17Technologies to sequence the transcriptome, genome or epigenome from thousands of 18 single cells in an experiment provide extraordinary resolution into the molecular states 19 present within a complex biological system at any given moment. However, it is a major 20 challenge to integrate single-cell sequencing data across experiments, conditions, batches, 21 timepoints and other technical considerations. New computational methods are required that 22can simultaneously preserve biological signals, while also integrating samples. Here, we 23propose an unsupervised reference-free data representation, Cluster Similarity Spectrum 24 (CSS), where each cell is represented by its similarities to clusters independently identified 25 across samples. We show that CSS can be used to assess cell heterogeneity and enable 26 differentiation trajectory reconstruction from cerebral organoid single-cell transcriptome data, 27and to integrate data across individuals and experimental conditions. We compare CSS to 28 other integration algorithms and show that CSS performs comparably well. We also show 29 that CSS allows projection of single-cell genomic data of different modalities to the CSS-30represented reference atlas for visualization and cell type identity prediction. We think CSS 31 provides a straightforward and powerful approach to understand and integrate challenging 32 single-cell multi-omic data. 33 34