Hierarchical Navigable Small World Graphs
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Hierarchical Navigable Small World Graphs
The Hierarchical navigable small world (HNSW) algorithm is a graph (discrete mathematics), graph-based Nearest neighbor search#Approximation methods, approximate nearest neighbor search technique used in many vector databases. Nearest neighbor search without an index involves computing the distance from the query to each point in the database, which for large datasets is computationally prohibitive. For high-dimensional data, tree-based exact vector search techniques such as the k-d tree and R-tree do not perform well enough because of the curse of dimensionality. To remedy this, ''approximate'' k-nearest neighbor searches have been proposed, such as locality-sensitive hashing (LSH) and product quantization (PQ) that trade performance for accuracy. The HNSW graph offers an approximate k-nearest neighbor search which scales logarithmically even in high-dimensional data. It is an extension of the earlier work on navigable small world graphs presented at the Similarity Search and Ap ...
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Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ...
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MariaDB
MariaDB is a community-developed, commercially supported Fork (software development), fork of the MySQL relational database management system (RDBMS), intended to remain free and open-source software under the GNU General Public License. Development is led by some of the original developers of MySQL, who forked it due to concerns over its takeover, acquisition by Oracle Corporation in 2009, but in 2024 MariaDB plc was itself bought by the K1 private equity group, which appointed a new CEO. MariaDB is intended to maintain high compatibility with MySQL, with exact matching with MySQL Application programming interface, APIs and commands, allowing it in many cases to function as a drop-in replacement for MySQL. However, new features are diverging. It includes new storage engines like Aria (storage engine), Aria, InfiniDB, ColumnStore, and MyRocks. Its CTO is Michael Widenius, Michael "Monty" Widenius, one of the founders of MySQL AB and the founder of Monty Program AB. On 16 January ...
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Database Index Techniques
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data have become widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash cards ...
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Search Algorithms
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. Although search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm to use often depends on the data structure being searched, and may also include prior knowledge about the data. Search algorithms can be made faster or more efficient by specially constructed database structures, such as search trees, hash maps, and database indexes. Search algorithms can be classified based on their mechanism of searching into three types of algorithms: linear, binary, and hashing. Linear search algorithms check every record for the one associated with a target key in a linear fashion. Binary, or half-interval, searches repeatedly target ...
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Network Science
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, Cognitive network, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by ''nodes'' (or ''vertices'') and the connections between the elements or actors as ''links'' (or ''edges''). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential statistics, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena." Background and history The study of networks has emerged in diverse disciplines as a means of analyzing complex relational ...
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Graphs
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties * Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function * Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning *Microsoft Graph, a Microsoft API developer platform that connects multiple services and devices Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also * Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Stati ...
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FAISS
FAISS (Facebook AI Similarity Search) is an open-source library for similarity search and clustering of vectors. It contains algorithms that search in sets of vectors of any size, up to ones that possibly do not fit in RAM. It also contains supporting code for evaluation and parameter tuning. FAISS is written in C++ with complete wrappers for Python and C. Some of the most useful algorithms are implemented on the GPU using CUDA. Features FAISS is organized as a toolbox that contains a variety of indexing methods that commonly involve a chain of components (preprocessing, compression, non-exhaustive search, etc.). The scope of the library is intentionally limited to focus on ANNS algorithmic implementation and to avoid facilities related to database functionality, distributed computing or feature extraction algorithms. FAISS is designed with the following assumptions: * Primary data type for vector representation is FP32. The support of other floating-point formats, s ...
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Kuzu (graph Database)
The were a people of ancient Japan believed to have lived along the Yoshino River in Nara Prefecture. They were mentioned in the Kojiki and Nihon Shoki. The name was also used for a population living in the old Hitachi province (today's Ibaraki Prefecture) mentioned by the Hitachi Fudoki. Their name may be at the origin of the name of the kudzu Kudzu (), also called Japanese arrowroot or Chinese arrowroot, is a group of climbing, coiling, and trailing deciduous perennial vines native to much of East Asia, Southeast Asia, and some Pacific islands. It is invasive species, invasive in ... plant, supposedly for being associated with the harvest and sale of kudzu roots or starch extracted from them. References Ancient Japan Tribes of ancient Japan {{japan-hist-stub ...
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DuckDB
DuckDB is an open-source column-oriented Relational Database Management System (RDBMS). It is designed to provide high performance on complex queries against large databases in embedded configuration, such as combining tables with hundreds of columns and billions of rows. Unlike other embedded databases (for example, SQLite) DuckDB is not focusing on transactional (OLTP) applications and instead is specialized for online analytical processing (OLAP) workloads. The project has over 6 million downloads per month. History DuckDB was originally developed by Mark Raasveldt and Hannes Mühleisen at the Centrum Wiskunde & Informatica (CWI) in the Netherlands. The project co-founders designed DuckDB to address the need for an in-process OLAP database solution. DuckDB was first released in 2019. DuckDB version 1.0.0 was released on June 3, 2024, under the codename SnowDuck. Features DuckDB uses a vectorized query processing engine. DuckDB is special amongst database management ...
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Milvus (vector Database)
Milvus is a distributed vector database developed by Zilliz. It is available as both open-source software and a cloud service. Milvus is an open-source project under LF AI & Data Foundation distributed under the Apache License 2.0. History Milvus has been developed by Zilliz since 2017. Milvus joined Linux Foundation as an incubation project in and became a graduate in . The details about its architecture and possible applications were presented on ACM SIGMOD Conference in 2021 Milvus 2.0, a major redesign of the whole product with a new architecture, was released in . Features Similarity search Major similarity search related features that are available in the active 2.4.x Milvus branch: * In-memory, on-disk and GPU indices, * Single query, batch query and range query search, * Support of sparse vectors, binary vectors, JSON and arrays, * FP32, FP16 and BF16 data types, * Euclidean distance, inner product distance and cosine distance support for floating-point da ...
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ClickHouse
ClickHouse is an open-source column-oriented DBMS (columnar database management system) for online analytical processing (OLAP) that allows users to generate analytical reports using SQL queries in real-time. ClickHouse Inc. is headquartered in the San Francisco Bay Area with the subsidiary, ClickHouse B.V., based in Amsterdam, Netherlands. In September 2021 in San Francisco, CA, ClickHouse incorporated to house the open source technology with an initial $50 million investment from Index Ventures and Benchmark Capital with participation by Yandex N.V. and others. On October 28, 2021 the company received Series B funding totaling $250 million at a valuation of $2 billion from Coatue Management, Altimeter Capital, and other investors. The company continues to build the open source project and engineering cloud technology. History ClickHouse’s technology was first developed over 10 years ago at Yandex, Russia's largest technology company. In 2009, Alexey Milovidov and developer ...
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