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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.14 No.4 pp.335-346
DOI : https://doi.org/10.7232/iems.2015.14.4.335

A New Latent Class Model for Analysis of Purchasing and Browsing Histories on EC Sites

Masayuki Goto*, Kenta Mikawa, Shigeichi Hirasawa, Manabu Kobayashi, Tota Suko, Shunsuke Horii
Department of Industrial and Management Systems Engineering, Waseda University, Tokyo, Japan
Department of Information Engineering, Shonan Institute of Technology, Yokohama, Japan
School of Social Sciences, Waseda University, Tokyo, Japan
Global Education Center, Waseda University, Tokyo, Japan
Corresponding Author, jypark@dgu.edu
June 12, 2015 November 7, 2015 November 20, 2015

ABSTRACT

The electronic commerce site (EC site) has become an important marketing channel where consumers can purchase many kinds of products; their access logs, including purchase records and browsing histories, are saved in the EC sites’ databases. These log data can be utilized for the purpose of web marketing. The customers who purchase many product items are good customers, whereas the other customers, who do not purchase many items, must not be good customers even if they browse many items. If the attributes of good customers and those of other customers are clarified, such information is valuable as input for making a new marketing strategy. Regarding the product items, the characteristics of good items that are bought by many users are valuable information. It is necessary to construct a method to efficiently analyze such characteristics. This paper proposes a new latent class model to analyze both purchasing and browsing histories to make latent item and user clusters. By applying the proposal, an example of data analysis on an EC site is demonstrated. Through the clusters obtained by the proposed latent class model and the classification rule by the decision tree model, new findings are extracted from the data of purchasing and browsing histories.


초록


    1.INTRODUCTION

    The electronic commerce site (EC site) has become an important marketing channel where consumers can purchase many kinds of products; their access logs, including purchase records and browsing histories, are saved in the EC sites’ databases. These log data can be utilized for the purpose of web marketing (Hughes, 2006). For the purpose of marketing, it is valuable to analyze the purchasing and browsing behaviors of customers. The customers who purchase many product items are considered good customers (Curry et al., 2000), whereas the other customers who do not purchase many items must not be good customers, even if they browse many items. If the attributes of good customers and those of other customers (normal and dormant customers) are clarified, such information can be valuable as input for making a new marketing strategy. Regarding the product items, the characteristics of good items that are bought by many users are valuable information. However, the numbers of product items and customers are quite large, and there are many attributes of customers and product items. It is, therefore, necessary to construct a method to efficiently analyze the relation between the customer attributes and purchasing and browsing activities.

    The effectiveness of the latent class model, which is a discrete type of the latent variable model, has been described in many studies (Green et al., 1976; Swait and Adnmowicz, 2001; Bhatnagar and Ghose, 2004; Train, 2009). The latent class model assumes hidden latent classes for users and items. By introducing a latent class model, the latent user and item clusters can be modeled, and this assumption is consistent with marketing models (Train, 2009). A well-known latent class model is the aspect model, which was proposed to represent the relation between documents and words (Hofmann, 1999). The original aspect model proposed by Hofmann (1999) was a model of the statistical structure between documents and words for the purpose of information retrieval and document analysis. In order to apply the aspect model to a recommender system on EC sites, the relation between users, items, and preference values was modeled by introducing a discrete variable of a latent class for predicting individual choices and preferences (Hofmann and Puzicha, 1999). This model was extended to the model predicting users’ ratings by introducing the Gaussian distribution (Hofmann, 2004). The flexible mixture model (FMM) is also an extended model that assumes two latent variables independently for users and items (Si and Jin, 2003; Jin et al., 2003). These models would be useful for customer segmentation (Green et al., 1976) for marketing purposes. The clustering of customers is one of the important problems in the field of marketing (Magidson and Vermunt, 2002). However, these conventional models do not use the browsing history data and do not take account of the differences between purchasing and browsing activities.

