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Microarray gene expression-based detection and classification of medical conditions have been prominent in research studies over the past few decades. However, extracting relevant data from the high-volume microarray gene expression with inherent nonlinearity and inseparable noise components raises significant challenges during data classification and disease detection. The dataset used for the research is the Lung Harvard 2 Dataset (LH2) which consists of 150 Adenocarcinoma subjects and 31 Mesothelioma subjects. The paper proposes a two-level strategy involving feature extraction and selection methods before the classification step. The feature extraction step utilizes Short Term Fourier Transform (STFT), and the feature selection step employs Particle Swarm Optimization (PSO) and Harmonic Search (HS) metaheuristic methods. The classifiers employed are Nonlinear Regression, Gaussian Mixture Model, Softmax Discriminant, Naive Bayes, SVM (Linear), SVM (Polynomial), and SVM (RBF). The two-level extracted relevant features are compared with raw data classification results, including Convolutional Neural Network (CNN) methodology. Among the methods, STFT with PSO feature selection and SVM (RBF) classifier produced the highest accuracy of 94.47%.