NON-LINEAR DATA ANALYSIS ON KANSEI ENGINEERING AND DESIGN EVALUATION BY GENETIC ALGORITHM

Engineering Vol.6 No.4 pp.55-62 (2006) ORIGINAL ARTICLES NON-LINEAR DATA ANALYSIS ON KANSEI ENGINEERING AND DESIGN EVALUATION BY GENETIC ALGORITHM Toshio TSUCHIYA*, Yukihiro MATSUBARA** *Shimonoseki City University, 2-1-1 Daigakucho, Shimonoseki, Yamaguchi, 751-8510 Japan ** Faculty of Information Sciences, Hiroshima City University 341 OzukaHigashi, Hiroshima, 731-3194 Japan Abstract: This paper discusses non-linearity in KANSEI evaluation data and attempts to better understand non-linear relationships between design attributes. Conventionally, the basis of KANSEI analysis has been multivariate analyses and linear modeling. These methods have proven unreliable and problematic. Non-linearity may be typically represented by the interaction between design elements, which often is represented as multicollinearity. To better understand such interactions, a method is proposed that expresses the effect of combining multiple design elements, and uses 'f-then' rules in conjunction with decision trees. The method is also described for constructing these decision trees by using genetic algorithms (GA). Our concern is to consider the adequateness of the proposed method for analyses of non-linear KANSEI data. Two actual examples are shown in order to investigate this problem. An example of KANSEI experiment on interior automobile space is used to examine divided partitions as tree representations. Another illustration of canned coffee design shows a comparison between the results of our method and quantification type I. We can conclude from these examples such that the proposed method indicates in more detailed rules and a deeper understanding of information extracted from KANSEI evaluation data. Keywords: KANSEI engineering, Data analysis, Product designing, Decision tree, Genetic Algorithm 1. INTRODUCTION KANSEI evaluation data (KANSEI data), which is usually collected by SD questionnaires to real design candidates, is extremely complex because human perception is ambiguous and influenced by many outside factors. This complexity is difficult to analyze. For example, when one studies color coordination, one finds that KANSEI differ, depending on color composition. There are substantial levels of interaction and ambiguity and, therefore, understanding KANSEI data has proven to be a very difficult task. This non-linearity or complexity can be better understood by looking at the distribution of evaluation data. In this paper, we propose a method for studying complexity that uses non-linear statistical distributions. We also describe the characteristics of non-linear relations by applying our method to a practical problem: automobile interior space design. The KANSEI data set used was obtained from an SD scaled questionnaire. Additionally we describe a method for automatically extracting KANSEI rules from design interactions, and apply this method to the above example. In our method, decision trees are generated that represent interactions, and production rules are extracted from these decision trees. The main advantage of this 'rule representation' lies in the relative ease of comprehension it offers; the trees reduce the applied attributes to a small number of characteristic design combinations. Additionally, a second practical example is set up in order to demonstrate our method for acquiring decision trees and confirm the differs to the conventional statistical method. In order to illustrate the availability of the decision tree, the method for acquiring decision tree using GA is shown by using canned coffee data. 2. NON-LINEARITY IN THE KANSEI DATA 2.1 Complexity and non-linearity The complexity of human perception is the most problematic factor in KANSEI engineering studies. Relationships between product design and perception are seldom clear. Several methods of analysis have been proposed that would facilitate a better understanding of KANSEI data [1]. Multivariate analysis has, so far, been the most reliable tool available. Even this method, however, can produce erroneous results, usually as a result of over fitting and non-linearity. To better understand KANSEI in situations where data are limited, we propose extracting the complexity, or non-linearity, from the situation. Interactions between design attributes are the most common cause of non-linearity. The effects of design combinations are unpredictable and difficult to assess during evaluation because of the occurrence of multiplications, set offs or exceptions. Only the use of real data distributions can overcome these difficulties. So, it is thought to be important that we discuss KANSEI data distributions. The data set used was obtained from a questionnaire-based experiment (using a five-point semantic differential scale). Design candidates were observed, and those performing the study checked the point. Received 2006.06.02 Accepted 2006.12.18

