Feature selection and sample clustering play an important role in bioinformatics. Traditional feature selection methods separate sparse regression and embedding learning. Later, to effectively identify the significant features of the genomic data, Joint Embedding Learning and Sparse Regression (JELSR) is proposed. However, since there are many redundancy and noise values in genomic data, the sparseness of this method is far from enough. In this paper, we propose a strengthened version of JELSR by adding the L1-norm constraint on the regularization term based on a previous model, and call it LJELSR, to further improve the sparseness of the method. Then, we provide a new iterative algorithm to obtain the convergence solution. The experimental results show that our method achieves a state-of-the-art level both in identifying differentially expressed genes and sample clustering on different genomic data compared to previous methods. Additionally, the selected differentially expressed genes may be of great value in medical research.