Related papers: Simple Distances for Trajectories via Landmarks

Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…

The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…

The development of approaches for trajectory prediction requires metrics to validate and compare their performance. Currently established metrics are based on Euclidean distance, which means that errors are weighted equally in all…

Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…

For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…

We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.

We introduce a new type of distinct distances result: a lower bound on the number of distances between points on a line and points on a two-dimensional strip. This can be seen as a generalization of the well-studied problems of distances…

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…

We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…

An efficient algorithm is required to extract moving objects (asteroids, satellites, and space debris) from enormous data with advances in observational instruments. We have developed an algorithm, tracee, to swiftly detect points aligned…

Many modern wireless devices with accurate positioning needs also have access to vision sensors, such as a camera, radar, and Light Detection and Ranging (LiDAR). In scenarios where wireless-based positioning is either inaccurate or…

For non-empty sets X we define notions of distance and pseudo metric with values in a partially ordered set that has a smallest element $\theta $. If $h_X$ is a distance in $X$ (respectively, a pseudo metric in $X$), then the pair $(X,h_X)$…