Engineering 2.2 KANSEI evaluation data To obtain our data, we performed a KANSEI experiment on interior automobile space [2]. Forty-one members of 2.3 an automobile company evaluated twenty passenger cars without with 1,000 to 1,500cc displacements. The number of words in the evaluation came to 100. The words 'roomy' and 'oppressive' were used to describe the interior. We which show the passenger car's evaluation `oppressive' on the value of interior di Data distributions First, we describe dimensions the relationships interaction effects. the angle of inclination as designer show Note, key the dimensions 3: Interior dimensions that simple to perception. of perceived data distributhe correlation and the KANSEI words is between Now, consider the non-linearity from a point of view. The data distributions between the interior the dimensions dimensions show and the are related to each other. have different effects of XH45 4: evaluation on lower H122 5: evaluation on higher H122 of H122 56 by automobile determinants however, little relation and 0.365. relation driver's- interior The interior dimensions evaluation the distance from eye point to recognized KANSEI because Item of the front wind- are widely no 2: mensions. or level. These factors design-element of 'roomy' the vertical view from eye 0.015 evaluation 1, 2 are the diagrams side view, and XH45 represents between the interior the relations hip point ( 3). H122 refers to the horizontal tions 1: shield, and XH45 represents spaciousness. between and the KANSEI to demonstrate H122 represents evaluated the average value given by the participants. Fifty-three interior dimensions were measured. Vol.6 No.4 because the

NON-LINEAR DATA ANALYSIS ON KANSEI ENGINEERING AND DESIGN EVALUATION BY GENETIC ALGORITHM vertical and horizontal views are inter-related. The design elements have no definite effect on the variation of other elements. To demonstrate the effect of this interaction, the cross data for dimensions H122 and XH45 are shown. The samples were divided into two equal groups of twenty using the average value for H122 as the line of division. The data for the group with the lower H122 value is shown in 4, and 5 shows the data for the other group. In the first group, the descriptive KANSEI `roomy' tends to increase as XH45 increases, and decreases as XH45 decreases. We therefore conclude that, for the group with the lower H122 values, increasing XH45 positively influences the perception of roominess, and decreasing XH45 negatively influences this perception. By contrast, 5 demonstrates the opposite for the group with the higher H122 value. The 'roomy' values don't seem to increase as XH45 increases. Thus, the perception of roominess seems to be a result of interactions between design elements. When evaluating the perception of interior space, the relationships between vertical and horizontal are very important. In areas of limited space, perceptions are strongly intertwined with this relation. This demonstrates the interaction that occurs between elements in KANSEI data and Non-linear data often complicate KANSEI analysis. 2.4 Extracting non-linear relations in KANSEI engineering The example of automobile interior space shows nonlinear relations between the "roominess" KANSEI and the interior dimensions. This type of non-linearity has been frequently treated as multicollinearity in the field of statistics. However, non-linearity of the above example can not be represented by simple correlation between variables, but it have to be treated as qualitative difference between design spaces divided by design elements. It is therefore difficult to estimate statistical correlations between variables. Ishihara advanced a method by using Local Linear Regression for splitting design space into linear subspaces to adopt linear regression [3, 4]. Inoue and Nishino employed rough sets theory which proficiently extracts effective design conjunctions to represent combination effects [5]. These methods, proposed for acquiring nonlinear relationship between KANSEI and design elements, required to be appropriate in terms of following criteria such as to perform under lack data - tracing or forecasting real KANSEI evaluation by resulted model, dividing input space according sample distribution, availability or generality to type of design - categorical or numerical representation of design element, understandable representation of the results of analysis for practicality and so on. Advantages of the decision tree method on the dividing input space are like that; a decision tree can cover whole input space, design elements don't need to be categorical data and each sample can be accepted any type of class such as normal sets, numerical value, mathematical expression (i.e. regression model) [2, 6]. A classification tree usually have a class. The tree method doesn't require the type of the class of sample. Regression models was used at the node in previous research [6]. We may therefore expect that the method is applicable to large domain of KANSEI analysis. The usefulness of the tree method is shown by a research using the real product evaluations for extracting important elements from design attributes [7]. 