Milvus (vector Database)
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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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GitHub
GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug tracking system, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, GitHub, Inc. has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. GitHub reported having over 100 million developers and more than 420 million Repository (version control), repositories, including at least 28 million public repositories. It is the world's largest source code host Over five billion developer contributions were made to more than 500 million open source projects in 2024. About Founding The development of the GitHub platform began on October 19, 2005. The site was launched in April 2008 by Tom ...
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JSON
JSON (JavaScript Object Notation, pronounced or ) is an open standard file format and electronic data interchange, data interchange format that uses Human-readable medium and data, human-readable text to store and transmit data objects consisting of name–value pairs and array data type, arrays (or other serialization, serializable values). It is a commonly used data format with diverse uses in electronic data interchange, including that of web applications with server (computing), servers. JSON is a Language-independent specification, language-independent data format. It was derived from JavaScript, but many modern programming languages include code to generate and parse JSON-format data. JSON filenames use the extension .json. Douglas Crockford originally specified the JSON format in the early 2000s. Transcript: He and Chip Morningstar sent the first JSON message in April 2001. Naming and pronunciation The 2017 international standard (ECMA-404 and ISO/IEC 21778:2017) ...
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Inverted Index
In computer science, an inverted index (also referred to as a postings list, postings file, or inverted file) is a database index storing a mapping from content, such as words or numbers, to its locations in a table, or in a document or a set of documents (named in contrast to a forward index, which maps from documents to content). The purpose of an inverted index is to allow fast full-text searches, at a cost of increased processing when a document is added to the database. The inverted file may be the database file itself, rather than its index. It is the most popular data structure used in document retrieval systems, used on a large scale for example in search engines. Additionally, several significant general-purpose mainframe-based database management systems have used inverted list architectures, including ADABAS, DATACOM/DB, and Model 204. There are two main variants of inverted indexes: A record-level inverted index (or inverted file index or just inverted file) contain ...
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Hierarchical Navigable Small World
The Hierarchical navigable small world (HNSW) algorithm is a graph-based 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 Applications (SISAP) conference in 2012 with an additional hierarchical navig ...
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Nearest Neighbor Search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set ''S'' of points in a space ''M'' and a query point ''q'' ∈ ''M'', find the closest point in ''S'' to ''q''. Donald Knuth in vol. 3 of '' The Art of Computer Programming'' (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post office. A direct generalization of this problem is a ''k''-NN search, where we need to find the ''k'' closest points. Most commonly ''M'' is a metric space and dissimilarity is expressed as a distance metric, which is symmetric and satisfies the triangle inequality. Even more common, ''M'' is take ...
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Binary Data
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including '' bit'' (binary digit) in computer science, '' truth value'' in mathematical logic and related domains and '' binary variable'' in statistics. Mathematical and combinatoric foundations A discrete variable that can take only one state contains zero information, and is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three dec ...
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Jaccard Distance
The Jaccard index is a statistic used for gauging the similarity and diversity of sample sets. It is defined in general taking the ratio of two sizes (areas or volumes), the intersection size divided by the union size, also called intersection over union (IoU). It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v) and now is often called the critical success index in meteorology. It was later developed independently by Paul Jaccard, originally giving the French name (coefficient of community), and independently formulated again by Taffee Tadashi Tanimoto. Thus, it is also called Tanimoto index or Tanimoto coefficient in some fields. Overview The Jaccard index measures similarity between finite non-empty sample sets and is defined as the size of the intersection divided by the size of the union of the sample sets: : J(A, B) = \frac = \frac. Note that by design, 0 \le J(A, B) \le 1. If the sets A and B have no elements in common, their intersectio ...
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Hamming Distance
In information theory, the Hamming distance between two String (computer science), strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to change one string into the other, or equivalently, the minimum number of ''errors'' that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming. A major application is in coding theory, more specifically to block codes, in which the equal-length strings are Vector space, vectors over a finite field. Definition The Hamming distance between two equal-length strings of symbols is the number of positions at which the corresponding symbols are different. Examples The symbols may be letters, bits, or decimal digits, am ...
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Floating-point Numbers
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the corresponding real number arithmetic operations ...
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Cosine Distance
In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not depend on the magnitudes of the vectors, but only on their angle. The cosine similarity always belongs to the interval 1, +1 For example, two proportional vectors have a cosine similarity of +1, two orthogonal vectors have a similarity of 0, and two opposite vectors have a similarity of −1. In some contexts, the component values of the vectors cannot be negative, in which case the cosine similarity is bounded in ,1/math>. For example, in information retrieval and text mining, each word is assigned a different coordinate and a document is represented by the vector of the numbers of occurrences of each word in the document. Cosine similarity then gives a use ...
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Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two Euclidean vector, vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the Product (mathematics), products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euc ...
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Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's ''Elements'', distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances b ...
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