تشخیص کلاهبرداری در قیمت گذاری در مراکز خرید آنلاین با استفاده از مدل مخلوط محدود

Although pricing fraud is an important issue for improving service quality of online shopping malls, research on automatic fraud detection has been limited. In this paper, we propose an unsupervised learning method based on a finite mixture model to identify pricing frauds. We consider two states, normal and fraud, for each item according to whether an item description is relevant to its price by utilizing the known number of item clusters. Two states of an observed item are modeled as hidden variables, and the proposed models estimate the state by using an expectation maximization (EM) algorithm. Subsequently, we suggest a special case of the proposed model, which is applicable when the number of item clusters is unknown. The experiment results show that the proposed models are more effective in identifying pricing frauds than the existing outlier detection methods. Furthermore, it is presented that utilizing the number of clusters is helpful in facilitating the improvement of pricing fraud detection performances.

Contemporary online shopping services allow comparison of shopping items in terms of their prices, and have increased price sensitivity of consumers (Alba et al., 1997 and Bakos, 1997). This phenomenon leads to severe competition among sellers since items that are not attractively priced receive less attention from customers. Accordingly, sellers are compelled to offer items at lower prices than their competitors in order to catch the eyes of customers (Iyer and Pazgal, 2003 and Kocas, 2002). Such severe competition often causes sellers to set inappropriate prices on their items, resulting in pricing fraud that attempts to deceive customers by offering seemingly lower prices on items as compared to normal market prices (Gregg and Scott 2006). Recent social commerce and online auction services such as eBay exacerbate the problem, since sellers are able to sell their items without being investigated for possible pricing fraud in those types of services (Dekleva, 2000, Chua and Wareham, 2004 and Gavish and Tucci, 2006). In practice, however, service providers still heavily rely on manual investigation for identifying pricing frauds, which is costly and time consuming (Zhang et al. 2012). Pricing fraud has been usually detected through examining some fraudulent seller behaviors reported in online auctions such as misrepresentation (Ba et al., 2003 and Zacharia et al., 2000), fee stacking (Chua and Wareham 2004), and price shilling (Kauffman and Wood, 2005 and Dong et al., 2012), which result in the irrelevance between an item’s price and its description. Gregg and Scott, 2006 and Gregg and Scott, 2008 reported that these behaviors account for approximately 27.5–32.3% of fraudulent activities in online auction services. Regardless of whether customers actually purchase fraudulently priced items, such items become a subject of major concern for both customers and service providers because pricing fraud significantly impairs service quality. Customers attempting to purchase a fraud item may be eventually required to pay additional charges or become embarrassed due to the difference between an item’s final price including additional charges and the initial price presented by a seller. On the other hand, eliminating pricing fraud is crucial for a service provider to improve customer trust, since customers repeatedly encountering pricing fraud become distrustful of item prices, leading to a decreased number of returning customers and lower turnover eventually (Gavish and Tucci 2008). As an example, we consider the item description of a camera package, “Cannon EOS 600D 1855 mm Genuine Full Package”, priced at 790,000 KRW (Korean won) from an online shopping service, Auction (http://www.auction.co.kr). This item would appeal to customers since its price is quite low compared to those of other items with the same purchase options. However, during checkout, the customer is requested to pay an additional 230,000 KRW for the camera lens, originally presented as an included component in the item description. With this extra charge, the item loses its price advantage. Identification of pricing fraud is a challenging problem owing to the following two major characteristics: First, actual data on fraudulently priced items are often unavailable due to the significant time and cost required for manual fraud detection, and this is particularly true for small and medium-sized online shopping malls. Second, item price changes dynamically due to the frequent price updates of shopping items by sellers (Nakamura, 1999 and Tang and Xing, 2001). In the dataset considered in this paper, about 10% of item prices were updated daily, and an item price changed at least every five days, implying that normal price range of an item varies over time. Accordingly, the existing fraud detection approaches based on the notion of similarities against the previously observed normal and fraud items cannot be directly applied to the considered pricing fraud