Related papers: The Harmonic Indel Distance
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…
Of all components of Prosody, Rhythm has been regarded as the hardest to address, as it is utterly linked to Pitch and Intensity. Nevertheless, Rhythm is a very good indicator of a speaker's fluency in a foreign language or even of some…
This paper defines a distance function that measures the dissimilarity between planar geometric figures formed with straight lines. This function can in turn be used in partial matching of different geometric figures. For a given pair of…
We define a multi-scale metric $d_\rho$ on strings by aggregating angle distances between all $n$-gram count vectors with exponential weights $\rho^n$. We benchmark $d_\rho$ in DBSCAN clustering against edit and $n$-gram baselines, give a…
The surge of research in image segmentation has yielded remarkable performance gains but also exposed a reproducibility crisis. A major contributor is performance evaluation, where both selection and implementation of metrics play critical…
We propose a new method to determine the unknown parameter associated to a self-consistent harmonic approximation. We check the validity of our technique in the context of the sine-Gordon model. As a non trivial application we consider the…
This paper revisits recent code similarity evaluation metrics, particularly focusing on the application of Abstract Syntax Tree (AST) editing distance in diverse programming languages. In particular, we explore the usefulness of these…
The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…
This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate…
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applications in data analysis and scientific visualization. In this…
Multi-modal image registration is a crucial pre-processing step in many medical applications. However, it is a challenging task due to the complex intensity relationships between different imaging modalities, which can result in large…
Nonparametric curve estimation by kernel methods has attracted widespread interest in theoretical and applied statistics. One area of conflict between theory and application relates to the evaluation of the performance of the estimators.…
Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria…
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determining the interleaving distance in several settings. We show…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance. For the gap edit distance problem, we give an $\tilde{O}(\frac{n}{k}+k^2)$-time greedy…
We present a new method for image feature-extraction which is based on representing an image by a finite-dimensional vector of distances that measure how different the image is from a set of image prototypes. We use the recently introduced…
A Hamming compatible metric is an integer-valued metric on the words of a finite alphabet which agrees with the usual Hamming distance for words of equal length. We define a new Hamming compatible metric, compute the cardinality of a sphere…