An accurate and rapid continuous wavelet dynamic time warping algorithm for end-to-end mapping in ultra-long nanopore sequencing.

Motivation: Long-reads, point-of-care and polymerase chain reaction-free are the promises brought by nanopore sequencing. Among various steps in nanopore data analysis, the end-to-end mapping between the raw electrical current signal sequence and the reference expected signal sequence serves as the key building block to signal labeling, and the following signal visualization, variant identification and methylation detection. One of the classic algorithms to solve the signal mapping problem is the dynamic time warping (DTW). However, the ultra-long nanopore sequencing and an order of magnitude difference in the sampling speed complexify the scenario and make the classical DTW infeasible to solve the problem. Results: Here, we propose a novel multi-level DTW algorithm, continuous wavelet DTW (cwDTW), based on continuous wavelet transforms with different scales of the two signal sequences. Our algorithm starts from low-resolution wavelet transforms of the two sequences, such that the transformed sequences are short and have similar sampling rates. Then the peaks and nadirs of the transformed sequences are extracted to form feature sequences with similar lengths, which can be easily mapped by the original DTW. Our algorithm then recursively projects the warping path from a lower-resolution level to a higher-resolution one by building a context-dependent boundary and enabling a constrained search for the warping path in the latter. Comprehensive experiments on two real nanopore datasets on human and on Pandoraea pnomenusa demonstrate the efficiency and effectiveness of the proposed algorithm. In particular, cwDTW can gain remarkable acceleration with tiny loss of the alignment accuracy. On the real nanopore datasets, cwDTW can finish an alignment task in few seconds, which is about 3000 times faster than the original DTW. By successfully applying cwDTW on the tasks of signal labeling and ultra-long sequence comparison, we further demonstrate the power and applicability of cwDTW.