相关论文: Infinity Search: Approximate Vector Search with Pr…

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…

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…

Fast k-Nearest Neighbor search over real-valued vector spaces (KNN) is an important algorithmic task for information retrieval and recommendation systems. We present a method for using reduced precision to represent vectors through…

We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…

The generation and collection of big data series are becoming an integral part of many emerging applications in sciences, IoT, finance, and web applications among several others. The terabyte-scale of data series has motivated recent…

In this work we explore the use of metric index structures, which accelerate nearest neighbor queries, in the scenario where we need to interleave insertions and queries during deployment. This use-case is inspired by a real-life need in…

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…

We introduce two spectral invariants of finite metric spaces, the $q$-spectrum and the transition $q$-spectrum, defined from similarity matrices. These invariants extend the adjacency and Laplacian spectra of graphs to general finite metric…

Similarity searching finds application in a wide variety of domains including multilingual databases, computational biology, pattern recognition and text retrieval. Similarity is measured in terms of a distance function, edit distance, in…

The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…

Vector representations and vector space modeling (VSM) play a central role in modern machine learning. We propose a novel approach to `vector similarity searching' over dense semantic representations of words and documents that can be…

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…

We present a new approach for efficient approximate nearest neighbor (ANN) search in high dimensional spaces, extending the idea of Product Quantization. We propose a two-level product and vector quantization tree that reduces the number of…

We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

For many years, exact metric search relied upon the property of triangle inequality to give a lower bound on uncalculated distances. Two exclusion mechanisms derive from this property, generally known as pivot exclusion and hyperplane…

Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi\colon X\to Y$. We find a structural characteristic of finite…

In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet. Using unequal costs coding, we associate a length function with each such fractal tree and show…

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…