    This paper focuses on the analysis of customers and product items for customizing marketing strategies on an EC site. From the viewpoint of marketing, it is useful to analyze the differences of characteristics between good customers and others. Here, the available data saved in an EC site’s database is not only purchasing history but also users’ attributes and browsing history data. A customer has to create an account with a password to purchase the product items and register attributes such as address, sex, and age. These user attributes are saved in a database table. Regarding product items, the attributes of the item, such as item category, maker (brand), and shop, are also available. Moreover, it is desirable to utilize the information of users’ browsing histories. This is because the number of purchased items is considerably smaller than that of browsed items. Some users may purchase only a small number of items, so that the purchasing history data may not be sufficient for determining a latent class model from the viewpoint of the relation between model structure and data size. Under those circumstances, we propose a new framework to analyze the data saved in the database on an EC site. The framework proposed in this paper includes the following distinctive points.

    • (1) In order to treat the browsing activities of customers, we propose a new latent class model expressing both purchasing and browsing activities directly in the model. The proposed model enables us to utilize not only the purchasing data but the huge browsing history data for model construction. It is desirable to construct a model expressing endogenously both purchasing and browsing activities, and it is advisable from the viewpoint of statistics.

    • (2) Additionally, we demonstrate a method for using the proposed model to make clusters of users and items. By using the proposed latent class model, the clusters of the good customers and the good product items are specified. The cluster sizes can be estimated by their probabilities of belonging to latent classes, and the conditional probabilities of purchasing and browsing activities can be useful for comprehending the estimated model and the meaning of each cluster.

    • (3) For the analysis of characteristics of each cluster, the decision tree model (Breiman et al., 1984) is introduced to investigate the relation between clusters given by the proposed latent class model and attributes of items and users. The CART algorithm can automatically construct a decision tree model expressing the relation between attributes and the latent classes of product items. Usually, there are many attributes of items and users. An efficient procedure to analyze the relation between the latent classes and attributes is provided by this analysis.

    By the combination of the proposed latent class model and the decision tree, a tool for the efficient analysis of characteristics of item and customer clusters is given in practice. The proposed analysis framework can be useful for clustering product items and customers and characterizing each cluster by using attributes.

    As an application of the proposal, an example of data analysis on an apparel EC site in Japan is demonstrated. This EC site provides a virtual shopping mall and apparel shops can open their virtual stores on the site by paying a store opening charge. In this site, the product items have the attributes of shops, brand, area, and item category. By applying the proposed model, the purchasing and browsing activities on the EC site can be modeled. As a result, the characteristics of each latent class of product items and users can be investigated from the viewpoint of the pattern of browsing and purchasing. On the application to the apparel EC site, we show the results obtained by applying the proposed latent class model and the analysis by the decision tree model. Through the proposed model and analysis approach, new findings are extracted from the data of purchasing and browsing histories. We show that effective discussions are possible on the basis of the result of our proposed analysis.

    2.ANALYSIS FRAMEWORK

    In this section, we show several related works and the overall framework of the proposed analysis.

    2.1.Notations

    A product item and a user (meaning a customer) are de-noted by xA and yU, respectively. Here, A ={a1, a2, L , aA} is the set of product items and U = {u1, u2, L , uU} is that of customers. The notations used in this study are listed here.

    • A = {a1, a2, L , aA} : the set of product items

    • U = {u1, u2, L , uU} : the set of customers

    • xA : a product item

    • yU : a customer (user)

    • W1 = {0, 1, 2, L , R1} : the set of numbers of purchasing actions

    • W2 = {0, 1, 2, L , R2} : the set of numbers of browsing actions

    • w1 =W1 : the number of purchasing actions

    • w2 =W2 : the number of browsing actions

    • w = (w1, w2 ) : the two-dimensional vector expressing both purchasing and browsing actions

    2.2.Overall Framework to Analyze the Data of Purchasing and Browsing Activities

    We propose a new framework to analyze the data saved in the database on an EC site, including the users’ purchasing and browsing history data and the attribute information of customers and product items. The main procedure of the analysis proposed in this paper is composed of modeling by a new latent class model, soft clustering of product items and customers, and analyzing the characteristics of each cluster on the basis of decision tree model.

    • (1) [Modeling by A Latent Class Model] In order to treat the browsing activities of customers, a new latent class model expressing both purchasing and browsing activities directly in the model is introduced. The proposed model enables us to utilize not only the purchasing data but the immense browsing history data for model construction. It is desirable to construct a model expressing endogenously both purchasing and browsing activities, and it is also desirable from the viewpoint of statistics.

