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Abstract MotivationSketching is now widely used in bioinformatics to reduce data size and increase data processing speed. Sketching approaches entice with improved scalability but also carry the danger of decreased accuracy and added bias. In this article, we investigate the minimizer sketch and its use to estimate the Jaccard similarity between two sequences. ResultsWe show that the minimizer Jaccard estimator is biased and inconsistent, which means that the expected difference (i.e. the bias) between the estimator and the true value is not zero, even in the limit as the lengths of the sequences grow. We derive an analytical formula for the bias as a function of how the shared k-mers are laid out along the sequences. We show both theoretically and empirically that there are families of sequences where the bias can be substantial (e.g. the true Jaccard can be more than double the estimate). Finally, we demonstrate that this bias affects the accuracy of the widely used mashmap read mapping tool. Availability and implementationScripts to reproduce our experiments are available at https://github.com/medvedevgroup/minimizer-jaccard-estimator/tree/main/reproduce. Supplementary informationSupplementary data are available at Bioinformatics online.
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Minmers are a generalization of minimizers that enable unbiased local Jaccard estimation
Abstract MotivationThe Jaccard similarity on k-mer sets has shown to be a convenient proxy for sequence identity. By avoiding expensive base-level alignments and comparing reduced sequence representations, tools such as MashMap can scale to massive numbers of pairwise comparisons while still providing useful similarity estimates. However, due to their reliance on minimizer winnowing, previous versions of MashMap were shown to be biased and inconsistent estimators of Jaccard similarity. This directly impacts downstream tools that rely on the accuracy of these estimates. ResultsTo address this, we propose the minmer winnowing scheme, which generalizes the minimizer scheme by use of a rolling minhash with multiple sampled k-mers per window. We show both theoretically and empirically that minmers yield an unbiased estimator of local Jaccard similarity, and we implement this scheme in an updated version of MashMap. The minmer-based implementation is over 10 times faster than the minimizer-based version under the default ANI threshold, making it well-suited for large-scale comparative genomics applications. Availability and implementationMashMap3 is available at https://github.com/marbl/MashMap.
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- PAR ID:
- 10469202
- Editor(s):
- Robinson, Peter
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Bioinformatics
- Volume:
- 39
- Issue:
- 9
- ISSN:
- 1367-4811
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract MotivationModern methods for computation-intensive tasks in sequence analysis (e.g. read mapping, sequence alignment, genome assembly, etc.) often first transform each sequence into a list of short, regular-length seeds so that compact data structures and efficient algorithms can be employed to handle the ever-growing large-scale data. Seeding methods using kmers (substrings of length k) have gained tremendous success in processing sequencing data with low mutation/error rates. However, they are much less effective for sequencing data with high error rates as kmers cannot tolerate errors. ResultsWe propose SubseqHash, a strategy that uses subsequences, rather than substrings, as seeds. Formally, SubseqHash maps a string of length n to its smallest subsequence of length k, k < n, according to a given order overall length-k strings. Finding the smallest subsequence of a string by enumeration is impractical as the number of subsequences grows exponentially. To overcome this barrier, we propose a novel algorithmic framework that consists of a specifically designed order (termed ABC order) and an algorithm that computes the minimized subsequence under an ABC order in polynomial time. We first show that the ABC order exhibits the desired property and the probability of hash collision using the ABC order is close to the Jaccard index. We then show that SubseqHash overwhelmingly outperforms the substring-based seeding methods in producing high-quality seed-matches for three critical applications: read mapping, sequence alignment, and overlap detection. SubseqHash presents a major algorithmic breakthrough for tackling the high error rates and we expect it to be widely adapted for long-reads analysis. Availability and implementationSubseqHash is freely available at https://github.com/Shao-Group/subseqhash.more » « less
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Abstract MotivationK-mer-based methods are used ubiquitously in the field of computational biology. However, determining the optimal value of k for a specific application often remains heuristic. Simply reconstructing a new k-mer set with another k-mer size is computationally expensive, especially in metagenomic analysis where datasets are large. Here, we introduce a hashing-based technique that leverages a kind of bottom-m sketch as well as a k-mer ternary search tree (KTST) to obtain k-mer-based similarity estimates for a range of k values. By truncating k-mers stored in a pre-built KTST with a large k=kmax value, we can simultaneously obtain k-mer-based estimates for all k values up to kmax. This truncation approach circumvents the reconstruction of new k-mer sets when changing k values, making analysis more time and space-efficient. ResultsWe derived the theoretical expression of the bias factor due to truncation. And we showed that the biases are negligible in practice: when using a KTST to estimate the containment index between a RefSeq-based microbial reference database and simulated metagenome data for 10 values of k, the running time was close to 10× faster compared to a classic MinHash approach while using less than one-fifth the space to store the data structure. Availability and implementationA python implementation of this method, CMash, is available at https://github.com/dkoslicki/CMash. The reproduction of all experiments presented herein can be accessed via https://github.com/KoslickiLab/CMASH-reproducibles. Supplementary informationSupplementary data are available at Bioinformatics online.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/bioinformatics/btad512
