## 2 Methods
### Statistical Analysis
#### 2.5.2 Multivariate Analysis  
Multivariate analysis was carried out using linear classifier (linear discrimination analysis--LDA), decision tree (DT), k-nearest neighbor (KNN) and support vector machine (SVM) to assess the diagnostic accuracy using all extracted metrics of textural, morphological and dynamic parameters. Configuration settings for each classifier are provided in Table 4.  
A brief informal description of pattern recognition approaches and of each classifier has already been discussed in a previous article [61]. The theoretical details of these classifiers can be found elsewhere [18; 19; 20; 25; 27; 28; 29; 30; 62; 63; 64]. Each classifier received the same set or subset of features. The analysis was made before and after a feature selection method: the robust features were selected by the least absolute shrinkage and selection operator (LASSO) method [65; 66]. In the LASSO method, 10-fold cross-validation was used to select the optimal regularization parameter alpha, as the average of mean square error of each patient was the smallest. With the optimal alpha, features with a non-zero coefficient in LASSO were reserved. Note that the shrinkage requires the selection of a tuning parameter (lambda) that determines the amount of penalization. Feature selection was carried out considering the \(\lambda\) value with the minimum mean squared error (minMSE) [67; 68]. The classification analysis was cross-validated using the 10-fold cross-validation approach, and median values of AUC, accuracy, sensitivity and specificity were obtained. Starting with existing less-represented class samples, two techniques were used to synthesize feasible and likely data and, therefore, to help balance the classes as well as to boost the performance in terms of confusion matrix as well as overall [69; 70]: the self-adaptive synthetic over-sampling (SAYNO) approach and the adaptive synthetic sampling (ADASYN) approach. The key idea of the SASYNO approach is to select neighboring minority class (benign lesions) samples based on their mutual distances and create both interpolations and extrapolations around neighboring samples for synthetic data generation. Specifically, SASYNO first identifies a population of pairwise neighboring samples from a minority class. Then, it imposes Gaussian disturbance on these identified neighboring samples to create extrapolations and, finally, generates synthetic samples by creating linear interpolations between these extrapolations [69]. The adaptive synthetic sampling (ADASYN) approach is one of the most successful advanced over-sampling approaches; it is an extension of the synthetic minority over-sampling technique (SMOTE) [70; 71]. Specifically, the SMOTE [71] tackles the class imbalance problem by creating linear interpolations between randomly selected minority class samples and their neighbors of the same class. The essential idea of ADASYN is to prioritize samples near decision boundaries and to focus on these hard-to-learn minority class samples by assigning weights calculated per \begin{table}
\begin{tabular}{c c} \hline \hline
**Classifier** & **Configuration Settings** \\ \hline LDA & Covariance structure: full; optimizer options: hyperparameter options disabled \\ \hline Decision tree & Fine Tree; maximum number of splits: 100; split criterion: Gini’s diversity index; surrogate decision splits: off; optimizer options: hyperparameter options disabled \\ \hline K-nearest neighbors & Fine KNN; number of neighbors: 100; distance metric: Euclidean; distance weight: equal; standardize data: true; optimizer options: hyperparameter options disabled \\ \hline Support vector machine & Linear SVM; kernel function: linear; kernel scale: automatic box constraint level: 1; multiclass method: one-vs-one; standardize data: true; optimizer options; hyperparameter options disabled \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Configuration settings for each classifier.