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Nearest-neighbor Density Estimator
Nearest neighbor may refer to: * Nearest neighbor search in pattern recognition and in computational geometry * Nearest-neighbor interpolation for interpolating data * Nearest neighbor graph in geometry * Nearest neighbor function in probability theory * Nearest neighbor decoding in coding theory * The k-nearest neighbor algorithm in machine learning, an application of generalized forms of nearest neighbor search and interpolation * The nearest neighbour algorithm for approximately solving the travelling salesman problem * The nearest neighbor method for determining the thermodynamics of nucleic acids * The nearest neighbor method for calculating distances between clusters in hierarchical clustering In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into .... See also * Moore neigh ... [...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 taken ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Recognition
Pattern recognition is the automated recognition of patterns and regularities in data. It 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. These activities can be viewed as two facets of the same field of application, and they have undergone substantial development over the past few decades. 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 stronger connection to business use. Pattern recognition focuses more on the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest-neighbor Interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping) in real-time 3D rendering to select color values for a textured surface. Connection to Voronoi diagram For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbour interpolation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest Neighbor Graph
The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from ''p'' to ''q'' whenever ''q'' is a nearest neighbor of ''p'', a point whose distance from ''p'' is minimum among all the given points other than ''p'' itself. In many uses of these graphs, the directions of the edges are ignored and the NNG is defined instead as an undirected graph. However, the nearest neighbor relation is not a symmetric one, i.e., ''p'' from the definition is not necessarily a nearest neighbor for ''q''. In theoretical discussions of algorithms a kind of general position is often assumed, namely, the nearest (k-nearest) neighbor is unique for each object. In implementations of the algorithms it is necessary to bear in mind that this is not always the case. For situations in which it is necessary to make the nearest neighbor for each object unique, the set '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest Neighbor Function
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution,A. Baddeley, I. Bárány, and R. Schneider. Spatial point processes and their applications. ''Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004'', pages 1–75, 2007. nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. ''Stochastic geometry and its applications'', volume 2. Wiley Chichester, 1995.D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, second edition, 2003. More specifically, nearest neighbor func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest Neighbor Decoding
In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel. Notation C \subset \mathbb_2^n is considered a binary code with the length n; x,y shall be elements of \mathbb_2^n; and d(x,y) is the distance between those elements. Ideal observer decoding One may be given the message x \in \mathbb_2^n, then ideal observer decoding generates the codeword y \in C. The process results in this solution: :\mathbb(y \mbox \mid x \mbox) For example, a person can choose the codeword y that is most likely to be received as the message x after transmission. Decoding conventions Each codeword does not have an expected possibility: there may be more than one codeword with an equal likelihood of mutating into the received message. In such a case, the sender and receiver(s) must a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-nearest Neighbor Algorithm
In statistics, the ''k''-nearest neighbors algorithm (''k''-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the ''k'' closest training examples in a data set. The output depends on whether ''k''-NN is used for classification or regression: :* In ''k-NN classification'', the output 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. :* In ''k-NN regression'', the output is the property value for the object. This value is the average of the values of ''k'' nearest neighbors. If ''k'' = 1, then the output is simply assigned to the v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest Neighbour Algorithm
The nearest neighbour algorithm was one of the first algorithms used to solve the travelling salesman problem approximately. In that problem, the salesman starts at a random city and repeatedly visits the nearest city until all have been visited. The algorithm quickly yields a short tour, but usually not the optimal one. Algorithm These are the steps of the algorithm: # Initialize all vertices as unvisited. # Select an arbitrary vertex, set it as the current vertex u. Mark u as visited. # Find out the shortest edge connecting the current vertex u and an unvisited vertex v. # Set v as the current vertex u. Mark v as visited. # If all the vertices in the domain are visited, then terminate. Else, go to step 3. The sequence of the visited vertices is the output of the algorithm. The nearest neighbour algorithm is easy to implement and executes quickly, but it can sometimes miss shorter routes which are easily noticed with human insight, due to its "greedy" nature. As a general gui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Travelling Salesman Problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour of at most ''L'') belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest-neighbor Thermodynamic Parameters
Nucleic acid thermodynamics is the study of how temperature affects the nucleic acid structure of double-stranded DNA (dsDNA). The melting temperature (''Tm'') is defined as the temperature at which half of the DNA strands are in the random coil or single-stranded (ssDNA) state. ''Tm'' depends on the length of the DNA molecule and its specific nucleotide sequence. DNA, when in a state where its two strands are dissociated (i.e., the dsDNA molecule exists as two independent strands), is referred to as having been denatured by the high temperature. Concepts Hybridization Hybridization is the process of establishing a non-covalent, sequence-specific interaction between two or more complementary strands of nucleic acids into a single complex, which in the case of two strands is referred to as a duplex. Oligonucleotides, DNA, or RNA will bind to their complement under normal conditions, so two perfectly complementary strands will bind to each other readily. In order to reduce the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
