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7. Conclusion
Because of the nature of competitive learning, the GHSOM, an unsupervised neural networks extended from the SOM, can work as a regularity detector that is supposed to help discover statistically salient features of the sample population (Hogan et al., 2008).
With the spatial correspondent hypotheses, this study presents a DSS architecture with four phases based on the proposed dual approach for FFD decision support, in which two GHSOMs (i.e., fraud samples are used to generate FT and non-fraud samples are used to generate NFT) are generated in the training phase. In the modeling phase, for each leaf node of FT, a feature extraction mechanism including the feature-extracting module and pattern-extracting module is developed to provide the associated fraud related features, and the extracted features will be used as a part of the evaluation for any risky investigated sample. The classification rules are formed to help identify fraud cases through applying the adaptive classification rules into each pair of fraud and non-fraud subgroups from FT and NFT. In the analyzing phase, the dominant classification rule is applied to examine the investigated samples. For the investigated samples which have been identified fraud, the relevant fraud categories and variables are retrieved and integrated in the decision support phase. All the provided information is helpful for the decision making process of FFD.
Unlike the traditional approach applying the SOM in FFD (Carlos, 1996) which uses all training samples to generate one SOM, our proposed DSS architecture takes advantage of being able to generate two GHSOMs (FT and NFT), in each of which two spatial hypotheses — for each pair of leaf nodes from FT and NFT, the fraud (or non-fraud) samples are cluster around their counterparts— are set to create the candidate classification rules. That is, using the statistic information among samples from different GHSOMs helps respectively generate the non-fraud-central and fraud-central rules. These two rules are tuned via inputting all samples to determine the optimal discrimination boundary of each candidate classification rule within each pair of leaf nodes from NFT and FT. This study derives the optimization technique that renders adjustable and effective rules for classifying fraud and non-fraud samples. The decision makers can objectively set their weightings of type I and type II errors. The candidate classification rule that dominates another is adopted as the classification rule in the following analyzing phase. The dominance of the non-fraud-central rule leads to
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an implication that most of fraud samples cluster around the non-fraud counterpart, meanwhile the dominance of fraud-central rule leads to an implication that most of non-fraud samples cluster around the fraud counterpart.
To the best of our knowledge, this is the first work that employs the GHSOM to provide topological insights of high-dimensional inputs in addition to hierarchical features. It is worth noting that the implementation of the DSS architecture based on the proposed dual approach is beyond the traditional unsupervised learning approach for FFD through developing a more delicate classifier that can reveal the spatial relationship among fraud and non-fraud subgroups, and the proposed feature extraction mechanism provides more information to represent the potential fraud behaviors for any suspected investigated sample, as a result, support the practical FFD decision making process.
Our preliminary result on FFR experiment confirms the spatial relationship among fraud and non-fraud financial statements, and has better classification performance than the SVM, SOM+LDA, GHSOM+LDA, SOM, BPNN and DT methods. Therefore, for cases with the regularity of the proposed two topological relationships among fraud and non-fraud samples, the implemented DSS architecture based on the proposed dual approach can perform well; furthermore, compared with conventional methods for FFD, the feature extracting results also add more fraud-related characteristics for the investigated samples which are identified fraud.
The limitations of this study would be: (1) compared with other FFD scenarios, the sample size for the FFR issue is limited, (2) subjective parameter setting of the GHSOM, (3) the fraud patterns are various depend on the focused FFD scenario and the results of the pattern-extracting module need to be verified by the domain experts, and (4) the proposed DSS architecture does not evaluated or refined practically until a system prototype is actually being developed.
Future works are suggested as follows: (1) derive the theoretical justification of the rule-forming module in the modeling phase, (2) improve the discrimination boundary setting in the rule-forming module with more sensitivity via an enhanced optimization approach for developing the classification rules, or try other good classifiers, (3) use other clustering methods in the clustering module and compare the results of classifying module in terms of the classification performance and the dominate classification rule derived from which spatial hypothesis, (4) improve the
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pattern-extracting module with systematic tools, and (5) conduct experiments on other FFD applications.
