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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 (pro ... [...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, execution of a plan, idea, scientific modelling, model, design, specification, Standardization, standard, algorithm, policy, or the Management, administration or management of a process or Goal, objective. Industry-specific definitions Information technology In the information technology industry, implementation refers to the post-sales process of guiding a client from purchase to use of the software or hardware that was purchased. This includes requirements analysis, scope analysis, customizations, systems integrations, user policies, user training and delivery. These steps are often overseen by a project manager using project management methodologies. Software Implementations involve several professionals that are relatively new to the knowledge based economy such as Business analysis, business analysts, software implementation specialists, solutions architects, and project managers. To implement a system successfully, many ... [...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 (mathematics), function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real number, real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a function, graph of a Gaussian is a characteristic symmetric "Normal distribution, 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 Root mean square, RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normal distribution, 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 describ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Backpropagation
In machine learning, backpropagation is a gradient computation method commonly used for training a neural network to compute its parameter updates. It is an efficient application of the chain rule to neural networks. Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single input–output example, and does so efficiently, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this can be derived through dynamic programming. Strictly speaking, the term ''backpropagation'' refers only to an algorithm for efficiently computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm – including how the gradient is used, such as by stochastic gradient descent, or as an intermediate step in a more complicated optimizer, such as Adaptive Moment Estimation. The ... [...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 example ... [...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 Spherical geometry * node, the points where a great circle crosses a plane of reference, or the equator of a sphere 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 atrioven ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, 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), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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R Programming
R is a programming language for statistical computing and data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of software packages, which contain reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C, Fortran, and R itself. Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a native command line interface. In addition, multiple third-party applications are available as graphical user interfaces; ... [...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. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...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 Positive-definite kernel, kernel function used in various kernel method, kernelized learning algorithms. In particular, it is commonly used in support vector machine statistical classification, classification. The RBF kernel on two samples \mathbf\in \mathbb^ and \mathbf, 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 Euclidean distance#Squared Euclidean distance, 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 dista ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Neural Network
A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perform complex tasks. There are two main types of neural networks. *In neuroscience, a '' biological neural network'' is a physical structure found in brains and complex nervous systems – a population of nerve cells connected by synapses. *In machine learning, an '' artificial neural network'' is a mathematical model used to approximate nonlinear functions. Artificial neural networks are used to solve artificial intelligence problems. In biology In the context of biology, a neural network is a population of biological neurons chemically connected to each other by synapses. A given neuron can be connected to hundreds of thousands of synapses. Each neuron sends and receives electrochemical signals called action potentials to its conne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Neuron
A neuron (American English), neurone (British English), or nerve cell, is an membrane potential#Cell excitability, excitable cell (biology), cell that fires electric signals called action potentials across a neural network (biology), neural network in the nervous system. They are located in the nervous system and help to receive and conduct impulses. Neurons communicate with other cells via synapses, which are specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. Neurons are the main components of nervous tissue in all Animalia, animals except sponges and placozoans. Plants and fungi do not have nerve cells. Molecular evidence suggests that the ability to generate electric signals first appeared in evolution some 700 to 800 million years ago, during the Tonian period. Predecessors of neurons were the peptidergic secretory cells. They eventually ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |