Sparse representation based classification (SRC) achieves good results by addressing recognition problem with sufficient training samples per subject. Tumor classification, however, is a typical small sample problem. In this paper, an inverse projection group sparse representation (IPGSR) model is presented for tumor classification based on constructing a low rank variation dictionary (LRVD), for short, LRVD-IPGSR model. Firstly, an IPGSR model is constructed based on making full use of existing training and test samples, and group sparsity effect of genetic data. Furthermore, from a new viewpoint, a LRVD is constructed for improving the performance of IPGSR-based tumor classification. The LRVD can be independently constructed by detecting and utilizing variations of normals and typical patients, rather than directly using and changed with the genetic data or their corresponding feature data. And the LRVD can be automatic updated and extended to fit the case of new types of diseases. Finally, the LRVD-IPGSR model is fully analyzed from feasibility, stability, optimization and convergence. The performance of the LRVD-IPGSR model-based tumor classification framework is verified on eight microarray gene expression datasets, which contain early diagnosis, tumor type recognition and postoperative metastasis.

基于稀疏表示的分类（SRC）通过解决识别问题并为每个主题提供足够的训练样本来取得良好的效果。但是，肿瘤分类是一个典型的小样本问题。本文在构建低秩变异字典（LRVD）的基础上，提出了一种逆投影群稀疏表示（IPGSR）模型用于肿瘤分类，简称LRVD-IPGSR模型。首先，在充分利用现有训练样本和测试样本以及遗传数据的稀疏效应的基础上，构建了IPGSR模型。此外，从新的观点出发，构建了LRVD以改善基于IPGSR的肿瘤分类的性能。LRVD可以通过检测和利用正常人和典型患者的变异来独立构建，而不是直接使用遗传数据或它们的相应特征数据并对其进行更改。LRVD可以自动更新和扩展，以适应新型疾病的情况。最后，从可行性，稳定性，优化性和收敛性等方面对LRVD-IPGSR模型进行了全面分析。在八个微阵列基因表达数据集上验证了基于LRVD-IPGSR模型的肿瘤分类框架的性能，该数据集包含早期诊断，肿瘤类型识别和术后转移。