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MVP 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 Yia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Tree
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 are not applicable for the more gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Space
In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a Conceptual metaphor , metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different bra ... [...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 (i.e., the root node as the top-most node in the tree hierarchy). 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 (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the Function (computer programming), functions or Operator (computer programming), 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 database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up Identifier (computer languages), identifiers. Data s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...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. Dr. Uhlmann is ranked in the top 2% among scientists worldwide in the Stanford University listing of most-cited researchers. 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 Lectures on Quantum Computing'' series for Morgan & C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bregman Divergence
In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. When the points are interpreted as probability distributions – notably as either values of the parameter of a parametric model or as a data set of observed values – the resulting distance is a statistical distance. The most basic Bregman divergence is the squared Euclidean distance. Bregman divergences are similar to metrics, but satisfy neither the triangle inequality (ever) nor symmetry (in general). However, they satisfy a generalization of the Pythagorean theorem, and in information geometry the corresponding statistical manifold is interpreted as a (dually) flat manifold. This allows many techniques of optimization theory to be generalized to Bregman divergences, geometrically as generalizations of least squares. Bregman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-d Tree
In computer science, a ''k''-d tree (short for ''k-dimensional tree'') is a space-partitioning data structure for organizing points in a ''k''-dimensional space. K-dimensional is that which concerns exactly k orthogonal axes or a space of any number of dimensions. ''k''-d trees are a useful data structure for several applications, such as: * Searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches) & * Creating point clouds. ''k''-d trees are a special case of binary space partitioning trees. Description The ''k''-d tree is a binary tree in which ''every'' node is a ''k''-dimensional point. Every non-leaf node can be thought of as implicitly generating a splitting hyperplane that divides the space into two parts, known as half-spaces. Points to the left of this hyperplane are represented by the left subtree of that node and points to the right of the hyperplane are represented by the right subtree. The hyperplane direction is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node (computer Science)
A node is a basic unit of a data structure, such as a linked list or Tree (data structure), tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by Pointer (computer programming), pointers. Nodes and trees Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes may contain a value or condition, or possibly serve as another independent data structure. Nodes are represented by a single parent node. The highest point on a tree structure is called a root node, which does not have a parent node, but serves as the parent or 'grandparent' of all of the nodes below it in the tree. The height of a node is determined by the total number of edges on the path from that node to the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular node and the root node. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle Inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of Degeneracy (mathematics)#Triangle, degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality. If , , and are the lengths of the sides of a triangle then the triangle inequality states that :c \leq a + b , with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about vectors and vector lengths (Norm (mathematics), norms): :\, \mathbf u + \mathbf v\, \leq \, \mathbf u\, + \, \mathbf v\, , where the length of the third side has been replaced by the length of the vector sum . When and are real numbers, they can be viewed as vectors in \R^1, and the triang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trees (data Structures)
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