3. KANSEI RULES BY DECISION TREE In this section, we attempt to inductively extract the interaction between design elements from the data to better understand the relationship between KANSEI data and design elements. Decision trees are popular tools for representing production rules [8]. There are many ways to construct decision trees, but most are used to minimize quadratic errors. In KANSEI engineering, the rules used to represent KANSEI must be properly structured to fully understand which design elements are interrelated. 3.1 Tree learning by genetic algorithm GA based structure learning is a useful technique for classifying samples. Unfortunately, GA is problematic because it encodes searching problems into chromosomes [9]. Assume tree structures could be encoded into chromosomes; however, because chromosomes tend to decrease in size, trees cannot be directly encoded into chromosomes. In a genetic operator, the population containing the solution is maintained, and this population evolves through successive generations. This is the reason our method uses indirect encoding ( 6). Each chromosome corresponds to an attribute, which is a node in 6: Coding of decision tree

Engineering Vol.6 No.4 the tree. An encoded chromosome has four functioning parts: an address, pointers, classification rules, and fitness values. The address and pointers are described by genotypes (i.e., 0, 1, or don't care), and together these form the tree through successive links from the top level node to the lowest ones. The classification rules place the examples into lower-level nodes, according to attribute. Genetic operators maintain a solution population, and the population is allowed to evolve through successive generations. The GA process is shown in 7. The tree construction operator generates a tree from the chromosomes in the current population. Then, according to the error rate of the classification, the tree-evaluation operator calculates the constructed tree. The recalculation operator calculates the fitness values for all chromosomes based on the evaluation, and then the genetic operator creates the next population. The most general genetic operators -reproduction, crossover, and mutation- are employed in the process. -according to the SD values. 62 interior dimensions are categorized into 3 to 5 membership functions which are named "A1" to "A5". KANSEI rules are extracted by our learning method with classifying these training data. The resulted decision tree for "roomy" is shown in 8. The tree is composed of nodes, leaves and links between nodes. A node means a dimension (e.g. top node is dimension H122). A number of the leaf means a membership function of the fuzzy class which proportional to the KANSEI evaluation. A link means a membership function of the dimension (Al means the smallest, A5 is the largest one). In a decision tree, level of 8 : Extracted decision tree of "roomy". Table 1 : Comparison of real value and decision tree 7 : Tree induction procedure 3.2 Resulted decision tree The proposed method is adopted for the interior automobile space to obtain KANSEI rules from the evaluation data. Semantic differential data of "roomy" which is shown in chapter 2 is used for the analysis. 20 samples of the automobile are classified into 5 membership functions which correspond to fuzzy classes -"class1" to "class5" 58

NON-LINEAR DATA ANALYSIS ON KANSEI ENGINEERING AND DESIGN EVALUATION BY GENETIC ALGORITHM node represents importance of the attribute. H122 of root node divides the attribute space into 3 subspace according to the size of the dimension. A design candidate is necessary classified by the dimension first. It is meant that H122 is the most effective dimension for classify the samples. This follows the aspect resulted from the distribution of 4, 5. The tree also resulted that XH45 is concerned with the classification (dividing attribute space) under the condition of lower H122. We may, therefore, say that our learning method appropriately structured the decision tree according to the data distribution. It also reflects vertical and horizontal relation between dimensions which dominate in "roomy" of the interior space. Table 1 shows a comparison of evaluation values between the real data and prediction by the decision tree. The order of predicted sample evaluation, given by defuzzify output membership function, is close to the real one. The accuracy of classification was 19/20 in this experiment. This means our method was appropriately able to trace the real data variable. It's believe that these results enough support the effectiveness of our method. design elements. The values are similar to the KANSEI words for the same factor. To illustrate, in this category, the scores for 'black = true' are negative in all KANSEI words (i.e., the quality black had a negative influence on the factor `soft'). Similarly, note that 'red', 'gold' and silver' also had negative impacts on the category scores. ' The design elements 'brown', 'white' and 'cream' had positive influences. These results seem to agree with our intuitive expectations. If we look more carefully at the relationship between design elements, we see that simply because a product contains a combination of design elements with positive images, it does not necessarily follow that a positive image will result. Table 2 : Items and categories of canned coffee 4. NUMERICAL EXAMPLE OF CANNED COFFEE DESIGN 4.1 Statistical analysis We confirmed the performance of our method in the term of dividing attribute space and tracing training data. Then, the next point concerning with difference from traditional statistical method. We applied our method to a KANSEI experiment for a canned coffee product and compared with the result of quantification type I [10]. The evaluations for this design were determined by using a SD scale. Ten participants evaluated 72 canned coffees using 88 KANSEI words. We extracted 14 design items from the candidates (Table 2). First, we analyzed the KANSEI words and the evaluation data using factor analysis. Table 3 shows the extracted three main factors and the KANSEI words used for each. The factors were 'soft', 'deluxe' and `unconventional (or conventional)'. Five KANSEI words were extracted for the first factor, 'soft', and analyzed by using quantification theory type I. Table 4 shows the category scores and the correlation coefficients for the 4.2 Decision Trees We generated decision trees to analyze the interactions along with the selected KANSEI words belonging to the Table 3 : Results of factor analysis

Engineering Vol.6 No.4 factor 'soft'. The classes for the canned coffee were determined by using KANSEI evaluation (SD profile), and samples were placed into one of three classes ('positive', negative', and 'neutral'). The items and categories ' were the same as for that above. 9 shows the extracted decision tree for the KANSEI word 'soft'. The attribute cream' was employed as the top node, and 'cream' = true' indicates class 3 (i.e., samples belong to the class 'positive'). This mirrors the results from quantification theory type I. The level of node basically reflects the importance of the design element. The item "cream" placed as the most important design element in the KANSEI word 'soft'. It agrees with the result of quantification theory type I. Next we focused on the effects of combining the design items in the lower nodes. For node 'blue', two attribute values resulted in placing samples into class 1 or 3. The condition 'white = true' was the same as for the two example classes. Note that the attribute 'blue' was dependent on the classification of the attribute 'white' (the classification of 'blue' is available under 'white' ). The positive influence of 'white' was already known from our analysis regarding 'soft'. However, in our analysis, combining 'white' and 'blue' had a negative effect. By contrast, the attributes 'white' and 'red' had the opposite effect. When 'white = true' and 'red = true', the classified examples belonged to class 3. Knowing that 'red' results in negative images (from quantification theory), we can conclude that 'red' has no dependence on, or conjunction relationship with, the attribute 'white'. This result of nonlinearity or interaction is different from the quantification theory type I. 10 shows the extracted decision tree for 'milky'. Here, the conditions 'red = true' and 'black = true' are under the condition of 'white = true'. The classes for the conditions are three and two, respectively. Based on the results provided by quantification theory, the design elements 'red' and 'black' have different effects when white = true'. ' Our proposed method focuses on the combined effects of multiple design elements. These effects are represented by dependence on attributes from the node at the top level to that at the lowest level. Any multiplication or counterbalance among attributes is described by using a tree structure. This allows us to measure the combined effect of multiple design attributes. The extracted combination effects by the decision trees didn't necessarily correspond to the