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Learning Vector Quantization
In computer science, learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems. Overview LVQ can be understood as a special case of an artificial neural network, more precisely, it applies a winner-take-all Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas, and to the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen. An LVQ system is represented by prototypes W=(w(i),...,w(n)) which are defined in the feature space of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly. An advantage of L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Gas
Neural gas is an artificial neural network, inspired by the self-organizing map and introduced in 1991 by Thomas Martinetz and Klaus Schulten. The neural gas is a simple algorithm for finding optimal data representations based on feature vectors. The algorithm was coined "neural gas" because of the dynamics of the feature vectors during the adaptation process, which distribute themselves like a gas within the data space. It is applied where data compression or vector quantization is an issue, for example speech recognition, image processing or pattern recognition. As a robustly converging alternative to the k-means clustering it is also used for cluster analysis. Algorithm Given a probability distribution P(x) of data vectors x and a finite number of feature vectors w_i, i = 1,\cdots,N. With each time step t, a data vector x randomly chosen from P(x) is presented. Subsequently, the distance order of the feature vectors to the given data vector x is determined. Let i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix, which allows computing in vector spaces. This provides a concise and synthetic way for manipulating and studying systems of linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-class Classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). While many classification algorithms (notably multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance. General strategies The existing multi-class classification techniques can be categorized into (i) transformation to binary (ii) extension from binary and (iii) hierarchical classification. Transformation to binary This section discusses strategies for reducing the problem of multiclass classification to multiple binary classifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feature Space
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern recognition, classification and regression. Features are usually numeric, but structural features such as strings and graphs are used in syntactic pattern recognition. The concept of "feature" is related to that of explanatory variable used in statistical techniques such as linear regression. Classification A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear predictor function (related to the perceptron) with a feature vector as input. The method consists of calculating the scalar product between the feature vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teuvo Kohonen
Teuvo Kalevi Kohonen (11 July 1934 – 13 December 2021) was a prominent Finnish academic ( Dr. Eng.) and researcher. He was professor emeritus of the Academy of Finland.Teuvo Kohonen. Dr. Eng., Emeritus Professor of the Academy of Finland; Academician a biography from his university, last accessed on 27 January 2022. Career Kohonen studied at the and graduated with a master's degree in engineering in 1957. He received his doctorate in 1962 and stayed at the university with a faculty position until 1993. He was an accademy professor of the |
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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-organizing Map
A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher dimensional data set while preserving the topological structure of the data. For example, a data set with p variables measured in n observations could be represented as clusters of observations with similar values for the variables. These clusters then could be visualized as a two-dimensional "map" such that observations in proximal clusters have more similar values than observations in distal clusters. This can make high-dimensional data easier to visualize and analyze. An SOM is a type of artificial neural network but is trained using competitive learning rather than the error-correction learning (e.g., backpropagation with gradient descent) used by other artificial neural networks. The SOM was introduced by the Finnish professor Teuvo Kohonen in the 1980s and therefore is someti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prototype
A prototype is an early sample, model, or release of a product built to test a concept or process. It is a term used in a variety of contexts, including semantics, design, electronics, and software programming. A prototype is generally used to evaluate a new design to enhance precision by system analysts and users. Prototyping serves to provide specifications for a real, working system rather than a theoretical one. In some design workflow models, creating a prototype (a process sometimes called materialization) is the step between the formalization and the evaluation of an idea. A prototype can also mean a typical example of something such as in the use of the derivation 'prototypical'. This is a useful term in identifying objects, behaviours and concepts which are considered the accepted norm and is analogous with terms such as stereotypes and archetypes. The word ''prototype'' derives from the Greek , "primitive form", neutral of , "original, primitive", from πρῶτ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebbian Learning
Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation of brain neurons during the learning process. It was introduced by Donald Hebb in his 1949 book '' The Organization of Behavior.'' The theory is also called Hebb's rule, Hebb's postulate, and cell assembly theory. Hebb states it as follows: Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability. ... When an axon of cell ''A'' is near enough to excite a cell ''B'' and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that ''A''’s efficiency, as one of the cells firing ''B'', is increased. The theory is often summarized as "Cells that fire together wire tog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winner-take-all (computing)
Winner-take-all is a computational principle applied in computational models of neural networks by which neurons compete with each other for activation. In the classical form, only the neuron with the highest activation stays active while all other neurons shut down; however, other variations allow more than one neuron to be active, for example the soft winner take-all, by which a power function is applied to the neurons. Neural networks In the theory of artificial neural networks, winner-take-all networks are a case of competitive learning in recurrent neural networks. Output nodes in the network mutually inhibit each other, while simultaneously activating themselves through reflexive connections. After some time, only one node in the output layer will be active, namely the one corresponding to the strongest input. Thus the network uses nonlinear inhibition to pick out the largest of a set of inputs. Winner-take-all is a general computational primitive that can be implemented usin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
