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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
1. Introduction
This study proposes a dual approach as a Decision Support System (DSS) architecture based on the Growing Hierarchical Self-Organizing Map (GHSOM) (Dittenbach et al., 2000; Dittenbach et al., 2002; Rauber et al., 2002), a type of unsupervised artificial neural networks (ANN), for the decision support in financial fraud detection (FFD). FFD involves distinguishing fraudulent financial data from authentic data, disclosing fraudulent behavior or activities, and enabling decision makers to develop appropriate strategies to decrease the impact of fraud (Lu and Wang, 2010). The decision for FFD can be aided by statistical methods such as the logistic regression, as well as data mining tools such as the ANN, in which the ANN has been widely used and plays an important role in FFD (Lu and Wang, 2010). Among the ANN applications in FFD, the Self-Organizing Map (SOM) (Kohonen, 1982) has been adopted in diagnosing bankruptcy (Carlos, 1996). The major advantage of the SOM is its great visualization capability of topological relationship among the high-dimensional inputs in the low-dimensional view. Other advantages are adaptive (i.e., the clustering can be redone if new training samples are set) and robust (i.e., the pattern recognition ability). There are numerous applications involving the SOM and the most widespread use is the identification and visualization of natural groupings in the sample data sets. However, the weaknesses of the SOM include its predefined and fixed topology size and its inability to provide the hierarchical relations among samples (Dittenbach et al., 2000).
An improvement of the SOM has been done by Dittenbach, Merkl and Rauber (2000). They developed the GHSOM which addresses the issue of fixed network architecture of the SOM through developing a multilayer hierarchical network structure. The flexible and hierarchical feature of the GHSOM generates delicate clustered subgroups with heterogeneous features, and makes it a powerful and versatile data mining tool. The GHSOM has been used in many fields such as the image recognition, web mining, text mining, and data mining (Dittenbach et al., 2000;
Schweighofer et al., 2001; Dittenbach et al., 2002; Rauber et al., 2002; Shih et al., 2008;
Zhang and Dai, 2009; Tsaih et al., 2009). It is worth of knowing that the GHSOM can be a useful clustering tool to do the pre-processing of feature extraction for a certain application field.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
In general, the GHSOM mainly takes the task of clustering and then visualizing the clustering results. To accomplish other purposes such as prediction or classification, the neural networks must be complemented with a statistical study of the available information (Serrano, 1996). However, this study finds that the development of the GHSOM into a classification model has been limited studied (Hsu et al., 2009; Lu and Wang, 2010; Guo et al., 2011). Besides, other than the hierarchical feature, the GHSOM studies have rarely provided the topological insight into high-dimensional inputs.
To better utilize the advantage of the GHSOM for the purpose of classification and feature extraction in helping FFD, this study pioneers a DSS architecture based on the proposed dual approach which helps extract the nature of the distinctive characteristics among different clustered groups generated by the GHSOM. This study develops an innovative way of observing the clustered data to form the optimal classification rule, and revealing more information regarding the relevant input variables and the potential fraud categories for the suspected samples as the knowledge base for facilitating FFD decision making.
This study examines the following topological relationships regarding high-dimensional inputs, of which there are two types: fraud and non-fraud, and matches the fraud counterpart of each non-fraud subgroup and vice versa. This study assumes that there is a certain spatial relationship among fraud and non-fraud samples.
The spatial hypothesis: The spatial distributions of fraud samples and their non-fraud counterparts are identical, and the spatial distributions of most fraud samples and their non-fraud counterparts are the same. Within each pair of clusters, either the fraud samples cluster around their non-fraud counterparts, or the non-fraud samples cluster around their fraud counterparts. If such a spatial relationship among fraud and non-fraud samples does exist, the associated classification rule can be set up to identify the fraud samples based on the correspondence of the fraud samples and their non-fraud counterparts and vice versa. Moreover, the proposed dual approach is data-driven. That is, the corresponding system modeling is performed via directly using the sampled data. Thus, different sampled data input to the proposed DSS architecture may result in distinctive DSSs. To practically utilize such a spatial relationship for identifying fraud cases and examine the applicability of the proposed
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
DSS architecture based on the dual approach, this study sets up the fraudulent financial reporting (FFR) experiment, a sub-field of FFD.