    • (2) [Soft Clustering by the Latent Classes Model] Additionally, we demonstrate a way to use the proposed model to make clusters of users and items. By using the proposed latent class model, the clusters of good customers and good items are specified. The cluster sizes can be analyzed by their probabilities of belonging to latent classes, and the conditional probabilities of purchasing and browsing activities can be useful for comprehending the estimated model and the meaning of each cluster.

    • (3) [The Analysis of Characteristics of Each Cluster by Decision Trees] For the analysis of characteristics of each cluster, the decision tree model (Breiman et al., 1984) is introduced to investigate the relation between clusters given by the proposed latent class model and attributes of items and users. The Classification and Regression Tree (CART) algorithm can automatically construct a decision tree model expressing the relation between attributes and the latent classes of product items. Usually, there are many attributes of items and users. An efficient procedure to analyze the relation between the latent classes and attributes is provided by this analysis.

    2.3.Related Works with Latent Class Models

    In the field of marketing science, the effectiveness of latent class models is well known. This is because market segmentation strategies are generally used to identify the target consumers in practice, and the concept of the discrete latent class is consistent with this fact. The market is usually characterized by an aggregate of many different consumer groups. The latent class model assumes this general situation, and each latent class represents a consumer group with similar preferences. Through experimental studies, many researchers have stated that the assumption of latent classes is reasonable in marketing problems.

    A basic latent class model is the aspect model (Hofmann, 1999). Introducing a latent class variable zV to model the statistical relation between an item xA and a customer yU, the conditional probability P(x ǀ y) of a latent class model is defined as follows:

    P x y = z V P x z P z y ,
    (1)

    where the latent variable z takes a discrete value expressing a latent class on V = {v1, v2, L , vz} . In this model, the conditional probabilities P(x ǀ z) and P(z ǀ y) are the parameters to be estimated by a set of training data. This model represents the purchase probability of each item xA by each user yU and does not contain the information about the probability of user P(y). Rewriting the model by using the Bayes rule, the following model is given:

    P , y = z V P x z P y z P z .
    (2)

    This expression gives the form of a joint probability of xA and yU, so that the log likelihood function given the training data (x1, y1), (x2, y2 ), L , (xn , yn ) can be directly expressed as

    L = i = 1 n log z = V P x i z P y i z P z .
    (3)

    This formulation of a latent class model is the aspect model proposed by Hofmann. The aspect model is also called the probabilistic latent semantic indexing (PLSI) model to represent a document-word statistical structure. The graphical model of the aspect model is shown in Figure 1.

    The parameters of the aspect model, P(x ǀ z), P( y ǀ z), and P(z), can be estimated from the training data set by applying the EM algorithm (Dempster et al., 1977; Mc- Lachlan and Krishnan, 2007). The procedure of the Expectation– maximization algorithm (EM algorithm) for the aspect model is shown in Appendix A.

    Many types of modified aspect models have been proposed. For the application to recommender systems, several models predicting users’ ratings of each item have been proposed. The FMM is one of the most basic latent class models to predict users’ ratings (Si and Jin, 2003). In FMM, the two independent latent classes for users and items are introduced. However, the purchasing and browsing history data cannot be treated in FMM because the prediction of users’ rating is the purpose. In order to estimate the parameters of FMM with high accuracy, a modified learning algorithm using both purchasing and browsing history data is effective (Oi et al., 2015). Suzuki et al. (2014) proposed a recommendation logic considering both predicted purchase probability and predicted ratings based on FMM.

    Though many kinds of latent class models have been proposed for the purpose of collaborative filtering (see Hofmann and Puzicha, 1999; Hofmann, 2004; Si and Jin, 2003; Jin et al., 2003; Magidson and Vermunt, 2002; Langseth and Nielsen, 2011; Jin et al., 2006; Sitkrongwong et al., 2013; Suzuki et al., 2014), there is no model to directly represent the purchasing and browsing actions in EC sites for marketing purposes. In order to increase the estimation accuracy of the FMM, the modified learning algorithm using both purchasing and browsing history data was proposed and its effectiveness was clarified by Oi et al. (2015). In this case, the browsing history data is used only for learning the parameters of FMM. For the purpose of clustering by a latent class model, both browsing and purchasing activities should be directly represented in the model.

