# Credit Card-Not-Present Fraud Detection and Prevention Using Big Data Analytics Algorithms
## 3 Credit Card-Not-Present Fraud Detection and Prevention Method
### Fraud Detection Process
#### 3.1.1 Dimensionality Feature Reduction
Figure 10: (**a**) Learning and validation curves for logistic regression, (**b**) Learning and validating curves for k-nears neighbors learning algorithm, (**c**) Learning and validation curves for support vector learning algorithm, and (**d**) Learning and validation curves for decision tree classifier algorithm. ### Statistical Performance Metrics

In statistical implication, model selection is typically performed using statistical performance metrics. The model that performs the best in terms of a chosen performance criterion is ultimately chosen from among a number of models that were trained with various sets of parameters and hyper-parameters. #### 4.4.1 Root Mean Square Error

It is an average squared deviation of forecasting from real amounts. Therefore, RMSE can be obtained as:

\[R_{sr}=\sqrt{\frac{\sum i(A_{v}-P_{v})^{2}}{d_{p}}} \tag{31}\]

where \(R_{sr}\) is the root mean square error, \(A_{v}\) is the actual values, \(P_{v}\) is the prediction value, and \(d_{p}\) is data points. Figure 11: (**a**) Fraud detection accuracy with 1% fraud proportion, (**b**) fraud detection accuracy with 2% fraud proportion, (**c**) fraud detection accuracy with 5% fraud proportion, and (**d**) fraud prevention accuracy with 1–5% fraud proportions. #### 4.4.2 Relative Root Mean Squared Error

Relative root mean squared error (RRMSE) is frequently expressed as a percentage and is normalized by the mean of the real amounts. RRMSE smaller values are preferred. The RRMSE \(R_{\gamma}\) can be calculated as:

Figure 4:0

#### 4.4.3 Mean Bias Error

The Mean Bias Error (MBE), which measures model error, is typically not used because high individual predicted values can also result in a low MBE. In order to determine whether any actions are required to rectify the model bias, the MBE is principally used to calculate the average bias in the model. The average bias in the estimation is captured by the MBE. Data from datasets are overestimated when there is a constructive bias or error in a variable, and vice versa. The average bias in the forecasting is measured using the MBE. The MBE \(M_{be}\) can be measured as:

Figure 4:1

#### 4.4.4 Mean Directional Accuracy

A metric to determine the likelihood that the prediction model can identify the proper direction of time series is provided by mean directional accuracy (MDA). Studies in macroeconomics and economics frequently employ this metric. The MDA \(A_{md}\) can be determined as:

Figure 4:2

where \(P_{\gamma(t)}\) and \(A_{\gamma(t)}\) are the prediction and actual values at the time \(t\), \(\mu\) is the indicator function, and \(sign\) represents the sign function. The statistical performance metrics (MDA, MBE, RRMSE, RMSE) are used to determine the performance of the proposed CCFDP and also compared with contending approaches CATCHM [27], LSTM-RNN [28], CSLMLE [29], CCFDM [30] enhance secure deep learning (ESDL) algorithm [31], Intelligent two-level credit card fraud detection (ITCCFD) [32], and Bridge to graph (BTG) [33]. Based on the experimental results, the performance of the proposed CCFDP is observed better than the contending approaches that are shown in Figure 12a-d and Figure 4:3 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **RMSE** & **RRMSE** & **MBE** & **MDA** \\ \hline CATCHM [27] & 0.068\% & 9.48\% & 0.294\% & 99.05\% \\ \hline LSTM-RNN [28] & 0.078\% & 9.77\% & 0.361\% & 99.24\% \\ \hline CSLMLE [29] & 0.076\% & 8.61\% & 0.122\% & 99.11\% \\ \hline CCFDM [30] & 0.095\% & 10.76\% & 0.554\% & 99.87\% \\ \hline ESDL [31] & 0.072\% & 9.62\% & 0.321\% & 99.45\% \\ \hline ITCCFD [32] & 0.059\% & 8.96\% & 0.192\% & 99.18\% \\ \hline BTG [33]. & 0.079\% & 10.38\% & 0.472\% & 99.54\% \\ \hline Proposed CCFDP & 0.056\% & 8.39\% & 0.078\% & 99.92\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The comparison of the proposed CCFDP with contending approaches using statistical metrics. ## 5 Discussion of Results

The proposed LRL is integrated with the proposed CCFDP which considerably enhances detection accuracy.