Classification in Marketing Research by Means of LEM2-generated Rules

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1 Classification in Marketing Research by Means of LEM2-generated Rules Reinhold Decker and Frank Kroll Department of Business Administration and Economics, Bielefeld University, D Bielefeld, Germany; {rdecker, Abstract. The vagueness and uncertainty of data is a frequent problem in marketing research. Since rough sets have already proven their usefulness in dealing with such data in important domains like medicine and image processing, the question arises, whether they are a useful concept for marketing as well. Against this background we investigate the rough set theory-based LEM2 algorithm as a classification tool for marketing research. Its performance is demonstrated by means of synthetic as well as real-world marketing data. Our empirical results provide evidence that the LEM2 algorithm undoubtedly deserves more attention in marketing research as it is the case so far. 1 Introduction Classification is a common problem in marketing, particularly in market segmentation (Which consumers belong to which market segment?), sales force management (Which customers should be targeted with which customer care program?), and direct marketing (Which advertising materials should be sent to which customer?). One way to solve such marketing tasks is the deduction of decision rules from appropriate survey data. A promising approach for generating decision rules is the LEM2 algorithm (Learning from Examples Module Version 2), which is based on the rough set theory. The concepts of rough set theory have been used successfully in medicine and in bio-informatics, among other things. Therefore, it is quite surprising that to our knowledge there is still no publication applying LEM2 to classification tasks in marketing. The present paper aims at filling this gap. Substantiating the adequacy of LEM2 for the above mentioned tasks opens new options for knowledge discovery in marketing databases and the development of decision support systems for marketing planning. The rough set theory was introduced by Pawlak (1982) and is a mathematical approach to deal with vagueness and uncertainty in data. The main

2 426 Reinhold Decker and Frank Kroll idea of rough set theory, which recently aroused increasing interest in data mining, is to describe a given set X with fuzzy boundaries by two sets called the lower and the upper approximation. Rough sets enable to partition a given universe U, i.e. the objects considered, into equivalence classes, which are also called elementary sets. The objects belonging to those elementary sets are indiscernible with regard to a given set of attributes B and set X.Thelower approximation BX contains all objects, whose elementary set is completely contained in X (with regard to the set of attributes B). The upper approximation BX, in return, contains all those objects, for which at least one element of the associated elementary set is contained in X. Those objects are possible elements of X.ThesetX is called rough, if the lower approximation does not equal the upper approximation, otherwise X is called crisp. Therefore, the main idea is to approximate a rough set X by two crisp sets, namely the very lower and upper approximation. For a more detailed introduction into rough set theory we refer to Pawlak (1991). The remainder of the paper is structured as follows: First, a brief description of the LEM2 algorithm is given. Then, the LEM2 algorithm is empirically compared to alternative methods based on three different classification tasks in marketing. 2 Remarks on the LEM2 algorithm The LEM2 algorithm was published in 1992 by Jerzy W. Grzymala-Busse as apartofthelers(learning from Examples based on Rough Sets) system. The basic principle of this approach needed for the marketing examples will be sketched in the following (see also Grzymala-Busse (1997) for details). Let T be a set of pairs of attributes a Band corresponding attribute values v. ThensetX depends on set T if and only if: [T ]= [(a, v)] X, (1) (a,v) T where [(a, v)] is the equivalence class or elementary set of pair (a, v). Furthermore, set T is a minimal complex of X if and only if X depends on T and no proper subset Q T exists such that X depends on Q. Because of the possible existence of various combinations of attributes a and values v, set X can have several minimal complexes. In rough set theory data is represented as a decision system S d.asimple decision system referring to a hypothetical car evaluation is shown in Table 1. The example at hand includes two condition attributes, i.e. B = {seating capacity, vibration} and one decision attribute d = {quality}. A set of objects with the same decision attribute value relation (e.g. (quality, low)) is called a decision class.