    2.4.Proposed Latent Class Model to Represent Both Purchasing and Browsing Activities

    The proposed model is a way to make use of the browsing history data in addition to the purchasing history data. There are two main reasons to use the data of both purchasing and browsing activities:

    • (1) The browsing activity of each customer is important to clarify the characteristics of each customer. Because customers browse product items depending on their own preferences, the browsing history data is valuable for making customer clusters reflecting user preferences. Moreover, more detailed analysis of customer characteristics can be realized by the combination of characteristics of both browsing and purchasing activities.

    • (2) Compared with the purchasing history data, the size of the browsing activity data is much larger. From the viewpoint of the accuracy caused by the sample size, it is useful to make use of both data of purchasing and browsing activities.

    In order to treat both purchasing and browsing activities, we define the two-dimensional vector w = (w1, w2 ). Here, w1W1 = {0, 1, 2, L , R1} is the number of purchasing actions, and w2W2 = {0, 1, 2, L , R2} is that of browsing actions.

    On the basis of the original idea of the aspect model, the following model is a simple expansion:

    P x y w z = P z P x z P y z P w z .
    (4)

    However, the interpretation of the latent class is difficult for the purpose of marketing analysis, though both latent clusters should be analyzed for marketing purposes. Therefore, the latent class of item x and that of user y are introduced independently in the same way as with FMM. Letting the latent class of item x be z_x and that of user y be z_y, the following latent class model is proposed:

    P x y w = z x V x z y V y P z x P z y P y z y P x z x P w z x , z y ,
    (5)

    where V x = v 1 x , v 2 x , L , v z x x and V y = v 1 y , v 2 y , L , v z x y are the sets of the latent classes of items and users, respectively. The probability model of the complete data including the latent classes is given by

    P , , , z x z y = P z x P z y P x z x P y z y P w z x , z y ,
    (6)

    where xA, yU, wW1 ×W2, zx ∈Vx , and zy ∈Vy. The components of Eq. (11) are defined as follows:

    • (1) P(zx ) is the multinomial distribution on Vx.

    • (2) P(zy ) is the multinomial distribution on Vy.

    • (3) P(x ǀ zx ) is the multinomial distribution on A.

    • (4) P( y ǀ zy ) is the multinomial distribution on U.

    • (5) P(w ǀ zx , zy ) is the multinomial distribution on W =W1 ×W2.

    That is, this model assumes the two latent classes for users and product items, and w follows the conditional multinomial distribution P(w ǀ zx , zy ).

    It is not a novelty point to assume two different latent classes for items and users. The FMM model proposed by Si and Jin (2003) assumes the two latent class variables of items and users independently. This assumption is reasonable in the field of marketing science. However, the FMM is a model proposed for the prediction of users’ rating values. Therefore, the proposed model is different from the probability model of the FMM.

    The graphical models of FMM and the proposed model are shown in Figure 2 and Figure 3. The structure of the graphical model of our proposal is similar to that of FMM because both latent classes of users and items are supposed.

    Because the probability model of FMM is given by

    P , , , z x z y = P z x P z y P x z x P y z y P x z x , z y ,
    (7)

    where r is a rating value of a user to an item, the equations of the probability model are also similar. However, the meanings of P(x ǀ zx ) and P( y ǀ zy ) are different from each other. For FMM, the meanings of P(x ǀ zx ) and P( y ǀ zy ) are interpreted as follows:

    • (1) P(x ǀ zx ) is the probability that the item x belonging to the latent class zx is given a rating value (by some user).

    • (2) P( y ǀ zy ) is the probability that the user y belonging to the latent class zy gives a rating (to some item).

    On the other hand, the meanings of P(x ǀ zx ) and P(y ǀ zy ) of the proposed model are interpreted as follows:

    • (1) P(x ǀ zx ) is the probability that the item x belonging to the latent class zx is purchased or browsed (by some user).

    • (2) P(y ǀ zy ) is the probability that the user y belonging to the latent class zy purchases or browses (some item).

