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Many data-based statistical algorithms require that one find \textit{near or nearest neighbors} to a given vector among a set of points in that vector space, usually with Euclidean topology. The k-d data structure and search algorithms are…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Matthew B. Kennel

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…

Computational Geometry · Computer Science 2021-04-01 Ahmed Abdelkader , David M. Mount

Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index, which replaces or complements traditional index structures with machine learning models, has been actively…

Databases · Computer Science 2022-08-01 Yao Tian , Tingyun Yan , Xi Zhao , Kai Huang , Xiaofang Zhou

The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…

Computational Geometry · Computer Science 2025-02-20 Tuyen Pham , Hubert Wagner

In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…

Machine Learning · Computer Science 2023-08-21 Jochen Jankowai , Talha Bin Masood , Ingrid Hotz

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

Machine Learning · Computer Science 2016-12-06 Ehsan Amid , Aristides Gionis , Antti Ukkonen

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Machine Learning · Computer Science 2020-07-08 Silviu Pitis , Harris Chan , Kiarash Jamali , Jimmy Ba

Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series…

We propose a family of graph structural indices related to the Matrix-forest theorem. The properties of the basic index that expresses the mutual connectivity of two vertices are studied in detail. The derivative indices that measure…

Combinatorics · Mathematics 2007-05-23 Pavel Chebotarev , Elena Shamis

This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed…

Data Structures and Algorithms · Computer Science 2021-12-22 Jeffrey Uhlmann , Miguel R. Zuniga

In this paper we investigate the geometric properties of quasi-trees, and prove some equivalent criteria. We give a general construction of a tree that approximates the ends of a geodesic space, and use this to prove that every quasi-tree…

Metric Geometry · Mathematics 2023-08-28 Alice Kerr

The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity,…

Information Retrieval · Computer Science 2016-11-17 Vladimir Pestov

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

General Mathematics · Mathematics 2025-05-01 Abeeb A. Awotunde

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…

Discrete Mathematics · Computer Science 2023-03-16 Eloi Araujo , Fábio V. Martinez , Carlos H. A. Higa , José Soares

Approximate k-Nearest Neighbour (ANN) methods are often used for mining information and aiding machine learning on large scale high-dimensional datasets. ANN methods typically differ in the index structure used for accelerating searches,…

Machine Learning · Computer Science 2025-02-04 Ben Harwood , Amir Dezfouli , Iadine Chades , Conrad Sanderson

Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…

Combinatorics · Mathematics 2022-01-06 Juan M. Alonso

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Computational Geometry · Computer Science 2019-03-20 Diego Ihara Centurion , Neshat Mohammadi , Anastasios Sidiropoulos

Image retrieval methods rely on metric learning to train backbone feature extraction models that can extract discriminant queries and reference (gallery) feature representations for similarity matching. Although state-of-the-art accuracy…

Computer Vision and Pattern Recognition · Computer Science 2024-12-12 Madhu Kiran , Kartikey Vishnu , Rafael M. O. Cruz , Eric Granger

As online dating has become more popular in the past few years, an efficient and effective algorithm to match users is needed. In this project, we proposed a new dating matching algorithm that uses Kendall-Tau distance to measure the…

Information Retrieval · Computer Science 2023-08-11 Wenqi Guo , Jeffrey Uhlmann

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…

Databases · Computer Science 2020-01-17 Tobias Emrich , Hans-Peter Kriegel , Andreas Züfle , Peer Kröger , Matthias Renz