Cancer is a significant cause of death worldwide. Early cancer detection is greatly aided by machine learning and artificial intelligence (AI) to gene microarray data sets (microarray data). Despite this, there is a significant discrepancy between the number of gene features in the microarray data set and the number of samples. Because of this, it is crucial to identify markers for gene array data. Existing feature selection algorithms, however, generally use long-standing, are limited to single-condition feature selection and rarely take feature extraction into account. This work proposes a Multi-stage algorithm for Biomedical Deep Feature Selection (MBDFS) to address this issue. In the first, three feature selection techniques are combined for thorough feature selection, and feature subsets are obtained; in the second, an unsupervised neural network is used to create the best representation of the feature subset to enhance final classification accuracy. Using a variety of metrics, including a comparison of classification results before and after feature selection and the performance of alternative feature selection methods, we evaluate MBDFS's efficacy. The experiments demonstrate that although MBDFS uses fewer features, classification accuracy is either unchanged or enhanced.