    On the condition that a user purchases or browses an item, the probability that the user y purchases the item x is given by

    P x , y , w 1 0 = z x z y w w 1 0 p x , y , w , z x , zy ,

    and the probability that the user y browses the item x is given by

    P x , y , w 2 0 = z x z y w w 2 0 p x , y , w , z x , zy ,

    As shown in the preceding discussion, there are some differences in the interpretations of FMM and the proposed model. The FMM was introduced with the motivation to model the multivalued rating for each combination (x, y). The proposed model can represent the case where there are different meanings of co-occurrence of x and y. That is, there are two meanings, purchasing activity and browsing activity. Obviously, our proposed model can be generalized to represent more actions, such as “browsing,” “searching,” “purchasing,” and “bookmarking.” If the users’ activities on an EC site are these four actions, we may construct a four-dimensional vector w whose elements are the numbers of these actions.

    The probability of the i-th complete data (xi , yi , wi , z i x , z i y ) is given by

    P x , y , w , z i x z i y = P z i x P z i y P x i z i x P y i z i y P w i z i x , z i y ,
    (8)

    where xiΑ, yiU, wiW, z i x Vx and z i y Vy Because the latent classes z i x and z i y cannot be observed, the parameters P(zx ), P(zy ), P(x ǀ zx ), P( y ǀ zy ), and P(wǀ zx , zy ) should be estimated by the EM algorithm. Here, the EM algorithm is formulated with the observed data (xi , yi , wi ).

    [E-Step]

    P % z x , z y x i , y i , w i = P x i , y i , w i , z x , z y z x z y P x i , y i , w i , z x , z y ,
    (9)
    P % z x x i , y i , w i = x y P % z x , z y x i , y i , w i
    (10)
    P % z y x i , y i , w i = x y P % z x , z y x i , y i , w i .
    (11)

    [M-Step]

    P z x , z y = 1 n i = 1 n P % z x , z y x i , y i , w i ,
    (12)
    P z x = z y V y P z x , z y
    (13)
    P z y = z x V x P z x , z y ,
    (14)
    P x z x = 1 nP z x i = 1 n δ x i = x P % z x x i , y i , w i ,
    (15)
    P y z y = 1 nP z y i = 1 n δ y i = y P % z y x i , y i , w i ,
    (16)
    P w z x , z y = 1 nP z x , z y i = 1 n δ w i = w P % z x , z y x i , y i , w i ,
    (17)

    For the derivation of the EM algorithm, see Appendix B.

    3.CASE STUDY

    3.1.Data and Analysis Policy

    In this study, we demonstrate the analysis by applying the proposed model for the data given by the 2013 data analysis competition of the Joint Association Study Group of Management Science in Japan (2014). These data are composed of the purchasing and browsing histories on an apparel EC site. In this case, the number of users is 99,924, and that of product items is 1,150,443. The purchasing and browsing data from September 1, 2011, to March 31, 2013, are used for this analysis. Usually, the size of the purchasing history is relatively small for the purpose of estimation of users’ preferences to the immense number of items, but the size of the browsing data is relatively large. In this case, the number of purchasing actions of all users in this period was 707,857, and the number of browsing actions was 37,278,907. In the analysis, the browsing history is also valuable log data expressing a tendency of users’ actions and preferences. Because the browsing activity is conducted by users on the basis of their interests and preferences, and the size of the browsing history is much larger than that of the purchasing history, the browsing history data is more valuable for building the model. Therefore, we consider the clustering of items and users by using both purchasing and browsing history data. Such clustering becomes possible by applying the proposed latent class model in Section 2.4.

    After the clustering, it is effective analysis to clarify the characteristics of the representative attributes of each given cluster. However, the numbers of attributes of users and items are large and it is difficult to find distinctive features by repeating stratifications by hand. If the relation between users’ attributes and given clusters can be analyzed by a machine learning technique, such a method provides a reasonable and easy way.

    On the basis of the preceding discussion, we analyze the data by the following two steps in order to analyze the relation between users’ attributes and their tendency of purchasing and browsing.

    • (1) The items and users are clustered respectively through both purchasing and browsing history data by applying the proposed latent class model.

    • (2) The relation between the given clusters and the attributes of items and users are analyzed by applying the decision tree classifier.

    3.2.Learning of Proposed Latent Class Model

    The browsing and purchasing histories, and the attributes of product items and users, are saved in tables separately in the database. Therefore, we should create a data matrix from the raw data for learning the latent class model. The image of the data structure for training the model is shown in Table 1.

