Microarray gene expression data-based breast tumor classification is an active and challenging issue. In this paper, a robust framework of breast tumor recognition is presented aiming at reducing clinical misdiagnosis rate and exploiting available information in existing samples. A wrapper gene selection method is established from a new perspective of reducing clinical misdiagnosis rate. The further feature selection of information genes is achieved using the modified NMF model, which is rooted in the use of hierarchical learning and layer-wise pre-training strategy in deep learning. For completing the classification, an inverse projection sparse representation (IPSR) model is constructed to exploit information embedded in existing samples, especially in the test ones. Moreover, the IPSR model is optimized through generalized ADMM and the corresponding convergence is analyzed. Extensive experiments on public microarray gene expression datasets show that the proposed method is stable and effective for breast tumor classification. Compared to the latest open literature, there is 14% higher in classification accuracy. Specificity and sensitivity achieve 94.17% and 97.5%, respectively.