SS) 13. Does your child imitate you? (a) Quite a lot (QL) (b) Does Not (NS)

Appendix B Experts’ suggestions for interrelationships between each one of the input concepts to the output concept of autism (C24) Concepts

Description

Exp 1 (Dr)

Exp 2 (OT)

Exp 3 (SPEDU)

C1

Enjoy being swung

(a) DA (b) PA (c) NA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C2

Take an interest in other children

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C3

Climbing on things

(a) NA (b) DA (c) PA

(a) DA (b) NA (c) PA

(a) NA (b) PA (c) DA

C4

Enjoy playing

(a) DA (b) PA (c) NA

(a) DA (b) PA (c) NA

(a) DA (b) PA (c) NA

C5

Pretend other things

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) DA (b) PA (c) NA

C6

Pointing index finger

(a) DA (b) NA (c) PA

(a) NA (b) DA (c) PA

(a) DA (b) PA (c) NA

C7

Indication of interest

(a) DA (b) NA (c) PA

(a) NA (b) DA (c) PA

(a) DA (b) PA (c) NA

C8

Playing with small toys

(a) NA (b) DA (c) PA

(a) NA (b) DA (c) PA

(a) DA (b) NA (c) PA

(c) Once a while (OW)

14. Does your child respond to his/her name when you call? (a) Yes, of course (b) Yes, (c) No, very little (YO) sometimes (NV) (YS) 15. If you point at a toy across the room does your child look at it? (a) Seldom does this (b) Yes, this (c) Once in a while (SD) is typical (OIW) (YTY) 16. Does your child walk? (a) with others help (b) No, very (WO) little (NV)

23. Does your child look at your face to check your reaction when faced with something unfamiliar? (a) Yes, definitely (b) Yes, (c) Does not look (YDY) slightly true (DNL) (YST)

(c) by himself (BH)

17. Does your child look at things you are looking at? (a) definitely not (b) Yes, (c) often (O) (DN) sometimes (YS) 18. Does your child make unusual finger movements near his/her face? (a) Yes, often and for (b) Very (c) No (N) rather long periods rarely (VR)

Arthi Kannappan et al. / Expert Systems with Applications 38 (2011) 1282–1292

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Appendix C (continued)

Appendix B (continued) Concepts

Description

Exp 1 (Dr)

Exp 2 (OT)

Exp 3 (SPEDU)

C9

Bringing objects to parents

(a) DA (b) PA (c) NA

(a) DA (b) PA (c) NA

(a) DA (b) PA (c) NA

C10

Eye contact

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

C11

Oversensitive to noise

(a) DA (b) PA (c) NA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C12

Smile in response to parents face

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

C13

Imitate

(a) NA (b) DA (c) PA

(a) NA (b) DA (c) PA

(a) DA (b) NA (c) PA

C14

Response to the name

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C15

Looking at a toy when pointing

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

C16

Walking

(a) PA (b) DA (c) NA

(a) PA (b) DA (c) NA

(a) PA (b) DA (c) NA

C17

Look at things you are looking at

(a) DA (b) PA (c) NA

(a) NA (b) PA (c) DA

(a) DA (b) PA (c) NA

C18

Unusual finger movements near his/her face

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

C19

Attract your attention

(a) NA (b) DA (c) PA

(a) NA (b) DA (c) PA

(a) NA (b) DA (c) PA

C20

Deafness

(a) DA (b) NA (c) PA

(a) DA (b) NA (c) PA

(a) NA (b) DA (c) PA

C21

Understanding what others say

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C22

Stare at nothing

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

C23

Look at your face to check reaction

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

(a) NA (b) PA (c) DA

DR – pediatrician, OT – occupational therapist, SPEDU – special educator; DA – definite autism; PA – probable autism; NA – no autism. Appendix C Dataset consisting of 40 cases used in prediction process. 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89

0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.73 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.72 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.76 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.75 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.71 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.78 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.73 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.73 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.72 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.20 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.70 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.71 0.43 0.54 0.12 0.34 0.11 0.21 0.11 0.03 0.34 0.57 0.54 0.78 0.23 0.64 0.12 0.45 0.76 0.12 0.34 0.25 0.45 0.23 0.21 0.33 0.01 0.23 0.34 0.54 0.56 0.43 0.54 0.12 0.34 0.11 0.21 0.11 0.67 0.61 0.63 0.75 0.67 0.00 0.12 0.34 0.34 0.51 0.55 0.20 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.45 0.23 0.45 0.11 0.02 0.34 0.44 0.2 0.4 0.3 0.21 0.2 0.11 0.02 0.11 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.01 0.23 0.34 0.54 0.56 0.43 0.54 0.12 0.34 0.33 0.32 0.63 0.75 0.67 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.01 0.23 0.34 0.54 0.56 0.43 0.54 0.12 0.34 0.33 0.02 0.12 0.23 0.20 0.67 0.73 0.51 0.53 0.55 0.57 0.59 0.30 0.02 0.34 0.94 0.11 0.38 0.46 0.23 0.64 0.12 0.45 0.76 0.12 0.36 0.24 0.12 0.3 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.51 0.53 0.55 0.57 0.59 0.30 0.02 0.34 0.30 0.56 0.51 0.53 0.55 0.57 0.59 0.30 0.02 0.34 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.30 0.22 0.39 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.23 0.19 0.23 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.67 0.73 0.51 0.53 0.55 0.57 0.59 0.30 0.02 0.34 0.34 0.23 0.28 0.67 0.73 0.51 0.53 0.55 0.57 0.59 0.30 0.02 0.34 0.43 0.54 0.12 0.34 0.11 0.21 0.11 0.03 0.34 0.57 0.54 0.78 0.23 0.25 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.73 0.75 0.77 0.76 0.23 0.22 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73 (continued on next page)

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Appendix C (continued) 0.75 0.77 0.79 0.81 0.69 0.71 0.73 0.75 0.77 0.76 0.81 0.83 0.85 0.87 0.89 0.91 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.71 0.34 0.57 0.43 0.54 0.12 0.34 0.11 0.21 0.11 0.03 0.34 0.57 0.54 0.78 0.23 0.64 0.12 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.710.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.710.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.75 0.71 0.46 0.36 0.36 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.67 0.43 0.54 0.12 0.34 0.11 0.21 0.11 0.03 0.34 0.57 0.54 0.78 0.23 0.64 0.12 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.73 0.51 0.53 0.67 0.61 0.63 0.75 0.67 0.69 0.71 0.73 0.34 0.73

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