problem. Specifically, while supervised approaches such as neural networks (Aleskerov et al., 1997 and Dorronsoro et al., 1997) and rule-based systems (Brause et al. 1999) yielded satisfactory results in various applications including the fraud detection, they are not applicable to the detection of pricing fraud because of their reliance on historical data to estimate model parameters. Moreover, unsupervised approaches such as clustering based methods (Bolton and Hand 2001) and outlier detection methods (Eskin, 2010, Liu et al., 2003, Sabuncu et al., 2010 and Yang et al., 2009) may not be effective for the considered problem, since they cannot accommodate the fact that the relevance between the item features such as item description and price varies depending on whether a seller’s behavior is fraudulent or not. Motivated by the challenges mentioned above, we propose novel models designed to automatically detect pricing fraud of items in online shopping malls by considering the relevance among the item features depending on a seller’s behavior. The idea of fraud identification based on the dependency among features is not new and was originally proposed by Huang et al., 2003 and Hu and Panda, 2005 in which cross-feature analysis was proposed to examine whether or not the features of instances are relevant to each other by using the frauds detected previously. Our approach utilizes this cross-feature analysis, but does not require actual fraud data for constructing a model. The proposed models base on a finite mixture model widely known for its effectiveness and flexibility (McLachlan and Peel 2000). In contrast to the supervised learning methods, such as support vector machines and decision trees, the finite mixture model is applicable even when labeled data are not available, and allows explicit modeling of the dependency between item description and price (Everitt and Hand 1981). In the proposed approach, two states, namely normal and fraud states, are defined for each item in a set of observed items according to a seller’s pricing behavior. These two item states are modeled by using three hidden variables that indicate the corresponding cluster of an item description, the cluster of item price, and the dependency between them. The proposed models then estimate the item state based on the dependency between the item description and price, and they determine the clusters of the item description and the price for each item through investigating the possible combinations of those clusters. The proposed approach further attempts to more precisely infer fraudulent items by utilizing the known number of item clusters. An item cluster represents a subset of items in an itemset, a set of items from the same item type, specified based on available purchase options. The number of item clusters for each itemset can be obtained easily from many online shopping malls, unlike the other information such as sellers’ reputation data and labels indicating whether or not an item is fraudulently priced, which are costly to obtain. For instance, USB drive products are usually grouped into multiple item clusters in terms of their capacity: “4 GB”, “8 GB”, and “16 GB” in online shopping malls. The paper is organized as follows. Section 2 reviews related studies to this research. In Section 3, we define the proposed model, called pricing fraud detection model with the known number of item clusters (PDMC), and we also examine its special case, called pricing fraud detection model (PDM). In Section 4, we present the experiment results to show the effectiveness of the proposed models by using a real-world dataset. In Section 5, we discuss the implications and limitations of the proposed models. Finally, the conclusions are presented in Section 6.

In order to detect fraudulent items automatically without the costly requirement for labeled items, we have presented two novel methods based on a finite mixture model. Two states, normal and fraud, for the observed items were introduced, and modeled by using three sets of hidden variables. We modeled the dependency between the description and the price of an item by considering the possible combinations of the item description and price clusters according to item clusters. Furthermore, we also proposed a special case of the proposed approach that accommodates the scenario in which the number of item clusters for an itemset is not known. We used a real-world dataset to evaluate the effectiveness of the proposed models and compared them to existing outlier detection methods. Our results show that the proposed models are more effective than the outlier detection methods. It is expected that the proposed approaches will significantly reduce the cost of pricing fraud detection in various online shopping services, including small- and medium-sized malls, obviating the need for manual detection or proprietary systems. The proposed models also have a room for further enhancement by utilizing historical logs to more accurately infer seller’s fraudulent behaviors, and this will be the subject of our future work.