Scoring Matrices That Induce Metrics on Sequences

Araujo, Eloi; Soares, José

doi:10.1007/11682462_11

Cited by 3 publications

(6 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 1: Representation of the relationship between scoring matrices. Araujo and Soares [AS06] showed that…”

Section: Preliminariesmentioning

confidence: 99%

“…If a given criterion v, depending on a scoring matrix γ, is a metric on Σ * , we say that the scoring matrix γ induces a v-distance. Sellers [Sel74] showed that matrices in M C induce an optA γ -metric on Σ * and Araujo and Soares [AS06] showed that γ ∈ M A if and only if γ induces an optA γ -metric on Σ * . Moreover, γ ∈ M N if and only if γ induces an optN γ -metric on Σ * .…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Algorithms for normalized multiple sequence alignments

Araujo,

Rozante,

Rubert

et al. 2021

Preprint

View full text Add to dashboard Cite

Sequence alignment supports numerous tasks in bioinformatics, natural language processing, pattern recognition, social sciences, and others fields. While the alignment of two sequences may be performed swiftly in many applications, the simultaneous alignment of multiple sequences proved to be naturally more intricate. Although most multiple sequence alignment (MSA) formulations are NP-hard, several approaches have been developed, as they can outperform pairwise alignment methods or are necessary for some applications.Taking into account not only similarities but also the lengths of the compared sequences (i.e. normalization) can provide better alignment results than both unnormalized or post-normalized approaches. While some normalized methods have been developed for pairwise sequence alignment, none have been proposed for MSA. This work is a first effort towards the development of normalized methods for MSA.We discuss multiple aspects of normalized multiple sequence alignment (NMSA). We define three new criteria for computing normalized scores when aligning multiple sequences, showing the NP-hardness and exact algorithms for solving the NMSA using those criteria. In addition, we provide approximation algorithms for MSA and NMSA for some classes of scoring matrices.

show abstract

“…Figure 1: Representation of the relationship between scoring matrices. Araujo and Soares [AS06] showed that…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Algorithms for normalized multiple sequence alignments

Araujo,

Rozante,

Rubert

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, there are many ways to generalize the concept of metric by relaxing the axioms that define the metric space, which gives rise to different generalized metric spaces such as quasimetric, semimetric, and others. In this work we extended investigations from Araujo and Soares (2006) establishing necessary and sufficient conditions for scoring matrices γ to induce optA γ -p for each axiom p of a metric on sequences. Marzal and Vidal (1993) set another scoring function based on edit operations and induced by a scoring matrix γ, called normalized edit distance and denoted by optN γ .…”

Section: Introductionmentioning

confidence: 99%

“…Sellers (1974) described a sufficient condition for a weighted edit distance be a metric on Σ * , i.e., proved that a scoring matrix γ induces an optA γ -metric on sequences. Araujo and Soares (2006) presented necessary and sufficient conditions for a scoring matrix γ induce a weighted edit distance as a metric on Σ * . For example, the scoring matrix…”

Section: Introductionmentioning

confidence: 99%

“…Marzal and Vidal (1993) set another scoring function based on edit operations and induced by a scoring matrix γ, called normalized edit distance and denoted by optN γ . Given sequences s and t, considering that each symbol in s must be edited exactly once, then optN γ (s, t) is the minimum average weight of a set of edit operations required to transform s into t. Similarly, not all scoring matrices γ induce an optN γ -metric and Araujo and Soares (2006) characterize the class of scoring matrices inducing normalized edit distances. In this work we also characterize each class of scoring matrices inducing optN γ -p on sequences for some generalized metric spaces p. Recently, Fisman et al (2022) proved that the normalized edit distance proposed in (Marzal and Vidal, 1993) is a metric when cost of all edit operations are the same.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Matrices inducing generalized metric on sequences

Araujo,

Martinez,

Higa

et al. 2023

Preprint

View full text Add to dashboard Cite

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving scoring function determines the degree of similarity between them. Many scoring functions are obtained from scoring matrices. However, not all scoring matrices induce scoring functions which are distances, since the scoring function is not necessarily a metric. In this work we establish necessary and sufficient conditions for scoring matrices to induce each one of the properties of a metric in weighted edit distances. For a subset of scoring matrices that induce normalized edit distances, we also characterize each class of scoring matrices inducing normalized edit distances. Furthermore, we define an extended edit distance, which takes into account a set of editing operations that transforms one sequence into another regardless of the existence of a usual corresponding alignment to represent them, describing a criterion to find a sequence of edit operations whose weight is minimum. Similarly, we determine the class of scoring matrices that induces extended edit distances for each of the properties of a metric.

show abstract

Algorithms for Normalized Multiple Sequence Alignments

Araujo¹,

Rozante²,

Rubert³

et al. 2021

View full text Add to dashboard Cite

Scoring Matrices That Induce Metrics on Sequences

Cited by 3 publications

References 10 publications

Algorithms for normalized multiple sequence alignments

Algorithms for normalized multiple sequence alignments

Matrices inducing generalized metric on sequences

Algorithms for Normalized Multiple Sequence Alignments

Contact Info

Product

Resources

About