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Appendix
The overall FFR fraud categories extracted from each leaf node of FT are summarized in Table A1. The common FFR fraud categories within each leaf node are marked with * in the column.
Table A1. Common FFR fraud categories within all leaf nodes of FT.
leaf node #11 *FC1 FC2 FC3 FC4 FC5 *FC6 FC7 *FC8 FC9 FC10 (code) (year)
2505 1998 ●
2529 1998 ● ●
8716 1999 ● ●
2334 1999 ● ●
3039 2004 ●
1601 1998 ●
1221 2002 ● ● ●
1221 2003 ● ● ●
2014 2003 ● ●
5901 1997 ● ●
5901 1998 ● ●
5901 1999 ● ●
leaf node #12-21 FC1 FC2 *FC3 FC4 FC5 FC6 FC7 FC8 FC9 FC10
5385 2001 ● ●
8713 1999 ●
1918 1998 ● ●
leaf node #12-22 *FC1 FC2 FC3 *FC4 FC5 *FC6 FC7 FC8 *FC9 FC10
2398 2001 ● ● ● ● ● ●
2398 1999 ● ● ● ● ● ●
2494 2002 ●
3001 2000 ● ●
3001 2001 ● ●
3001 1999 ● ●
5385 2000 ● ●
6145 2003 ● 6145 2004 ●
6250 2004 ● ● ●
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1602 1994 ● ● ● ●
leaf node #12-23 FC1 *FC2 FC3 *FC4 FC5 *FC6 FC7 *FC8 *FC9 FC10
8702 1994 ● ●
8702 1995 ● ●
5504 2000 ●
8710 1999 ●
8719 1997 ●
8701 1995 ● ●
8701 1996 ● ●
1602 1995 ● ● ● ●
1918 1996 ● ●
1918 1997 ● ●
2101 1997 ● ● ●
2613 1999 ● ●
2913 1996 ● ●
leaf node #12-24 *FC1 FC2 FC3 FC4 FC5 FC6 FC7 FC8 *FC9 FC10
4113 2004 ● ●
leaf node #13-21 FC1 FC2 FC3 FC4 FC5 FC6 *FC7 *FC8 FC9 FC10
8712 1998 ● ●
5503 2000 ● ● ●
8719 1998 ●
2014 2001 ● ●
2014 2002 ● ●
8717 1998 ● ●
leaf node #13-22 FC1 FC2 FC3 FC4 FC5 *FC6 *FC7 FC8 FC9 FC10
2553 1999 ● ●
8716 1998 ● ●
8188 2001 ●
8724 2000 ● ●
8724 1999 ● ●
2005 1999 ●
2019 2000 ●
2019 1999 ●
8711 1999 ● ● ●
leaf node #13-23 FC1 FC2 FC3 *FC4 FC5 FC6 *FC7 *FC8 FC9 FC10
8705 1998 ● ● ● ● ●
8714 1999 ● ●
8382 1998 ● ● ●
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8706 1998 ● ● ●
leaf node #13-24 FC1 FC2 FC3 FC4 FC5 FC6 FC7 *FC8 *FC9 FC10
1505 1998 ●
1505 1999 ●
8708 1998 ● ●
8708 1999 ● ●
2101 1998 ● ● ●
2101 1999 ● ● ●
leaf node #14-21 FC1 FC2 FC3 FC4 FC5 *FC6 FC7 *FC8 *FC9 FC10
5504 1999 ●
2328 1998 ● ● ●
2334 1998 ● ●
1505 1997 ●
5007 1998 ● ●
2614 1999 ● ● ● ● ●
1466 1998 ● ● ●
leaf node #14-22 *FC1 FC2 FC3 FC4 FC5 FC6 FC7 *FC8 FC9 FC10 2505 1997 ●
2328 1997 ● ● ●
2334 1997 ● ●
2350 1997 ●
2398 2000 ● ● ● ● ● ●
2490 2001 ● ●
1601 1997 ●
1602 1996 ● ● ● ●
leaf node #14-23 FC1 FC2 FC3 FC4 FC5 *FC6 *FC7 *FC8 FC9 FC10
2206 2000 ●
1436 1997 ●
1436 1998 ●
2553 1998 ● ●
1207 2000 ● ● ● ● ●
1207 1998 ● ● ● ● ●
1207 1999 ● ● ● ● ●
2005 1998 ●
2016 1997 ● ●
2016 1998 ● ●
2017 1996 ● ●
2017 1998 ● ●
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2019 1998 ●
8705 1997 ● ● ● ● ●
8708 1997 ● ●
8714 1997 ● ●
8714 1998 ● ●
9911 1998 ● ●
9801 2000 ● ● ● ● ●
9801 1998 ● ● ● ● ●
