# 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
Thus, the data foundation \(\Delta\gamma\) for the dataset can be defined as:

\[\Delta\gamma=(A_{s}\times S_{d})+\rho-A \tag{10}\]

where \(\rho\) is a mean, and \(S_{d}\) is a standard deviation. The matrix can be used to express the PCA is given by:

\[Q_{6}= \begin{bmatrix}Q_{1}\\ \cdot\\ \cdot\\ Q_{4}\end{bmatrix} = \begin{bmatrix}S_{1.1}&\cdots&S_{1.4}\\ \vdots&\ddots&\vdots\\ S_{4.1}&\cdots&S_{4.4}\end{bmatrix}\begin{bmatrix}P_{1}\\ \cdot\\ \cdot\\ P_{4}\end{bmatrix}  \tag{11}\]

where \(S\) is the transformation matrix, \(P\) is the vector of the original data, and \(Q\) is the vector of the main components. The eigenvectors that diagonalize the covariance matrix of the original bands are the coefficients of the transformation matrix \(S\). The accuracy of the principal component \(A_{pca}\) depends on the number of coefficients available \(c_{v}\) in each data point \(d_{p}\). \[A_{pca}=\frac{1}{c_{v}}\sum_{i=1}^{T_{c_{v}}}\bigl{(}d_{p}\times\gamma(g)\bigr{)} ^{2} \tag{12}\]

where \(\gamma(g)\) is the properties of data point, and \(T_{c_{v}}\) is total number of the coefficients. Therefore, Figure 3a,b demonstrate the accuracy of PCA with 2 and 3 components. The result demonstrates that the accuracy with 2 components is achieved 97.76% and 99.49% with 2 components. #### 3.1.4 Singular Value Decomposition

It is a method of matrix factorization that extends the eigenmode composition of a square matrix (n \(\times\) n) to any matrix (n \(\times\) m) (source). Thus, SVD can be obtained as:

\[Z=S\sum T^{*} \tag{13}\]

where, \(Z\) is the original matrix to be decomposed. The left singular matrix \(S\) is (columns are left singular vectors). The SVD lowers the number of features in a dataset by changing the space dimension from N to K. It is organized as a matrix, with each row representing a user and each column representing an object. SVD handles the entire process of diagonalizing a matrix into specific matrices that are easier to manipulate and analyze. It laid the groundwork for untangling data into distinct components. ### Fraud Prevention Process

Implementing a strategy to prevent fraudulent transactions boosts the customer's confidence. In prevention process, the user sends a secret code to the user telephone, and if the code entered by the user is not the same as sent code, the transaction will be blocked, and the secret question will be sent. In addition, if the answer to the question is wrong, then the system will block the user. The Algorithm 2 describes the fraud prevention process. Figure 3: (**a**) shows the accuracy 97.76% with 2 components, and (**b**) shows the accuracy 99.49% with 3 components. In Algorithm 2, Step 1 shows the initialization of variables. Steps-2- 3 define input and output processes. Step 4 sends the secret code to the telephone. In Steps 5-8, the code verification process is described to ensure that code is reached the legitimate user. If the user is legitimate, then it can respond with the correct code to enter into the system. If the user is not legitimate, then the transaction will be blocked. Step-9 initiates the second process of determining the identity of the user by sending the secret question. Steps 10-12 ensure if the secret question is answered correctly, then the user continues the transaction process. Step-13 explains that if the secret question is not answered properly, then the transaction is blocked permanently. Steps-16-17 show that all of the information of transactions is securely stored in the database to improve the fraud detection model. All procedure is written to log. The FPP involves the logic regression learning (LLP) that tries to quantify the relationship between a categorical dependent variable and one or more independent variables by plotting the probability scores of the dependent variables. Logistic Regression Learning Modeling for FPP

The FPP applies the LRL model to prevent the fraud transaction. The LRL simulates the interaction of predictor factors and a categorical response variable.