Matrix completion with weighted constraint for haplotype estimation

Abstract Estimation of haplotype sequences from DNA sequencing samples is a challenging task whose mathematical formulation leads to an NP-hard problem. Also, accuracy of the estimates plays an essential role in providing the required information for personalized medicine. In order to fully incorporate the available quality of measurements with higher accuracy into the estimates, in this paper, we propose a new optimization design using a weighted version of the well-established matrix completion approach. This is performed by penalizing the difference between the measurements and the desired matrix using some weights, which are used to form an optimization constraint. Accordingly, we derive the corresponding error bound for the desired matrix, which shows that a larger noise power increases the estimation error with a factor proportional to the inverse of the mentioned weights. This leads to devising a new algorithm called the Haplotype reconstruction using nuclear norm minimization with Weighted Constraint (HapWeC). Computer simulations show the outperformance of the HapWeC compared to some recent algorithms in terms of the normalized reconstruction error and reconstruction rate.