3 Classification in Marketing Research by Means of LEM2-generated Rules 427 Table 1. A simple decision system S d for car evaluation Seating capacity Vibration Quality c 1 5 medium low c 2 4 medium low c 3 5 medium low c 4 5 low medium c 5 2 low medium c 6 4 medium high c 7 4 low high c 8 2 low high If we consider the decision class (quality, low), for example, this results in the set X = {c 1,c 2,c 3 }. In addition, let T be a set of pairs (seating capacity, 5) and (vibration, medium). The elementary sets of these two pairs are {c 1,c 3,c 4 } and {c 1,c 2,c 3,c 6 }. Then, according to Equation (1), [T ] = [(seating capacity, 5)] [(vibration, medium)] = {c 1,c 3,c 4 } {c 1,c 2,c 3,c 6 } = {c 1,c 3 } {c 1,c 2,c 3 } = X.ThusX depends on T.Furthermore,T = {(seating capacity, 5); (vibration, medium)} is a minimal complex because there is no proper subset Q T, which depends on X. Let T be a nonempty set of minimal complexes. Then T is a local covering of X if and only if the following conditions are satisfied (Grzymala-Busse (1997)): a) Each T T is a minimal complex of X. b) Each object in X is covered by at least one minimal complex, i.e. T T [T ]=X holds. c) T is minimal and no proper subset of T exists, which satisfies conditions a) and b). If all conditions are satisfied, then set X is covered by the smallest set of pairs (a, v) it depends on. In addition each minimal complex of the local covering represents a decision rule for set X. So far, we solely considered the decision class associated with the pair (quality, low). To generate rules for the whole decision system, the algorithm sketched above has to be run for each decision class and each approximation of X. If the data set is inconsistent, then the lower approximation BX is used to determine certain decision rules, whereas the upper approximation BX is used to determine uncertain ones. However, if the data set is consistent, then BX = BX applies and we solely generate certain decision rules by using the lower approximation BX. For a more detailed description of the corresponding pseudo-code see Grzymala-Busse (1997). Continuing the example given in Table 1, the lower approximation of X is BX = {c 1,c 3 }. With all conditions a) to c) satisfied, the set T = {{(seating capacity, 5); (vibration, medium)}} is a local covering of X and the minimal

4 428 Reinhold Decker and Frank Kroll complex T represents a certain decision rule: (seating capacity, 5) (vibration, medium) (quality, low). 3 Synthetic data example The data set used in the following is a synthetic one published by Zupan (1997). It is used to demonstrate the general performance of the LEM2 algorithm and comprises 1,728 car evaluations based on six condition attributes, such as estimated safety (values: low, medium, high) and the number of doors (values: 2, 3, 4, 5 and more) and one decision attribute, namely the degree of acceptance of the car (values: no, rather no, rather yes, yes). The data set is consistent since the quality of classification X equals 100 %. That is to say, there are no objects with identical condition attribute values but different decision attribute values. All attributes were included in the analysis. The computations were made with the rough set analyzing tool RSES (Bazan et al. 2004). The method for resolving conflicts was standard covering, hence the decision rule with the highest support fires. To validate the generated decision rules 10-fold cross validation was applied. Thereto, the data set was randomly divided into ten similar subsets. Then, nine subsets were used to learn and one subset to validate the generated rules. This procedure was repeated until each subset was validated. To assess the performance of the LEM2 algorithm three benchmarks were employed for comparison purposes, namely the decomposition tree approach by Nguyen (1999), the Local Transfer Function Classifier (LTF-C), and linear discriminant analysis as the standard classification method in marketing practice. LTF-C is an artificial neural network approach particularly developed to solve classification problems which has already proven its outstanding performance in a recent study by Wojnarski (2003). Table 2 shows that LEM2 outperforms linear discriminant analysis by 22 % and LTF-C by 16.4 % and results in a hit rate of almost 100 %, i.e. nearly four times as high as random assignment. The difference between the decomposition tree and LEM2 is quite marginal. Table 2. Performance based on the synthetic data Method Hit rate Random assignment Rank LEM % 1 Decomposition tree 97.8 % % LTF-C 81.6 % 3 Discriminant analysis 76.0 % 4 By using the LEM2 algorithm altogether 269 decision rules could be generated from the available car data. Some of these decision rules are depicted

