Related papers: Surprises in approximating Levenshtein distances
Dictionary lookup methods are popular in dealing with ambiguous letters which were not recognized by Optical Character Readers. However, a robust dictionary lookup method can be complex as apriori probability calculation or a large…
Levenshtein distance is a commonly used edit distance metric, typically applied in language processing, and to a lesser extent, in molecular biology analysis. Biological nucleic acid sequences are often embedded in longer sequences and are…
Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
This paper introduces the sequence covering similarity, that we formally define for evaluating the similarity between a symbolic sequence (string) and a set of symbolic sequences (strings). From this covering similarity we derive a…
Identifying document similarity has many applications, e.g., source code analysis or plagiarism detection. However, identifying similarities is not trivial and can be time complex. For instance, the Levenshtein Distance is a common metric…
String edit distances have been used for decades in applications ranging from spelling correction and web search suggestions to DNA analysis. Most string edit distances are variations of the Levenshtein distance and consider only…
Phylogenetic trees can be reconstructed from the matrix which contains the distances between all pairs of languages in a family. Recently, we proposed a new method which uses normalized Levenshtein distances among words with same meaning…
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…
The evolution of languages closely resembles the evolution of haploid organisms. This similarity has been recently exploited \cite{GA,GJ} to construct language trees. The key point is the definition of a distance among all pairs of…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
We introduce the notion of Levenshtein graphs, an analog to Hamming graphs but using the edit distance instead of the Hamming distance; in particular, Levenshtein graphs allow for underlying strings (nodes) of different lengths. We…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts,…
Probabilistic context-free grammars (PCFGs) are used to define distributions over strings, and are powerful modelling tools in a number of areas, including natural language processing, software engineering, model checking, bio-informatics,…
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler…
In many applications, it is necessary to determine the similarity of two strings. A widely-used notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one…
In this paper, we present a novel interpretation of the so-called Weisfeiler-Lehman (WL) distance, introduced by Chen et al. (2022), using concepts from stochastic processes. The WL distance aims at comparing graphs with node features, has…