Title: Cancer homogeneity in single cell revealed by Bi-state model and Binary matrix factorization. Abstract: Single cell RNA sequencing (scRNAseq) technology enables quantifying gene expression profiles by individual cells within cancer. Dimension reduction methods have been commonly used for cell clustering analysis and visualization of the data. Current dimension reduction methods tend overly eliminate the expression variations correspond to less dominating characteristics, such we fail to find the homogenious properties of cancer development. In this paper, we proposed a new and clustering analysis method for scRNAseq data, namely BBSC, via implementing a binarization of the gene expression profile into on/off frequency changes with a Boolean matrix factorization. The low rank representation of expression matrix recovered by BBSC increase the resolution in identifying distinct cell types or functions. Application of BBSC on two cancer scRNAseq data successfully discovered both homogeneous and heterogeneous cancer cell clusters. Further finding showed potential in preventing cancer progression.