Abstract Intratumor heterogeneity has long been a confounding factor in interpreting cancer genomic data, but has also been useful in reconstructing progression processes based on variation between clonal populations in single tumors. We previously developed a strategy of applying computational deconvolution algorithms to gene expression or DNA copy number data to reconstruct models of progression of cell populations from bulk tumor samples. Many tools have since been proposed for similar deconvolution analysis, but all are limited by the computational difficulty of unambiguously distinguishing small cell populations and variants from noise in genomic assays. We present a novel approach to infer tumor progression pathways from deconvolved genomic data designed to leverage the fact that tumors that partition into subtypes with similar evolutionary trajectories would be expected to lead to a mathematical substructure in the genomic data, known as a simplicial complex, which can be modeled computationally to better deconvolve cell populations across tumor types. We have developed a computational pipeline to perform tumor deconvolution while taking into consideration this kind of mathematical structure. The pipeline clusters tumors to identify genetically distinct subgroups, fits mixture models to these subgroups, and uses overlap between them to infer a refined deconvolution of major cellular populations and possible pathways of progression between them. We apply our methods to a set of RNASeq data from the TCGA breast cancer data set and to synthetic data modeling distinct scenarios of tumor progression. We first compare our methods on the synthetic data to our earlier work and to a comparative Gaussian mixture model. All methods perform comparably on unstructured data but the new method substantially outperforms the others on data consistent with simple scenarios for tumor progression along multiple discrete subtypes. The novel method, however, shows lower tolerance for noisy data than a Gaussian mixture model. Application to the TCGA RNASeq data showed our method could partition tumors into discrete subcategories associated with HER2+, ER/PR+, and triple-negative status and could exploit the resulting substructure of the data to deconvolve tumor data and infer progression models reflecting partial sharing of progression states between subtypes. Gene enrichment analysis showed association of deconvolved cell populations with a variety of gene functional categories suggestive of distinct progression mechanisms of the subtypes. Citation Format: Theodore Roman, Russell Schwartz. Improved deconvolution of heterogeneous tumor data to reconstruct clonal evolution from bulk genomic samples. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 1934. doi:10.1158/1538-7445.AM2015-1934