5 Classification in Marketing Research by Means of LEM2-generated Rules 429 in Table 3. The numbers in squared brackets indicate how often the respective rule was identified in the data set. For example, if the purchase price of a car is high and the estimated safety is high and the seating capacity is 4 persons and the maintenance costs are medium then the respective offer would be accepted by the respondents. This decision rule is supported by 12 respondents. On the other hand, reductions in safety can not be compensated by a lower purchase price (see last rule). Obviously, safety ranks higher than inexpensiveness. Table 3. Selected LEM2 decision rules (estimated safety = low) (acceptance = no) [576] (purchase price = high) (maintenance costs = very-high) (acceptance = no) [108] (seating capacity = 5 and more) (number of doors = 2) (luggage volume = small) (acceptance = no) [48] (purchase price = high) (estimated safety = high) (seating capacity = 4) (maintenance costs = medium) (acceptance = yes) [12] (purchase price = low) (estimated safety = medium) (seating capacity = 4) (maintenance costs = medium) (luggage volume = large) (acceptance = rather no) [4] 4 Real world data examples After having demonstrated the basic suitability of the LEM2 approach by means of synthetic marketing data, we will now consider real world marketing data. The data set at hand was generated from a customer survey conducted by a German car manufacturer. Each respondent had purchased a new car within the last three months before the survey started. Considering only completed questionnaires, the data set contains 793 objects (respondents), each of them being characterized by 45 condition attributes (namely the items referred to in the questionnaire) and one decision attribute (namely the car currently owned: model A, B, C or D). 4.1 Customer selection in direct mailing The first example is a typical problem of direct mailing: Assuming that the car manufacturer wants to send out different information brochures on the four models (A, B, C and D) to potential new customers, a customized shipping suggests itself to minimize the marketing costs and to enhance the likelihood of use. Each recipient should get only the brochure of that model he presumptively is interested in most. Therefore, we used the following condition attributes to generate appropriate decision rules and to draw a comparison between the methods considered: pre-owned car brand, sex, employment status, and size of household. In contrast to the synthetic data used above the present

6 430 Reinhold Decker and Frank Kroll data has a low quality of classification X of only 9.7 %, which corresponds with a high level of inconsistency. 10-fold cross validation resulted in the hit rates depicted in Table 4. Once again, the LEM2 algorithm clearly outperforms the benchmarks. Altogether, 92 decision rules could be generated, e.g., (pre-owned car brand = Porsche) (employment status = employee) (model = A). Table 4. Performance based on the direct mailing data Method Hit rate Random assignment Rank LEM % 1 Decomposition tree 38.2 % % LTF-C 49.1 % 2 Discriminant analysis 44.9 % Customer advisory service In the second example we assume that a car retailer wants to improve his recommendation policy with regard to the four models. The basis for these recommendations is a set of indicators regarded to be crucial in car purchase decision making. From the above mentioned car manufacturer survey such information is available in terms of 21 binary coded condition attributes like driving comfort, styling and handling. The question belonging to the first condition attribute, for example, reads: Has driving comfort been a crucial car attribute when making your last car purchase decision?. The decision attribute was composed of two variables, namely model (values: model A, B, C, D) and customer satisfaction (values: satisfied, not satisfied). Therefore, there are eight decision classes with attribute values (A, satisfied), (A, not satisfied),..., (D, not satisfied). Since the quality of classification X equals 95 % the data set is only slightly inconsistent. Once again the LEM2 algorithm outperforms LTF-C and linear discriminant analysis (see Table 5). But the differences are less distinct than in the example before. The difference between LEM2 and the decomposition tree is negligible. Altogether, 416 decision rules could be generated from the available data, e.g., (economy = yes) (driving comfort = no) (reliability =yes) (brand image = yes) (model = A, customer = satisfied). Table 5. Performance based on the customer advisory service data Method Hit rate Random assignment Rank LEM % 2 Decomposition tree 37.7 % % LTF-C 30.9 % 3 Discriminant analysis 29.6 % 4 Since the number of variables or rather attributes included in a survey usually directly correlates with the willingness of the respondents to participate

