Single-cell sequencing (SCS) data provide unprecedented insights into intratumoral heterogeneity. With SCS, we can better characterize clonal genotypes and build phylogenetic relationships of tumor cells/clones. However, high technical errors bring much noise into the genetic data, thus limiting the application of evolutionary tools in the large reservoir. To recover the low-dimensional subspace of tumor subpopulations from error-prone SCS data in the presence of corrupted and/or missing elements, we developed an efficient computational framework, termed RobustClone, to recover the true genotypes of subclones based on the low-rank matrix factorization method of extended robust principal component analysis (RPCA) and reconstruct the subclonal evolutionary tree. RobustClone is a model-free method, fast and scalable to large-scale datasets. We conducted a set of systematic evaluations on simulated datasets and demonstrated that RobustClone outperforms state-of-the-art methods, both in accuracy and efficiency. We further validated RobustClone on 2 single-cell SNV and 2 single-cell CNV datasets and demonstrated that RobustClone could recover genotype matrix and infer the subclonal evolution tree accurately under various scenarios. In particular, RobustClone revealed the spatial progression patterns of subclonal evolution on the large-scale 10X Genomics scCNV breast cancer dataset. RobustClone software is available at https://github.com/ucasdp/RobustClone. * Corresponding Authors. Emails: lwan@amss.ac.cn (Lin Wan) and maliang@ioz.ac.cn (Liang Ma).pioneering work utilizes single-cell copy number variation (scCNV) profiles to construct tumor cell phylogenies (14; 15), many others work on single-cell single nucleotide variation (scSNV) data with application of traditional phylogenetic methods. (16) and (17) applied distance-based methods, such as UPGMA or neighbor-joining (NJ) (18). Methods based on more complex models, like maximum likelihood or Bayesian (19), have also been applied to infer tumor phylogeny with scSNV data (20; 21).However, because of technique issues, such as library preparation and dropout events, current SCS data are known to be error-prone, thereby limiting the direct application of traditional phylogenic approaches. Three common types of errors are often associated with SCS data: false positive (FP) and false negative (FN) mutations, as well as missing bases (MBs). FPs and FNs are usually caused by allelic dropout events, a very common problem in SCS in which the mutant allele fails to amplify. The false positive rate (FPR) varies from 0.1 to 0.43, as reported in many studies (15; 16; 22; 23). False positives occur on the order ∼ 10 −5 , exceeding the somatic mutation rate (15; 16; 22). MBs may have issues involving sequencing depth, and they occur in low-coverage regions during sequencing. The reported missing rate (MR) can be as high as 58% in single-cell sequencing (22; 23). When these errors in the data occur together, downstream analysis can be biased.Methods that explicitly account for errors ...