Related papers: Simple Distances for Trajectories via Landmarks
When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…
Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…
In $K$-means classification, a set of data will form clusters, i.e. classes, if the measured distances between data points (or some common point in each class) are below a certain threshold. With the assumption that the data points are…
The primary distance indicators are established in our Galaxy and the Local Group. There are at least four different methods which give good distances: methods using proper motions, RR Lyraes, Cepheid variables, and Type II supernovae.…
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Since there is no effective formula to compute the distance of a point and a set, it is hard to…
We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTASs) to several well-known problems in Computational Geometry, such as $k$-center clustering and farthest nearest neighbor.…
We present a method for determining the unknown location of a sensor placed in a known 2D environment in the presence of unknown dynamic obstacles, using only few distance measurements. We present guarantees on the quality of the…
We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose…
In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
The rise of synoptic sky surveys has ushered in an era of big data in time-domain astronomy, making data science and machine learning essential tools for studying celestial objects. While tree-based models (e.g. Random Forests) and deep…
In this paper, we propose a novel trajectory learning method that exploits motion trajectories on topological map using recurrent neural network for temporally consistent geolocalization of object. Inspired by human's ability to both be…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to…
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…
The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use…
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…