    In the learning phase, the data whose frequencies of purchasing and browsing are both 0 are not used. The multinomial distribution is assumed in the proposed latent class model, so that the frequencies of purchasing and browsing are quantized. Regarding the frequency of purchasing data, all frequencies over 4 are transformed to 4. The frequencies of browsing are quantized to 14 levels. That is, R1 = 4 and R2 =14.

    In order to analyze the characteristics of good customers and good product items, the numbers of the latent class are set as 2, such that zx ∈{0, 1} and zy ∈{0, 1}. We can make four clusters by the combination (zx , zy ): (0, 0), (0, 1), (1, 0), and (1, 1). After the learning phase, the characteristics of each cluster are clarified by the conditional probability P(w ǀ zx , zy ). Figure 4 shows an example of the cluster (zx = 0, zy = 0).

    From Figure 4 showing the probabilities P(wǀzx = 0, zy = 0) of the cluster (0, 0), we find out that the users belonging to the latent class zy = 0 tend to browse the item in the latent class zx = 0 a few times, but they do not tend to purchase it.

    As shown in Figure 4, the proposed model can treat both browsing and purchasing events. Therefore, the clusters can be characterized by the patterns of browsing and purchasing frequencies. This is a desirable characteristic of the proposed model in practice.

    Figure 5 shows a comparison of the same figures between four clusters: (zx = 0, zy = 0), (zx =1, zy = 0), (zx = 0, zy =1), and (zx =1, zy =1). The probability of each cluster P(zx , zy ) and the purchase probability P(w1 ≥1) are shown in Table 2 and Table 3.

    From these results, we learn the following facts.

    • a) When the user latent class zy is fixed, the purchase probability of item latent class zx =1 is larger than that of zx = 0.

    • b) When the item latent class zx is fixed, the purchase probability of the latent item class zy = 0 is larger than that of zy =1.

    From these results, the clusters from the viewpoints of “good” or “others” are obtained. Here, “good” means that the purchase probability is relatively high. Conversely, “others” means that the purchase probability is relatively lower than that of “good.” Therefore, the matrix of clusters by the “good” and the “other” customers, and the “good” and the “other” items, is shown in Table 4.

    Through the proposed latent class model, the “good” and the “other” clusters can be extracted. The attributes of product items and users are not used for the clustering. If the factors to distinguish “good” or “others” are easily clarified, it is useful for marketing research.

    3.3.Analysis by Decision Tree Model

    In this section, the factors to distinguish “good” from “other” are analyzed. In this study, we formulated a classification problem of the latent class based on the attributes of items and users. If the classification rule is learned from the training data, then the relation between the latent class and the attributes is modeled. We apply the decision tree model with the CART learning algorithm (Breiman et al. 1984). The decision tree model has an advantage in that an analyst can easily interpret the model structure.

    3.3.1.Analysis for Product Items

    First, the results of the analysis for item clusters are shown. For the learning of the decision tree, the following attributes of product items are used. The number of broad categories is 26, that of subcategories is 216, that of shops is 535, that of brand is 5,456, and that of zone is 35. The code numbers are used for the attributes of items in Table 5. Using the item table, the category name can be known in practice. Examples of the broad item categories are “Bags,” “TOPS,” “Shoes,” “Pants,” and “Skirt.” Examples of subcategories for “TOPS” are “Tank top,” “Shirt Blouse,” “T-Shirt,” “Parka (Hooded Sweatshirt),” and “Cardigan.” Table 5 shows an example of the item data structure.

    In order to clarify the performance of CART, the classification tree is learned by the set of 800,000 training samples, and the error rate for the test data with 350,000 samples is evaluated. The error rate of CART for different numbers of nodes is shown in Figure 6.

    From this result, the error rate converges to approximately 11% when increasing the number of nodes. The given classifier can classify the item to “good” or “others” with approximately an 11% error rate. When a new product item is added, we can predict the latent class of this item by using its attributes.

    An example for the case where the number of nodes is 11 is shown in Figure 7.

    The error rate for test data in this case was 22.8%. The code number “111” of the broad category is “Onepiece dress.” The customers who tend to purchase onepiece dresses may not become good customers.

