Related papers: Parallel Nearest Neighbors in Low Dimensions with …
In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph…
K-nearest neighbor search is one of the fundamental tasks in various applications and the hierarchical navigable small world (HNSW) has recently drawn attention in large-scale cloud services, as it easily scales up the database while…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
Incremental data mining algorithms process frequent updates to dynamic datasets efficiently by avoiding redundant computation. Existing incremental extension to shared nearest neighbor density based clustering (SNND) algorithm cannot handle…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
This paper proposes an efficient data structure, ikd-Tree, for dynamic space partition. The ikd-Tree incrementally updates a k-d tree with new coming points only, leading to much lower computation time than existing static k-d trees.…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
A buffer k-d tree is a k-d tree variant for massively-parallel nearest neighbor search. While providing valuable speed-ups on modern many-core devices in case both a large number of reference and query points are given, buffer k-d trees are…
We describe a simple and fast algorithm for identifying friends-of-friends features and prove its correctness. The algorithm avoids unnecessary expensive neighbor queries, uses minimal memory overhead, and rejects slowdown in high…
We present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain $P$ with $n$ vertices. Our goal is to store a dynamic set of $m$ point sites…
We study the classic Euclidean Minimum Spanning Tree (MST) problem in the Massively Parallel Computation (MPC) model. Given a set $X \subset \mathbb{R}^d$ of $n$ points, the goal is to produce a spanning tree for $X$ with weight within a…
High-performance implementations of $k$-Nearest Neighbor Search ($k$NN) in low dimensions use tree-based data structures. Tree algorithms are hard to parallelize on GPUs due to their irregularity. However, newer Nvidia GPUs offer hardware…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
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…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…