ones of quantification type I. We can say certainly that our method reflect non-linearity in learning of KANSEI evaluation data. 5. CONCLUSIONS We have discussed the non-linearity of KANSEI data and proposed a method for understanding interactions in real KANSEI data. The automobile interior space is followed to concern qualitative interaction in the KANSEI evaluation data. Then, the decision tree which is based on learning by GA is used for analyzing the interaction. The method is confirmed the capability of dividing attribute space according non-linear data distribution and examined in the terms of ability of tracing training data too. These relationships are easily and understandably represented by the use of production rules. Using an actual case involving a canned coffee design, we demonstrated the usefulness of our method over conventional KANSEI engineering and showed that it can be used to better understand the effects of design combinations. In this Table 4 : Results of quantification theory type I 60

NON-LINEAR DATA ANALYSIS ON KANSEI ENGINEERING AND DESIGN EVALUATION BY GENETIC ALGORITHM research, the represented design combinations are treated as differences from quantification theory type I. But, it is necessary obtained from the acquired decision trees and independently extracted as linguistic rules to use in the actual analysis without any other results. Even so, it seems reasonable that our method is available in case where it's combined with other linear models such as quantification theory type I. Alternatively, our method can be used for dividing attribute space, so it can be applied for hybrid approach with a linear model. 9 : Extracted decision tree of 'soft' 10 :Extracted decision tree of 'milky' REFERENCES 1. M. Nagamachi, "KANSEI Engineering: A new ergonomic consumer-oriented technology for product development", International Journal of Industrial Ergonomics, vol.15, no.1, pp.3-12, 1995. 2. T. Tsuchiya, T. Maeda, Y. Matsubara and M. Nagamachi, "A fuzzy rule induction method using genetic algorithm", International Journal of Industrial Ergonomics, vol.18, pp.135-145, 1996. 3. S. Ishihara, Keiko Ishihara, Mitsuo Nagamachi and Tatsuo Nishino, "Smoothing of ordinal categorical data and its application to analysis of 2-dimensional data of hair design KANSEI evaluation data, Proc. Of International Ergonomics Association (CD-ROM) 2003. 4. T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning; Data mining, Inference, and Prediction, Springer-Verlag, 2001. 5. S. Ishihara et al., Product Development and KANSEI, Kaibundo, 2005 (in Japanese). 6. T. TSUCHIYA, Y. MATSUBARA, M. NAGAMA- CHI, "KANSEI Engineering for Design of Basic 3D Rectangular", Proc. of the 2005 International Conference on Active Media Technology (AMT 2005), pp.443-448, 2005. 7. M. Tokumaru, et al., "Decision Tree Analysis to Investigate what has an Influence of Facility and Preference with the Product - Making Up the Rules about Easeof-hitting and Preference of a Golf Club, Journal of KANSEI Engineering, pp.65-72, 2002 (in Japanese). 8. J. R. Quinlan, "Learning Efficient Classification Process and Their Application to Chess End Games", in Machine Learning: An artificial intelligence approach (Vol. 1), ed. R. S. Michalski, J. G. Carbonell, & T. M. Mitchell, pp.463-482, CA, 1983. Morgan Kaufmann, 9. D. E. Goldberg, ed., Genetic Algorithm in Search, Optimization and Machine Learning, Addison Wesley, MA, 1989. 10. T. Tsuchiya, S. Ishihara, Y. Matsubara and M. Nagamachi, "A Method for Learning Decision Tree and Its Application for Design of Canned Coffee", Proc. of the International Conf. on TQM and Human Factors, Linkopin, Sweden, pp. 385-388, June 1999.

Engineering Vol.6 No.4 Yukihiro MATSUBARA received his B.E., M.E., and D.Eng degrees from Hiroshima University in 1987, 1989, and 1996. Since 2003, he has been a professor in the Faculty of Information Sciences, Hiroshima City University. He was a visiting researcher at the University of Nottingham in 1997 and 2000. He is a member of JSKE, IPSJ, JSAI, JES, and JSiSE. Toshio TSUCHIYA was educated as a system engineer at Hiroshima University and is currently an associate professor of Department of International Commerce in the Faculty of Economics at Shimonoseki City University. He was an assistant at faculty of engineering, Hiroshima University from 1994 to 1996, a lecturer at Shimonoseki City University from 1996 to 1998, an associate professor at Shimonoseki city university from 1998. He received B.S. and M.S. degrees from Hiroshima University in 1990 and 1992 and received Doctor degree in Information Engineering from Hiroshima City University in 2006. His research interests include data mining, knowledge engineering, fuzzy set theory and KANSEI engineering. He is a member of Japanese Society for AI, JES, JSKE and SOFT.