    By the analysis based on CART, we found the result that the “Zone” and “Shop” are selected on the early stage of branch making. This fact means that the “Zone” and “Shop” are more important than “Broad category” or “Subcategory.” The items of popular shops are being purchased with high frequencies. There is a possibility that the users are narrowing down an item in their favorite shops.

    3.3.2.Analysis for Users

    Next, the results of the analysis for user clusters are shown. For the learning of decision tree, the attributes of users in Table 6 are used.

    In order to clarify the performance of CART, the classification tree is learned by the set of 70,000 training samples, and the error rate for the test data with 27,000 samples is evaluated. The error rate of CART for different numbers of nodes is shown in Figure 8.

    From this result, the error rate is not improved by increasing the node number. The tree when the number of nodes is 3 is shown in Figure 9.

    The error rate for test data in this case was 11.3%. That is, the user latent class can be explained by the attribute “Sex.” The rate of male and female in each latent user class is shown in Table 7.

    Females tend to become good customers, but most male users are not good customers. The reason for this result may be the target of the web design. Because this EC site is focused on fashions, the web design may be more attractive to women customers.

    3.4.Discussion

    From the analysis based on CART, we can discuss the necessary strategies of the EC site.

    Regarding the product items, the “Zone” and “Shop” were more important than “Broad category” or “Subcategory” of items. There are several ways for a user to search an item in this EC site. The users can search an item through the links of “Broad category” and “Subcategory” of items. However, if a user clicks the link of “One-piece dress,” then a large number of one-piece dresses will be listed. It may be impossible for users to find the best one from a list with a large number of items. It is necessary to build a strategy to raise the sales of the ordinary shops (i.e., other than the popular shops).

    For the user latent cluster, females tend to become good customers, but most male users are not good customers. The construction and design of web pages that are attractive to male customers may be different from those to females. If the present web design is modified to be attractive to males, such a design may not be preferred by females. It may be better to build two different top pages, for males and females. The recommended product items and information can be customized separately for males and females. In order to increase the product items for males, a different strategy may be effective for the different target. This EC site already has good female customers who are purchasing many items. It is an effective way to promote gift items for a boyfriend or a husband and to expand the web page to have women purchase products for men as gifts. For example, the function to choose a lapping may be important for gift items.

    4.CONCLUSION

    This paper proposes a new latent model to analyze both purchasing and browsing histories efficiently. By using the proposed latent class model, customer clustering was conducted and the clusters of good customers and good product items were extracted. Moreover, the relations between these clusters and attributes of items and users were analyzed by the decision tree model. An example of data analysis on an EC site is demonstrated. Through the proposed model and approach of our analysis, new findings are extracted from the data of purchasing and browsing histories.

    Although the latent class model was constructed for the purpose of clustering and analyzing the characteristics of good items and good customers, the other types of latent class models expressing both purchasing and browsing actions may be useful for other purposes. For example, a model for recommendation is proposed by Fujiwara et al. (2014). The relation with such other extensions should be discussed as a future work. Moreover, the idea of Bayesian statistics is sometimes effective in the field of machine learning and data analysis, so that a combination with the Bayesian model can realize a more exquisite model. The Bayesian estimation of the parameters can be introduced for our proposed model. These improvements are also planned for future works.

    Figure

    IEMS-14-335_F1.gif

    Graphical representation of the aspect model.

    IEMS-14-335_F2.gif

    Graphical representation of FMM (Si and Jin, 2003).

    IEMS-14-335_F3.gif

    Graphical representation of the proposed model.

    IEMS-14-335_F4.gif

    Probabilities P(w ǀ zx = 0, zy = 0).

    IEMS-14-335_F5.gif

    Result of clustering by applying the proposed latent class model.

    IEMS-14-335_F6.gif

    Error rate of item class for test data.

    IEMS-14-335_F7.gif

    CART for item when the number of nodes is 11

    IEMS-14-335_F8.gif

    Error rate of user class for test data.

    IEMS-14-335_F9.gif

    CART for user when the number of nodes is 3.

    Table

    Data structure

    Belonging probabilities P(zx , zy )

    Purchasing probabilities P(w1 ≥1)

    Cluster matrix

    Data of item cluster analysis

    Data of user cluster analysis

    The rate of sex in each latent user class

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