On the Size of Balls and Anticodes of Small Diameter Under the Fixed-Length Levenshtein Metric

Bar-Lev, Daniella; Etzion, Tuvi; Yaakobi, Eitan

doi:10.1109/tit.2022.3227128

Cited by 7 publications

(1 citation statement)

References 33 publications

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“…It is utilized in tasks such as multiple sequence alignment (Li and Homer 2010), biological database retrieval (Berger, Waterman, and Yu 2020), sequence hierarchical clustering (Sberro et al 2019), etc. In recent years, the rapid development of DNA storage (Goldman et al 2013;Church, Gao, and Kosuri 2012;Grass et al 2015) has introduced numerous applications of the Levenshtein distance, including sequence clustering (Rashtchian et al 2017;Zorita, Cuscó, and Filion 2015;Qu, Yan, and Wu 2022;Logan et al 2022), sequence alignment (Li and Homer 2010;Corso et al 2021), synchronization channel coding (Press et al 2020;Bar-Lev, Etzion, and Yaakobi 2023;Welzel et al 2023), etc. However, as the scale of information stored by DNA molecules continues to grow, the computational complexity of the Levenshtein distance becomes a significant challenge for the aforementioned applications.…”

Section: Introductionmentioning

confidence: 99%

Levenshtein Distance Embedding with Poisson Regression for DNA Storage

Wei,

Guo,

Sun

et al. 2024

AAAI

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Efficient computation or approximation of Levenshtein distance, a widely-used metric for evaluating sequence similarity, has attracted significant attention with the emergence of DNA storage and other biological applications. Sequence embedding, which maps Levenshtein distance to a conventional distance between embedding vectors, has emerged as a promising solution. In this paper, a novel neural network-based sequence embedding technique using Poisson regression is proposed. We first provide a theoretical analysis of the impact of embedding dimension on model performance and present a criterion for selecting an appropriate embedding dimension. Under this embedding dimension, the Poisson regression is introduced by assuming the Levenshtein distance between sequences of fixed length following a Poisson distribution, which naturally aligns with the definition of Levenshtein distance. Moreover, from the perspective of the distribution of embedding distances, Poisson regression approximates the negative log likelihood of the chi-squared distribution and offers advancements in removing the skewness. Through comprehensive experiments on real DNA storage data, we demonstrate the superior performance of the proposed method compared to state-of-the-art approaches.

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