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Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this…
Among various distance functions for graphs, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a…
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…
Detecting poorly textured objects and estimating their 3D pose reliably is still a very challenging problem. We introduce a simple but powerful approach to computing descriptors for object views that efficiently capture both the object…
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast…
The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
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…
Data clustering, the task of grouping observations according to their similarity, is a key component of unsupervised learning -- with real world applications in diverse fields such as biology, medicine, and social science. Often in these…
We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…
Learning a metric of natural image patches is an important tool for analyzing images. An efficient means is to train a deep network to map an image patch to a vector space, in which the Euclidean distance reflects patch similarity. Previous…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…