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Generative Topographic Mapping
Generative topographic map (GTM) is a machine learning method that is a probabilistic counterpart of the self-organizing map (SOM), is probably convergent and does not require a shrinking neighborhood or a decreasing step size. It is a generative model: the data is assumed to arise by first probabilistically picking a point in a low-dimensional space, mapping the point to the observed high-dimensional input space (via a smooth function), then adding noise in that space. The parameters of the low-dimensional probability distribution, the smooth map and the noise are all learned from the training data using the expectation-maximization (EM) algorithm. GTM was introduced in 1996 in a paper by Christopher Bishop, Markus Svensen, and Christopher K. I. Williams. Details of the algorithm The approach is strongly related to density networks which use importance sampling and a multi-layer perceptron to form a non-linear latent variable model. In the GTM the latent space is a discrete gr ... [...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] |
Linear Transform
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a (linear) ''endomorphism''. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Network Software
Neural network software is used to simulate, research, develop, and apply artificial neural networks, software concepts adapted from biological neural networks, and in some cases, a wider array of adaptive systems such as artificial intelligence and machine learning. Simulators Neural network simulators are software applications that are used to simulate the behavior of artificial or biological neural networks. They focus on one or a limited number of specific types of neural networks. They are typically stand-alone and not intended to produce general neural networks that can be integrated in other software. Simulators usually have some form of built-in visualization to monitor the training process. Some simulators also visualize the physical structure of the neural network. Research simulators Historically, the most common type of neural network software was intended for researching neural network structures and algorithms. The primary purpose of this type of software is, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Dimensionality Reduction
Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis. Applications of NLDR Consider a dataset represented as a matrix (or a database table), such that each row represents a set of attributes (or features or dimensions) that describe a particular instance of something. If the number of attributes is large, then the space of unique possible rows is exponentially large. Thus, the larger the dimensionality, the more difficult it becomes to sample the spa ... [...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] |
Connectionism
Connectionism refers to both an approach in the field of cognitive science that hopes to explain mental phenomena using artificial neural networks (ANN) and to a wide range of techniques and algorithms using ANNs in the context of artificial intelligence to build more intelligent machines. Connectionism presents a cognitive theory based on simultaneously occurring, distributed signal activity via connections that can be represented numerically, where learning occurs by modifying connection strengths based on experience. Some advantages of the connectionist approach include its applicability to a broad array of functions, structural approximation to biological neurons, low requirements for innate structure, and capacity for graceful degradation. Some disadvantages include the difficulty in deciphering how ANNs process information, or account for the compositionality of mental representations, and a resultant difficulty explaining phenomena at a higher level. The success of deep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
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. Typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation Maximization
Expectation or Expectations may refer to: Science * Expectation (epistemic) * Expected value, in mathematical probability theory * Expectation value (quantum mechanics) * Expectation–maximization algorithm, in statistics Music * ''Expectation'' (album), a 2013 album by Girl's Day * ''Expectation'', a 2006 album by Matt Harding * ''Expectations'' (Keith Jarrett album), 1971 * ''Expectations'' (Dance Exponents album), 1985 * ''Expectations'' (Hayley Kiyoko album), 2018 **"Expectations/Overture", a song from the album * ''Expectations'' (Bebe Rexha album), 2018 * ''Expectations'' (Katie Pruitt album), 2020 **"Expectations", a song from the album * "Expectation" (waltz), a 1980 waltz composed by Ilya Herold Lavrentievich Kittler * "Expectation" (song), a 2010 song by Tame Impala * "Expectations" (song), a 2018 song by Lauren Jauregui * "Expectations", a song by Three Days Grace from ''Transit of Venus'', 2012 See also *''Great Expectations'', a novel by Charles Dickens ... [...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] |
Principal Components Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
