NGS Based Haplotype Assembly Using Matrix Completion

We apply matrix completion methods for haplotype assembly from NGS reads to develop the new HapSVT, HapNuc, and HapOPT algorithms. This is performed by applying a mathematical model to convert the reads to an incomplete matrix and estimating unknown components. This process is followed by quantizing and decoding the completed matrix in order to estimate haplotypes. These algorithms are compared to the state-of-the-art algorithms using simulated data as well as the real fosmid data. It is shown that the SNP missing rate and the haplotype block length of the proposed HapOPT are better than those of HapCUT2 with comparable accuracy in terms of reconstruction rate and switch error rate. A program implementing the proposed algorithms in MATLAB is freely available at https://github.com/smajidian/HapMC

Identifying Sparse Low-Dimensional Structures in Markov Chains: A Nonnegative Matrix Factorization Approach

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired to be representative of only a small subset of original states. To promote this structural property, we constrain the number of nonzero entries of the mappings between the state space and the kernel space. By imposing the desired characteristics of the representation, we cast the problem as a constrained nonnegative matrix factorization. To compute the solution, we propose an efficient block coordinate gradient descent and theoretically analyze its convergence properties.Comment: Accepted for publication in American Control Conference (ACC) Proceedings, 202

Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids

Abstract Background Haplotype assembly is the task of reconstructing haplotypes of an individual from a mixture of sequenced chromosome fragments. Haplotype information enables studies of the effects of genetic variations on an organism’s phenotype. Most of the mathematical formulations of haplotype assembly are known to be NP-hard and haplotype assembly becomes even more challenging as the sequencing technology advances and the length of the paired-end reads and inserts increases. Assembly of haplotypes polyploid organisms is considerably more difficult than in the case of diploids. Hence, scalable and accurate schemes with provable performance are desired for haplotype assembly of both diploid and polyploid organisms. Results We propose a framework that formulates haplotype assembly from sequencing data as a sparse tensor decomposition. We cast the problem 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 V̲ $\underline {\mathbf {V}}$; tensor V̲ $\underline {\mathbf {V}}$ 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 iteratively solving this decomposition problem is proposed. 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. The developed framework is applicable to diploid, biallelic and polyallelic polyploid species. The code for AltHap is freely available from https://github.com/realabolfazl/AltHap. Conclusion AltHap was tested in a number of different scenarios and was shown to compare favorably to state-of-the-art methods in applications to haplotype assembly of diploids, and significantly outperforms existing techniques when applied to haplotype assembly of polyploids

Additional file 1 of Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids

Supplement for “Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids”. Additional file 1 provides details on derivation of the proposed step size, and derivation of MEC and CPR bounds. (PDF 210 kb