相关论文: Approximate Algorithms for Chamfer Distance Under …

The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…

Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves'…

In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…

We study the problem of computing the Fr\'echet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves $\pi$ and $\sigma$ of total complexity $n$ and a threshold…

We design an additive approximation scheme for estimating the cost of the min-weight bipartite matching problem: given a bipartite graph with non-negative edge costs and $\varepsilon > 0$, our algorithm estimates the cost of matching all…

Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a…

The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…

Earth Mover's Distance (EMD) is an important similarity measure between two distributions, used in computer vision and many other application domains. However, its exact calculation is computationally and memory intensive, which hinders its…

The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis…

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…

An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by…

Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet distance for a…

Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for…

We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…

In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…

The Fr\'echet distance is a similarity measure between two curves $A$ and $B$: Informally, it is the minimum length of a leash required to connect a dog, constrained to be on $A$, and its owner, constrained to be on $B$, as they walk…

Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…

We propose an algorithm for approximative dictionary lookup, where altered strings are matched against reference forms. The algorithm makes use of a divergence function between strings -- broadly belonging to the family of edit distances;…

The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…