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R Tree
R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" (to display them in a navigation system) or "find the nearest gas station" (although not taking roads into account). The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance. R-tree idea The key idea of the data structure is to group nearby objects and represent t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antonin Guttman
Antonin may refer to: People * Antonin (name) Places ;Poland * Antonin, Jarocin County, Greater Poland Voivodeship * Antonin, Kalisz County, Greater Poland Voivodeship * Antonin, Oborniki County, Greater Poland Voivodeship * Antonin, Ostrów Wielkopolski County, Greater Poland Voivodeship * Antonin, Poznań County, Greater Poland Voivodeship * Antonin, Środa Wielkopolska County, Greater Poland Voivodeship * Antonin, Sieradz County, Łódź Voivodeship * Antonin, Zduńska Wola County, Łódź Voivodeship * Antonin, Masovian Voivodeship * Antonin, Podlaskie Voivodeship * Antonin, Pomeranian Voivodeship * Antonin, part of Nowe Miasto, Poznań, Greater Poland Voivodeship See also *Antolin (name) *Antonina (other) *Antonini (other) *Antonino (other) *Antoniny (other) *Antoninus (other) *Antoniu *Antonen Antonen is a Finnish surname. Notable people with the surname include: *Joose Antonen (born 1995), Finnish ice hockey player *Juuso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worst-case Performance
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Child Node
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 tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leaf Node
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 tree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-tree
In computer science tree data structures, an X-tree (for ''eXtended node tree'') is an index tree structure based on the R-tree used for storing data in many dimensions. It appeared in 1996, and differs from R-trees (1984), R+-trees (1987) and R*-trees (1990) because it emphasizes prevention of overlap in the bounding boxes, which increasingly becomes a problem in high dimensions. In cases where nodes cannot be split without preventing overlap, the node split will be deferred, resulting in super-nodes. In extreme cases, the tree will linearize, which defends against worst-case behaviors observed in some other data structures. Structure The X-tree consists of three different types of nodes—data nodes, normal directory nodes and supernodes. The data nodes of the X-tree contain rectilinear minimum bounding rectangle In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents of a two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert R-tree
Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects. The performance of R-trees depends on the quality of the algorithm that clusters the data rectangles on a node. Hilbert R-trees use space-filling curves, and specifically the Hilbert curve, to impose a linear ordering on the data rectangles. There are two types of Hilbert R-trees: one for static databases, and one for dynamic databases. In both cases Hilbert space-filling curves are used to achieve better ordering of multidimensional objects in the node. This ordering has to be "good", in the sense that it should group "similar" data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Packed Hilbert R-trees are suitable for static databases in which updates are very rare or in which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R+ Tree
R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" (to display them in a navigation system) or "find the nearest gas station" (although not taking roads into account). The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance. R-tree idea The key idea of the data structure is to group nearby objects and represent t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R*-tree
In data processing R*-trees are a variant of R-trees used for indexing spatial information. R*-trees have slightly higher construction cost than standard R-trees, as the data may need to be reinserted; but the resulting tree will usually have a better query performance. Like the standard R-tree, it can store both point and spatial data. It was proposed by Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, and Bernhard Seeger in 1990. Difference between R*-trees and R-trees Minimization of both coverage and overlap is crucial to the performance of R-trees. Overlap means that, on data query or insertion, more than one branch of the tree needs to be expanded (due to the way data is being split in regions which may overlap). A minimized coverage improves pruning performance, allowing exclusion of whole pages from search more often, in particular for negative range queries. The R*-tree attempts to reduce both, using a combination of a revised node split algorithm and the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OPTICS Algorithm
Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major weaknesses: the problem of detecting meaningful clusters in data of varying density. To do so, the points of the database are (linearly) ordered such that spatially closest points become neighbors in the ordering. Additionally, a special distance is stored for each point that represents the density that must be accepted for a cluster so that both points belong to the same cluster. This is represented as a dendrogram. Basic idea Like DBSCAN, OPTICS requires two parameters: , which describes the maximum distance (radius) to consider, and , describing the number of points required to form a cluster. A point is a ''core point'' if at least points are found within its -neighborhood N_\vare ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster Analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistics, statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small Distance function, distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Outlier Factor
In anomaly detection, the local outlier factor (LOF) is an algorithm proposed by Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng and Jörg Sander in 2000 for finding anomalous data points by measuring the local deviation of a given data point with respect to its neighbours. LOF shares some concepts with DBSCAN and OPTICS such as the concepts of "core distance" and "reachability distance", which are used for local density estimation. Basic idea The local outlier factor is based on a concept of a local density, where locality is given by ''k'' nearest neighbors, whose distance is used to estimate the density. By comparing the local density of an object to the local densities of its neighbors, one can identify regions of similar density, and points that have a substantially lower density than their neighbors. These are considered to be outliers. The local density is estimated by the typical distance at which a point can be "reached" from its neighbors. The definition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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