7 Classification in Marketing Research by Means of LEM2-generated Rules 431 in the questioning and, thus, with the survey costs in general, it is interesting to see what happens if the number of condition attributes is reduced successively. The result of a random reduction of condition attributes is shown in Figure 1. Hit rate [percent] discriminant analysis LEM Number of condition attributes Fig. 1. Hit rates for different numbers of condition attributes From the two curves we see that popular linear discriminant analysis outperforms the LEM2 algorithm if the number of condition attributes is small, at least in the present case of binary coded data. But with an increasing number of condition attributes LEM2 performs better and better and finally clearly outperforms the standard classification method in marketing research. Obviously, LEM2 needs an appropriate amount of information to adequately learn the existing causalities. In the previous example this problem did not arise due to the higher explanatory power of the condition attributes considered. In so far LEM2 is not necessarily the best choice but seems to be promising if the number of variables to be included in the classification process is large. Furthermore, it should be taken into account if easy-to-interpret decision rules are required, e.g., as a foundation of customer advisory service optimization. Here, the availability of natural language like rules is often more helpful than abstract discriminant functions, for example. 5 Concluding remarks The present study has shown that the LEM2 algorithm is a promising tool to solve common classification problems in a user-friendly way by providing shortest possible, easy-to-interpret decision rules. Furthermore, those decision rules are distinguishable into certain and uncertain ones. It could be shown that the LEM2 algorithm outperforms both linear discriminant analysis and LTF-C in all data examples considered. Only the decomposition tree slightly outperformed the LEM2 algorithm once. The direct mailing example has shown that already small numbers of condition at-

8 432 Reinhold Decker and Frank Kroll tributes can lead to adequate classification results. But, as obvious from the customer advisory service example, the LEM2 algorithm is not necessarily the best choice and requires an adequate amount of information if more complex causalities have to be uncovered. Unlike other methods with similar foci like neural networks and association rules an a priori parameterization is not required. A more technical advantage of LEM2 is its low computational costs. On the other hand, if the variables to be included are continuous a discretization must precede, which in some cases may reduce their expressiveness. Without this step, each object would be an elementary set and the generation of meaningful rules becomes impossible. Further research should be devoted to more extensive comparisons which also include the recent modification of the original LEM2 algorithm suggested by Grzymala-Busse (2003), which combines discretization and rule generation. Furthermore, the application of the rough set theory to new domains in marketing and business administration in general seems to be worth closer consideration. A very up-to-date challenge in this respect would the application to web-based recommender systems, where the concept of the lower and upper approximation of sets can be used to suggest items (e.g. consumer goods) in a customized way. References BAZAN, J.G., SZCZUKA, M.S., WOJNA, A. and WOJNARSKI, M. (2004): On the Evolution of Rough Set Exploration System. In: S. Tsumoto, R. Slowinski, J. Komorowski, and J.W. Grzymala-Busse (Eds.): Rough Sets and Current Trends in Computing, Proceedings of the 4th International RSCTC 04 Conference. Springer, Berlin, GRZYMALA-BUSSE, J.W. (1997): A New Version of the Rule Induction System LERS. Fundamenta Informaticae, 31, 1, GRZYMALA-BUSSE, J.W. (2003): MLEM2 Discretization During Rule Induction. In: M.A. Klopotek, T.T. Wierzchon, and K. Trojanowski (Eds.): Intelligent Information Processing and Web Mining, Proceedings of the International IISPWM 03 Conference. Springer, Berlin, NGUYEN, S.H. (1999): Data Regularity Analysis and Applications in Data Mining. Ph.D. Thesis, Department of Mathematics, Computer Science and Mechanics, Warsaw University, Warsaw. PAWLAK, Z. (1982): Rough Sets. International Journal of Computer and Information Sciences, 11, 5, PAWLAK, Z. (1991): Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht. WOJNARSKI, M. (2003): LTF-C: Architecture, Training Algorithm and Applications of New Neural Classifier. Fundamenta Informaticae, 54, 1, ZUPAN, B., BOHANEC, M. and DEMSAR, J. (1997): Machine Learning by Function Decomposition, In: D.H. Fisher (Ed.): Proceedings of the 14th International Conference on Machine Learning. Morgan Kaufmann Publishers, Nashville,