Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids

Abstract

A framework that formulates haplotype assembly as sparse tensor decomposition is proposed. The problem is cast as that of decomposing a tensor having special structural constraints and missing a large fraction of its entries into a product of two factors, U and V; tensor V reveals haplotype information while U is a sparse matrix encoding the origin of erroneous sequencing reads. An algorithm, AltHap, which reconstructs haplotypes of either diploid or polyploid organisms by solving this decomposition problem is proposed. Starting from a judiciously selected initial point, AltHap alternates between two optimization tasks to recover U and V by relying on a modi ed gradient descent search that exploits salient structural properties of U and V. The performance and convergence properties of AltHap are theoretically analyzed and, in doing so, guarantees on the achievable minimum error correction scores and correct phasing rate are established. AltHap was tested in a number of di erent scenarios and was shown to compare favorably to state-of-the-art methods in applications to haplotype assembly of diploids, and signi cantly outperform existing techniques when applied to haplotype assembly of polyploids.

A Graph Auto-Encoder for Haplotype Assembly and Viral Quasispecies Reconstruction

“…where M is the one-to-one mapping from the set of reconstructed haplotype to the set of true haplotype (Hashemi 2018), i.e., mapping that determines the best possible match between the two sets of haplotypes. To characterize performance of methods for reconstruction of viral quasispecies with generally a priori unknown number of components, in addition to correct phasing rate we also quantify recall rate, defined as the fraction of perfectly reconstructed components in a population (i.e., recall rate = T P T P +F N ), and predicted proportion, defined as the ratio of the estimated and the true number of components in a genomic mixture (Ahn 2018).…”

“…The semi-experimental data is obtained by simulating mutations, shotgun sequencing procedure, read alignment and SNP calling steps in a fictitious experiment on a single individual Solanum Tuberosum (polyploid with k = 4). Details on how exactly the semi-experimental data is generated and processed can be found in Supplementary Document C. We compare the performance of GAEseq on this data with publicly available software HapCompass (Aguiar 2012), an algorithm that relies on graph-theoretic models to perform haplotype assembly, H-PoP (Xie 2016), a dynamic programming method, and AltHap (Hashemi 2018), a method based on tensor factorization. The performance of different methods is evaluated in terms of the MEC score and CPR.…”

“…High-throughput DNA sequencing technologies generate massive amounts of reads that sample an individual genome and thus enable studies of genetic variations (Schwartz 2010;Clark 2004;Sabeti 2002). Haplotype reconstruction, however, remains challenging due to limited * This work was funded in part by the NSF grant CCF 1618427. lengths of reads and presence of sequencing errors (Hashemi 2018). Particularly difficult is the assembly of haplotypes in polyploids, organisms with chromosomes organized in ktuples with k > 2, where deep coverage is typically required to achieve desired accuracy.…”

“…Existing methods often approach haplotype assembly as the task of grouping sequencing reads according to their chromosomal origin into as many clusters as there are chromosomes. Separation of reads into clusters is rendered challenging by their limited lengths and the presence of sequencing errors (Hashemi 2018); such artifacts create ambiguities regarding the origin of the reads. The vast majority of existing haplotype assembly methods attempt to remove the aforementioned ambiguity by altering or even discarding the data, leading to minimum SNP removal (Lancia 2001), maximum fragments cut (Duitama 2010), and minimum error correction (MEC) score optimization criteria.…”

“…Among the aforementioned methods, only HapCompass (Aguiar 2012), SD-haP (Das 2015) and BP (Puljiz 2016) are capable of solving the haplotype assembly problem for k > 2. Other techniques that can handle reconstruction of haplotypes for both diploid and polyploid genomes include a Bayesian method HapTree (Berger 2014), a dynamic programming method H-PoP (Xie 2016) shown to be more accurate than the techniques in (Aguiar 2012;Berger 2014;Das 2015), and the matrix factorization schemes in (Cai 2016;Hashemi 2018).…”