The breast cancer automatic diagnosis is a critical real world medical challenge. This study proposes a classifying cancer tumor method based on their gene expression signatures to specific diagnostic categories. The developed neural network model holds promise for patients, surgeons, and radiologists, providing them with information, which was only available using biopsy. This significantly reduces the number of pointless surgical procedures. This study utilizes Wave Atom Transform as feature extraction method, and Back Propagation Algorithm to classify cancer into pre-defined classes. The proposed model provides automatic detection with a high level of accuracy (90%).