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IDistance
In pattern recognition, iDistance is an indexing and query processing technique for ''k''-nearest neighbor queries on point data in multi-dimensional metric spaces. The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. iDistance is designed to process kNN queries in high-dimensional spaces efficiently and performs extremely well for skewed data distributions, which usually occur in real-life data sets. iDistance employs a two-phase search strategy involving an initial filtering of candidate regions and a subsequent refinement of results, an approach aligned with the Filter and Refine Principle (FRP). This means that the index first prunes the search space to eliminate unlikely candidates, then verifies the true nearest neighbors in a refinement step, following the general FRP paradigm used in database search algorithms. The iDistance index can also be augmented with machine learning models to learn data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Recognition
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-nearest Neighbors Algorithm
In statistics, the ''k''-nearest neighbors algorithm (''k''-NN) is a Non-parametric statistics, non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Lawson Hodges Jr., Joseph Hodges in 1951, and later expanded by Thomas M. Cover, Thomas Cover. Most often, it is used for statistical classification, classification, as a ''k''-NN classifier, the output of which is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its ''k'' nearest neighbors (''k'' is a positive integer, typically small). If ''k'' = 1, then the object is simply assigned to the class of that single nearest neighbor. The ''k''-NN algorithm can also be generalized for regression analysis, regression. In ''-NN regression'', also known as ''nearest neighbor smoothing'', the output is the property value for the object. This value is the average of the values of ''k'' nearest neighbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that w ... [...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] |
Curse Of Dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise when the number of datapoints is small (in a suitably defined sense) relative to the intrinsic dimension of the data. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data become sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewed Distribution
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real number, real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter And Refine
Filter and Refine Principle (FRP) is a general computational strategy in computer science. FRP is used broadly across various disciplines, particularly in information retrieval, database management, and pattern recognition, which efficiently processes large sets of objects through a two-stage approach: filtering and refinement. The filtering stage quickly eliminates less promising or irrelevant objects from a large set using efficient, less resource-intensive algorithms. This stage is designed to reduce the volume of data that needs to be processed in the more resource-demanding refinement stage. Following filtering, the refinement stage applies more complex and computationally expensive techniques to the remaining objects to achieve higher accuracy via finer-grained processing. This stage is essential for obtaining the desired quality and precision in the results. FRP is a general method for completing a computationally intensive task as quickly as possibleFilter and Refine S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idistance
In pattern recognition, iDistance is an indexing and query processing technique for ''k''-nearest neighbor queries on point data in multi-dimensional metric spaces. The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. iDistance is designed to process kNN queries in high-dimensional spaces efficiently and performs extremely well for skewed data distributions, which usually occur in real-life data sets. iDistance employs a two-phase search strategy involving an initial filtering of candidate regions and a subsequent refinement of results, an approach aligned with the Filter and Refine Principle (FRP). This means that the index first prunes the search space to eliminate unlikely candidates, then verifies the true nearest neighbors in a refinement step, following the general FRP paradigm used in database search algorithms. The iDistance index can also be augmented with machine learning models to learn data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster Analysis
Cluster analysis or clustering is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more Similarity measure, similar (in some specific sense defined by the analyst) 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 refers to a family of algorithms and tasks rather than one specific algorithm. 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 pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. Simplest case In the simplest case, shown in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B+ Tree
A B+ tree is an m-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. The root may be either a leaf or a node with two or more children. A B+ tree can be viewed as a B-tree in which each node contains only keys (not key–value pairs), and to which an additional level is added at the bottom with linked leaves. The primary value of a B+ tree is in storing data for efficient retrieval in a Block (data storage), block-oriented storage context—in particular, filesystems. This is primarily because unlike binary search trees, B+ trees have very high fanout (number of pointers to child nodes in a node, typically on the order of 100 or more), which reduces the number of I/O operations required to find an element in the tree. History There is no single paper introducing the B+ tree concept. Instead, the notion of maintaining all data in leaf nodes is repeatedly brought up as an interesting variant of the B- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sort Key
Collation is the assembly of written information into a standard order. Many systems of collation are based on numerical order or alphabetical order, or extensions and combinations thereof. Collation is a fundamental element of most office filing systems, library catalogs, and reference books. Collation differs from ''classification'' in that the classes themselves are not necessarily ordered. However, even if the order of the classes is irrelevant, the identifiers of the classes may be members of an ordered set, allowing a sorting algorithm to arrange the items by class. Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information (items with the same identifier are not placed in any defined order). A collation algorithm such as the Unicode collation algorithm defines an order through the process of comparing two given character strings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
