# Fraud Detection Using Neural Networks: A Case Study of Income Tax
## 4 Results and Discussion
### Test Result  
For the performance evaluation of any classification model, the confusion matrix is the first and easiest way to use so as to compare the actual class with the predicted one, as well as compute the model's precision and recall. As it is seen on the below test confusion matrix Figure 3, more than 700 taxpayers were correctly predicted while 2 were predicted as non fraudulent when they were fraudulent, and 49 were predicted as fraudulent when they were not. From the test confusion matrix, the results look promising, despite some taxpayers being predicted as fraudulent even if they are not, the model is trustworthy as it captures almost all the fraudulent taxpayers, which is the main goal. Many other evaluation metrics have been used and the collective outcomes suggest that ANN would be a considerable  
Figure 2: Training and Validation loss vs. Training and Validation Accuracy. Through feature importance evaluation using VIANN, a number of features proved to be very important to the income model's accuracy, where the top 15 features based on their importance are as follows: The Customs Department (0.5447) was the most important, followed by the Domestic Department (0.3496), Time of Business (0.2799), Scale_Small (0.2636) and others. The importance values tend to vary as the model is re-run, but a small number of features shown in Table 3 are found to be very important in every run, which highlight their influence on the model. From the features in Table 3, the \"Department\" from which a taxpayer is registered is a big factor in whether the taxpayer is fraudulent or not. This variable shows that taxpayers who are doing cross-border businesses and those who are doing businesses domestically are all related to income tax fraud. The findings revealed that taxpayers who import and export goods and services are highly related to income tax fraud than those who are doing their businesses domestically. Moreover, the 'time of business' which shows how long a business has been operating from the time of its registration to the time of the audit, was revealed to be an important factor in income tax fraud. Followed by \"Scale\" of business, where small scale businesses are more likely to be involved in income tax fraud than Large Scale businesses. The description of a taxpayer or business variable as either non-individual (company) or individual is also among the important variable for income tax fraud. While the location of a business is also another factor to consider, this shows that businesses in Kigali City districts are more likely to be found in income tax fraud than other districts. The features related to the income tax fraud identified by this study are consistent with the ones revealed by the previous submitted paper on predicting tax fraud using different supervised machine learning models [40]. That submitted paper covered the dataset with all tax types and the cross-border businesses, small businesses and time of the business were amongst features that are related to tax fraud. Although more research is needed to delve deeply into the use of machine learning in tax fraud detection, this study has provided new insight into how tax fraud should be detected with minimal cost. Aside from demonstrating which characteristics are important when detecting fraud, the findings of this study are consistent with the previous study that compared different supervised machine learning models to a dataset with all tax types [40]. As [15] stated, neural networks not only distinguish between the fraudulent and non-fraudulent, but also compute the probability of one being fraudulent, which is useful in tax auditing and inspection so that tax auditing can be planned and focused on those with a high likelihood of being fraudulent or high risky departments like customs and small businesses.