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Metric Trees
A metric tree is any tree data structure specialized to index data in metric spaces. Metric trees exploit properties of metric spaces such as the triangle inequality to make accesses to the data more efficient. Examples include the M-tree, vp-trees, cover trees, MVP trees, and BK-trees. Multidimensional search Most algorithms and data structures for searching a dataset are based on the classical binary search algorithm, and generalizations such as the k-d tree or range tree work by interleaving the binary search algorithm over the separate coordinates and treating each spatial coordinate as an independent search constraint. These data structures are well-suited for range query problems asking for every point (x,y) that satisfies \mbox_x \leq x \leq \mbox_x and \mbox_y \leq y \leq \mbox_y. A limitation of these multidimensional search structures is that they are only defined for searching over objects that can be treated as vectors. They aren't applicable for the more general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (data Structure)
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent. These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Search Algorithm
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Naval Research Laboratory
The United States Naval Research Laboratory (NRL) is the corporate research laboratory for the United States Navy and the United States Marine Corps. It was founded in 1923 and conducts basic scientific research, applied research, technological development and prototyping. The laboratory's specialties include plasma physics, space physics, materials science, and tactical electronic warfare. NRL is one of the first US government scientific R&D laboratories, having opened in 1923 at the instigation of Thomas Edison, and is currently under the Office of Naval Research. As of 2016, NRL was a Navy Working Capital Fund activity, which means it is not a line-item in the US Federal Budget. Instead of direct funding from Congress, all costs, including overhead, were recovered through sponsor-funded research projects. NRL's research expenditures were approximately $1 billion per year. Research The Naval Research Laboratory conducts a wide variety of basic research and applied re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matlab (programming Language)
MATLAB (an abbreviation of "MATrix LABoratory") is a Proprietary software, proprietary multi-paradigm programming language, multi-paradigm programming language and numerical analysis, numeric computing environment developed by MathWorks. MATLAB allows matrix (mathematics), matrix manipulations, plotting of function (mathematics), functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD computer algebra system, symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamical system, dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergey Brin
Sergey Mikhailovich Brin (russian: link=no, Сергей Михайлович Брин; born August 21, 1973) is an American business magnate, computer scientist, and internet entrepreneur, who co-founded Google with Larry Page. Brin was the president of Google's parent company, Alphabet Inc., until stepping down from the role on December 3, 2019. He and Page remain at Alphabet as co-founders, controlling shareholders, board members, and employees. As of November 2022, Brin is the 12th-richest person in the world, with an estimated net worth of $78.0 billion. Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his bachelor's degree at the University of Maryland, College Park, following in his father's and grandfather's footsteps by studying mathematics, as well as computer science. After graduation, he enrolled in Stanford University to acquire a PhD in computer science. There he met Page, with whom he built a web search e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vantage-point Tree
A vantage-point tree (or VP tree) is a metric tree that segregates data in a metric space by choosing a position in the space (the "vantage point") and partitioning the data points into two parts: those points that are nearer to the vantage point than a threshold, and those points that are not. By recursively applying this procedure to partition the data into smaller and smaller sets, a tree data structure is created where neighbors in the tree are likely to be neighbors in the space. One generalization is called a multi-vantage-point tree (or MVP tree): a data structure for indexing objects from large metric spaces for similarity search queries. It uses more than one point to partition each level. History Peter Yianilos claimed that the vantage-point tree was discovered independently by him (Peter Yianilos) and by Jeffrey Uhlmann. Yet, Uhlmann published this method before Yianilos in 1991. Uhlmann called the data structure a metric tree, the name VP-tree was proposed by Yianilo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeffrey Uhlmann
Jeffrey K. Uhlmann is an American research scientist who is probably best known for his mathematical generalizations of the Kalman filter. Most of his publications and patents have been in the field of data fusion. He is also known for being a cult filmmaker and former recording artist. Uhlmann has also began a career in YouTube under the anonymous persona uhlmannj with two feature videos: Man With No Hat, and The Glass. Both videos have gained hundreds of views. Biography Uhlmann has degrees in philosophy, computer science, and a doctorate in robotics from the University of Oxford. He began work in 1987 at NRL's Laboratory for Computational Physics and Fluid Dynamics in Washington, DC, and remained at NRL until 2000. Since 2000 he has been a professor of computer science at the University of Missouri. He served for ten years as a co-founding member of the editorial board of the ''ACM Journal of Experimental Algorithmics'' (1995–2006) before becoming co-editor of the ''Synthesis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brute Force Search
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement. A brute-force algorithm that finds the divisors of a natural number ''n'' would enumerate all integers from 1 to n, and check whether each of them divides ''n'' without remainder. A brute-force approach for the eight queens puzzle would examine all possible arrangements of 8 pieces on the 64-square chessboard and for each arrangement, check whether each (queen) piece can attack any other. While a brute-force search is simple to implement and will always find a solution if it exists, implementation costs are proportional to the number of candidate solutionswhich in many practical problems tends to grow very quickly as the size of the problem increases ( §Combinator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similarity Measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Use in clustering In spectral clustering, a similarity, or affinity, measure is used to transform data to overcome difficulties related to lack of convexity in the shape of the data distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Query
A range query is a common database operation that retrieves all records where some value is between an upper and lower boundary. For example, list all employees with 3 to 5 years' experience. Range queries are unusual because it is not generally known in advance how many entries a range query will return, or if it will return any at all. Many other queries, such as the top ten most senior employees, or the newest employee, can be done more efficiently because there is an upper bound to the number of results they will return. A query that returns exactly one result is sometimes called a singleton. Partial match query Match at least one of the requested keys. *B+ tree * k-d tree * R-tree See also * Range searching In computer science, the range searching problem consists of processing a set ''S'' of objects, in order to determine which objects from ''S'' intersect with a query object, called the ''range''. For example, if ''S'' is a set of points correspond ... References Dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Tree
In computer science, a range tree is an ordered tree data structure to hold a list of points. It allows all points within a given range to be reported efficiently, and is typically used in two or higher dimensions. Range trees were introduced by Jon Louis Bentley in 1979. Similar data structures were discovered independently by Lueker, Lee and Wong, and Willard. The range tree is an alternative to the ''k''-d tree. Compared to ''k''-d trees, range trees offer faster query times of (in Big O notation) O(\log^dn+k) but worse storage of O(n\log^ n), where ''n'' is the number of points stored in the tree, ''d'' is the dimension of each point and ''k'' is the number of points reported by a given query. Bernard Chazelle improved this to query time O(\log^ n + k) and space complexity O\left(n\left(\frac\right)^\right). Data structure A range tree on a set of 1-dimensional points is a balanced binary search tree on those points. The points stored in the tree are stored in the leav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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