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Hyper Basis Function Network
In 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 ..., a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”.T. Poggio and F. Girosi (1990). "Networks for Approximation and Learning". ''Proc. IEEE'' Vol. 78, No. 9:1481-1497.R.N. Mahdi, E.C. Rouchka (2011)"Reduced HyperBF Networks: Regularization by Explicit Complexity Reduction and Scaled Rprop-Based Training" ''IEEE Transactions of Neural Networks'' 2:673–686. Network Architecture The typical HyperBF network structure consists o ... [...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 pred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Mahalanobis Distance
The Mahalanobis distance is a measure of the distance between a point ''P'' and a distribution ''D'', introduced by P. C. Mahalanobis in 1936. Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls based on measurements in 1927. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away ''P'' is from the mean of ''D''. This distance is zero for ''P'' at the mean of ''D'' and grows as ''P'' moves away from the mean along each principal component axis. If each of these axes is re-scaled to have unit variance, then the Mahalanobis distance corresponds to standard Euclidean distance in the transformed space. The Mahalanobis distance is thus unitless, scale-invariant, and takes into account the correlations of the data set. Definition Given a probability distribution Q on \R^N, with mean \vec = (\mu_1, \mu_2, \mu_3, \dots , \mu_N)^\mathsf and positive-definite covariance matrix S, the Mahalanobis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Activation Function
In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs. A standard integrated circuit can be seen as a digital network of activation functions that can be "ON" (1) or "OFF" (0), depending on input. This is similar to the linear perceptron in neural networks. However, only ''nonlinear'' activation functions allow such networks to compute nontrivial problems using only a small number of nodes, and such activation functions are called nonlinearities. Classification of activation functions The most common activation functions can be divided in three categories: ridge functions, radial functions and fold functions. An activation function f is saturating if \lim_ , \nabla f(v), = 0. It is nonsaturating if it is not saturating. Non-saturating activation functions, such as ReLU, may be better than saturating activation functions, as they don't suffer from vanishing gradient. Ridge activation functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Networks Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called ''edges''. Neurons and edges typically have a '' weight'' that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
