Related papers: Analysis of approximate nearest neighbor searching…

We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…

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…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data…

When performing an analysis on a collection of molecular sequences, it can be convenient to reduce the number of sequences under consideration while maintaining some characteristic of a larger collection of sequences. For example, one may…

The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…

Modern neural network technologies, including large language models, have achieved remarkable success in various applied artificial intelligence applications, however, they face a range of fundamental limitations. Among them are…

Cluster analysis is one of the primary data analysis technique in data mining and K-means is one of the commonly used partitioning clustering algorithm. In K-means algorithm, resulting set of clusters depend on the choice of initial…

Given a collection of points in R^3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on space partitioning and spatial indexing techniques. However, when the query point is far from the data points or…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

We compare the performance of three nearest neighbor search algorithms: the Orchard, ball tree, and VP-tree algorithms. These algorithms are commonly used for nearest-neighbor searches and are known for their efficiency in large datasets.…

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…

Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…

A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to…

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a…

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…

Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees…