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The high dimensionality and sparsity of the microarray gene expression data make it challenging to analyze and screen the optimal subset of genes as predictors of breast cancer (BC). The authors in the present study propose a novel hybrid Feature Selection (FS) sequential framework involving minimum Redundancy-Maximum Relevance (mRMR), a two-tailed unpaired t-test, and meta-heuristics to screen the most optimal set of gene biomarkers as predictors for BC. The proposed framework identified a set of three most optimal gene biomarkers, namely, MAPK 1, APOBEC3B, and ENAH. In addition, the state-of-the-art supervised Machine Learning (ML) algorithms, namely Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Neural Net (NN), Naïve Bayes (NB), Decision Tree (DT), eXtreme Gradient Boosting (XGBoost), and Logistic Regression (LR) were used to test the predictive capability of the selected gene biomarkers and select the most effective breast cancer diagnostic model with higher values of performance matrices. Our study found that the XGBoost-based model was the superior performer with an accuracy of 0.976 ± 0.027, an F1-Score of 0.974 ± 0.030, and an AUC value of 0.961 ± 0.035 when tested on an independent test dataset. The screened gene biomarkers-based classification system efficiently detects primary breast tumors from normal breast samples.