9801 1999 ● ● ● ● ●
leaf node #14-24 *FC1 FC2 FC3 *FC4 FC5 FC6 FC7 *FC8 FC9 FC10
2206 1999 ●
2350 1998 ●
2407 2002 ● ● ● ● ● ●
2407 2003 ● ● ● ● ● ●
2407 2004 ● ● ● ● ● ●
2490 2000 ● ●
2490 2002 ● ●
8295 1998 ● ●
1221 2001 ● ● ●
8723 1998 ● ● ●
2017 1997 ● ●
5007 1999 ● ●
Note: The common FFR fraud categories of each leaf node are marked with *.
Table A2 summarizes the commonly adopted FFR fraud categories of the testing samples identified as the fraud class in all leaf nodes of the FT. The code and year in the first two columns indicate the company SIC code and the year of financial statements. The common FFR fraud categories extracted from the feature-extracting module are marked in gray. The common FFR fraud categories within each leaf node are marked with * in the column.
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立 政 治 大 學
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N a tio na
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Table A2. Common FFR fraud categories of the testing samples.
leaf node #11 *FC1 FC2 FC3 FC4 FC5 FC6 FC7 *FC8 FC9 FC10
1606 2008 ● ●
2418 2006 ● ●
2418 2008 ● ●
4413 2005 ● ●
leaf node #12-22 *FC1 FC2 FC3 *FC4 FC5 FC6 FC7 FC8 FC9 FC10
3506 2003 ● ● ● ●
3506 2004 ● ● ● ●
6232 2006 ● 6232 2007 ●
6103 2008 ● ● ●
3079 2005 ● ●
5017 2003 ●
1606 2006 ● ●
leaf node #12-23 FC1 *FC2 FC3 FC4 FC5 *FC6 FC7 *FC8 FC9 FC10
3506 2002 ● ● ● ●
1532 2008 ● ● ● ●
5605 2002 ● ● ●
5605 2003 ● ● ●
5605 2004 ● ● ●
5605 2005 ● ● ●
leaf node #14-22 *FC1 FC2 FC3 FC4 FC5 FC6 FC7 *FC8 FC9 FC10 6232 2002 ●
6103 2004 ● ● ●
3350 2004 ●
2418 2004 ● ●
leaf node #14-24 *FC1 FC2 FC3 *FC4 FC5 FC6 FC7 *FC8 FC9 *FC10
6103 2005 ● ● ● ● ●
6103 2006 ● ● ● ● ●
2614 2008 ● ● ● ●
2614 2006 ● ● ● ●
2614 2007 ● ● ● ●
FC1: recording fictitious revenues; FC2: recording revenues prematurely;
FC3: no description/overstated about revenues; FC4: overstating existing assets;
FC5: recording fictitious assets or assets not owned; FC6: capitalizing items that should be expensed;
FC7: understatement of expenses/liabilities; FC8: misappropriation of assets;
FC9: inappropriate disclosure; FC10: other miscellaneous techniques.
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The identification performance of the FFR fraud categories are summarized in Table A3, in which the classification errors (type I error and type II error) are calculated.
Table A3. The identification performance of the FFR fraud categories.
leaf node
true predict fraud->
fraud
fraud->
non-fraudtrue predict non-fraud->
non-fraud
1,8 1,6,8 100.00% 0.00% 2,3,4,5,6 ,7,9,10
true predict fraud->
fraud
fraud->
non-fraudtrue predict non-fraud->
non-fraudtrue predict non-fraud->