Related papers: The Harmonic Indel Distance
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the…
The usual Euclidean distance may be generalized to extended objects such as polymers or membranes. Here, this distance is used for the first time as a cost function to align structures. We examined the alignment of extended strands to…
Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance…
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that…
This work introduces two new distance metrics for comparing labeled arrays, which are common outputs of image segmentation algorithms. Each pixel in an image is assigned a label, with binary segmentation providing only two labels…
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…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
Distances on symbolic musical sequences are needed for a variety of applications, from music retrieval to automatic music generation. These musical sequences belong to a given corpus (or style) and it is obvious that a good distance on…
Distance-based metrics, such as the Hausdorff distance (HD), are widely used to validate segmentation performance in (bio)medical imaging. However, their implementation is complex, and critical differences across open-source tools remain…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
We define edit distance for hierarchically structured data compatible with the hierarchical multi-instance learning paradigm. Example of such data is dataset represented in JSON format where inner Array objects are interpreted as unordered…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…
We propose the Fr\'echet Audio Distance (FAD), a novel, reference-free evaluation metric for music enhancement algorithms. We demonstrate how typical evaluation metrics for speech enhancement and blind source separation can fail to…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by…