Specifically, the proposed DSS architecture contains four phases. In the training phase, the sampling and variable selection are done first, and then it adopts the hierarchal-topology mapping advantage of the GHSOM to build up two GHSOMs (named non-fraud tree, NFT, and fraud tree, FT) from two classes of training samples collected from the financial statements.
In the modeling phase, following the majority principle, the corresponsive FT leaf node for each NFT leaf node are identified using all (fraud and non-fraud) training samples. Then, each training sample is classified into these two GHSOMs to develop the discrimination boundaries according to the candidate classification rules. The candidate classification rules in this study involve a non-fraud-central rule and a fraud-central rule, which are tuned via inputting the clustered training samples to determine the optimal discrimination boundary within each leaf node of the FT and NFT. For the candidate classification rules, a decision maker can set up his/her preference for the weights of classification error (type I and type II error) that makes the developed classification rule more acceptable and domain specific. The dominant classification rule with the best classification performance is applied in the analyzing phase. Besides, this study involves a feature extraction mechanism with two modules, feature-extracting module and pattern-extracting module, in the modeling phase that focus on discovering the common features and patterns in each FT leaf node. For the features regarding the input variables, the principal component analysis (PCA) is applied to provide the associated principal components. For the patterns such as the FFR fraud categories, the corresponding verdict contents of the fraud samples are investigated to determine the associated FFR fraud categories.
In the analyzing phase, each investigated sample is classified into the winning leaf nodes of FT and NFT, and applies the dominant classification rule to determine whether this sample is fraud or not. In the decision support phase, for an investigated sample, the result of the analyzing phase is used to help the decision makers speculate its FFR potentiality and. If it is identified as fraud, the associated potential FFR behaviors will be retrieved. The released information of the implemented DSS architecture based on the proposed dual approach can help decision makers better identify FFR and interpret the distinctive FFR behaviors among the clustered groups,
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
comprehend the difference between fraud and non-fraud samples, and finally facilitate the real-world decision making.
In sum, the implementation of the DSS architecture based on the proposed dual approach can be leveraged both to justify the spatial hypothesis, and when the spatial hypothesis holds, to disclose the information that better supports FFD. The proposed DSS architecture based on the dual approach is expected to be potentially applicable to other similar scenarios, and is able to be implemented as a DSS that helps detect suspicious samples and at the same time provide their possible fraud categories beforehand.
There are four objectives of this study:
(1) Develop a DSS architecture based on the proposed dual approach that (a) adopt the GHSOM to separately cluster fraud training samples and non-fraud training samples; (b) set up the discriminant boundaries for each pair of leaf nodes following the candidate classification rules based on the proposed spatial hypotheses; (c) use the determined classification rule to classify unknown samples;
(d) observe whether spatial hypothesis holds and (d) illustrate the embedded information from the evaluation results including the extracted features and fraud patterns from the FT leaf nodes.
(2) Justify whether the implemented dual approach is capable of helping distinguish fraud and non-fraud samples.
(3) Compare the outcomes of our classification with other supervised or unsupervised learning methods.
(4) Provide implications regarding FFD decision support and research implications.
The rest of this dissertation is organized as follows. Chapter Two presents the literature reviews of the DSS, clustering methods, the GHSOM, PCA and FFR.
Chapter Three explains the design of the proposed dual approach in details. Chapter Four demonstrates the experimental results. Chapter Five provides the comparison against other methods and the discussion of experiment of results. The implications are shown in Chapter Six. Chapter Seven gives the final conclusion and future works.