Related papers: Distances between Data Sets Based on Summary Stati…

We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.

Statistical distance measures have found wide applicability in information retrieval tasks that typically involve high dimensional datasets. In order to reduce the storage space and ensure efficient performance of queries, dimensionality…

Statistical moments of the intensity distributions are used as molecular descriptors. They are used as a basis for defining similarity distances between two model spectra. Parameters which carry the information derived from the comparison…

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the…

Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples…

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…

In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex…

Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…

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…

Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…

Metric learning makes it plausible to learn distances for complex distributions of data from labeled data. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well.…

We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…

Given two distinct datasets, an important question is if they have arisen from the the same data generating function or alternatively how their data generating functions diverge from one another. In this paper, we introduce an approach for…

Distance metric learning has attracted much attention in recent years, where the goal is to learn a distance metric based on user feedback. Conventional approaches to metric learning mainly focus on learning the Mahalanobis distance metric…

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…

Big Data involves both a large number of events but also many variables. This paper will concentrate on the challenge presented by the large number of variables in a Big Dataset. It will start with a brief review of exploratory data…

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…

Deep Learning performs well when training data densely covers the experience space. For complex problems this makes data collection prohibitively expensive. We propose to intelligently select samples when constructing data sets in order to…

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…