Related papers: A fast nearest neighbor search algorithm based on …
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
Curve-based representations, particularly integral curves, are often used to represent large-scale computational fluid dynamic simulations. Processing and analyzing curve-based vector field data sets often involves searching for neighboring…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…
The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…
Nearest neighbor (NN) graph based visual re-ranking has emerged as a powerful approach for improving retrieval accuracy, offering the advantages of effectively exploring high-dimensional manifolds without requiring additional fine-tuning.…
Approximate nearest neighbour (ANN) search is one of the most important problems in computer science fields such as data mining or computer vision. In this paper, we focus on ANN for high-dimensional binary vectors and we propose a simple…
Nearest neighbor search on high-dimensional vectors is fundamental in modern AI and database systems. In many real-world applications, queries involve constraints on multiple numeric attributes, giving rise to range-filtering approximate…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…
This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a…
Billion-scale high-dimensional approximate nearest neighbour (ANN) search has become an important problem for searching similar objects among the vast amount of images and videos available online. The existing ANN methods are usually…
Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points…
In our previous works, we proposed a physically-inspired rule to organize the data points into an in-tree (IT) structure, in which some undesired edges are allowed to occur. By removing those undesired or redundant edges, this IT structure…
This work addresses the problem of billion-scale nearest neighbor search. The state-of-the-art retrieval systems for billion-scale databases are currently based on the inverted multi-index, the recently proposed generalization of the…
This paper tackles the task of storing a large collection of vectors, such as visual descriptors, and of searching in it. To this end, we propose to approximate database vectors by constrained sparse coding, where possible atom weights are…
Image classification is an important task in the field of machine learning and image processing. However, the usually used classification method --- the K Nearest-Neighbor algorithm has high complexity, because its two main processes:…