It is a major challenge to integrate single-cell sequencing data across experiments, conditions, batches, time points, and other technical considerations. New computational methods are required that can integrate samples while simultaneously preserving biological information. Here, we propose an unsupervised reference-free data representation, cluster similarity spectrum (CSS), where each cell is represented by its similarities to clusters independently identified across samples. We show that CSS can be used to assess cellular heterogeneity and enable reconstruction of differentiation trajectories from cerebral organoid and other single-cell transcriptomic data, and to integrate data across experimental conditions and human individuals.