Related papers: Distances for Comparing Multisets and Sequences
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
It is challenging to get access to datasets related to the physical performance of soccer players. The teams consider such information highly confidential, especially if it covers in-game performance.Hence, most of the analysis and…
In machine learning, the performance of a classifier depends on both the classifier model and the dataset. For a specific neural network classifier, the training process varies with the training set used; some training data make training…
Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity.…
Real-world images used for training machine learning algorithms are often unstructured and inconsistent. The process of analysing and tagging these images can be costly and error prone (also availability, gaps and legal conundrums).…
Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two…
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
Complex networks can be used for modeling street meshes and urban agglomerates. With such a model, many aspects of a city can be investigated to promote a better quality of life to its citizens. Along these lines, this paper proposes a set…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is…
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
K-means algorithm is a very popular clustering algorithm which is famous for its simplicity. Distance measure plays a very important rule on the performance of this algorithm. We have different distance measure techniques available. But…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
We consider the problem of determining the number of distinct distances between two point sets in $\mathbb{R}^2$ where one point set $\mathcal{P}_1$ of size $m$ lies on a real algebraic curve of fixed degree $r$, and the other point set…
We aim to select data subsets for the fine-tuning of large language models to more effectively follow instructions. Prior work has emphasized the importance of diversity in dataset curation but relied on heuristics such as the number of…