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General Regression Neural Network
Generalized regression neural network (GRNN) is a variation to radial basis neural networks. GRNN was suggested by D.F. Specht in 1991. GRNN can be used for regression, prediction, and classification. GRNN can also be a good solution for online dynamical systems. GRNN represents an improved technique in the neural networks based on the nonparametric regression. The idea is that every training sample will represent a mean to a radial basis neuron. Mathematical representation : Y(x) = \frac where: * Y(x) is the prediction value of input x * y_k is the activation weight for the pattern layer neuron at k * K(x, x_k) is the Radial basis function kernel (Gaussian kernel) as formulated below. Gaussian Kernel K(x, x_k) = e^, \qquad d_k = (x-x_k)^T(x-x_k) where d_k is the squared euclidean distance between the training samples x_k and the input x. Implementation GRNN has been implemented in many computer languages including MATLAB, R- programming language, Python (prog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Radial Basis Function Network
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including function approximation, time series prediction, classification, and system control. They were first formulated in a 1988 paper by Broomhead and Lowe, both researchers at the Royal Signals and Radar Establishment. Network architecture Radial basis function (RBF) networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer. The input can be modeled as a vector of real numbers \mathbf \in \mathbb^n. The output of the network is then a scalar function of the input vector, \varphi : \mathbb^n \to \mathbb , and is given by :\varphi(\mathbf) = \sum_^N a_i \rho(, , \mathbf-\mathbf_i, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Implementation
Implementation is the realization of an application, or execution of a plan, idea, model, design, specification, standard, algorithm, or policy. Industry-specific definitions Computer science In computer science, an implementation is a realization of a technical specification or algorithm as a program, software component, or other computer system through computer programming and deployment. Many implementations may exist for a given specification or standard. For example, web browsers contain implementations of World Wide Web Consortium-recommended specifications, and software development tools contain implementations of programming languages. A special case occurs in object-oriented programming, when a concrete class implements an interface; in this case the concrete class is an ''implementation'' of the interface and it includes methods which are ''implementations'' of those methods specified by the interface. Information technology In the information technology d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Gaussian Function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric " bell curve" shape. The parameter is the height of the curve's peak, is the position of the center of the peak, and (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value and variance . In this case, the Gaussian is of the form g(x) = \frac \exp\left( -\frac \frac \right). Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Backpropagation
In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions generally. These classes of algorithms are all referred to generically as "backpropagation". In fitting a neural network, backpropagation computes the gradient of the loss function with respect to the weights of the network for a single input–output example, and does so efficiently, unlike a naive direct computation of the gradient with respect to each weight individually. This efficiency makes it feasible to use gradient methods for training multilayer networks, updating weights to minimize loss; gradient descent, or variants such as stochastic gradient descent, are commonly used. The backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, computing the gradient one laye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Multinomial Logistic Regression
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. Background Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently ''categorical'', meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Node
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics * Vertex (graph theory), a vertex in a mathematical graph * Vertex (geometry), a point where two or more curves, lines, or edges meet. * Node (autonomous system), behaviour for an ordinary differential equation near a critical point * Singular point of an algebraic variety, a type of singular point of a curve In science and engineering Astronomy * Orbital node, the points where an orbit crosses a plane of reference ** Lunar node, where the orbits of the sun and moon intersect ** Longitude of the ascending node, how orbital nodes are parameterized Biology * Lymph node, an immune system organ used to store white blood cells * Node of Ranvier, periodic gaps in the insulating myelin sheaths of myelinated axons *Sinoatrial node and atrioventricular node, specialized tissues in the heart responsible for initiating and coordinating the heartbeat * Primitive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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R Programming
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Radial Basis Function Kernel
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. The RBF kernel on two samples \mathbf\in \mathbb^ and x', represented as feature vectors in some ''input space'', is defined asJean-Philippe Vert, Koji Tsuda, and Bernhard Schölkopf (2004)"A primer on kernel methods".''Kernel Methods in Computational Biology''. :K(\mathbf, \mathbf) = \exp\left(-\frac\right) \textstyle\, \mathbf - \mathbf\, ^2 may be recognized as the squared Euclidean distance between the two feature vectors. \sigma is a free parameter. An equivalent definition involves a parameter \textstyle\gamma = \tfrac: :K(\mathbf, \mathbf) = \exp(-\gamma\, \mathbf - \mathbf\, ^2) Since the value of the RBF kernel decreases with distance and ranges between zero (in the limit) and one (when ), it has a ready interpretation as a similarity measure. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Neural Network
A neural network is a network or neural circuit, circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Neuron
A neuron, neurone, or nerve cell is an membrane potential#Cell excitability, electrically excitable cell (biology), cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all Animalia, animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to Stimulus (physiology), stimuli such as touch, sound, or light that affect the cells of the Sense, sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to gland, glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |