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FastICA
FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify. FastICA can also be alternatively derived as an approximative Newton iteration. Algorithm ''Prewhitening'' the data Let the \mathbf := (x_) \in \mathbb^ denote the input data matrix, M the number of columns corresponding with the number of samples of mixed signals and N the number of rows corresponding with the number of independent source signals. The input data matrix \mathbf must be ''prewhitened'', or centered and whitened, before applying the FastICA algorithm to it. *Centering the data entails demean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FastICA
FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify. FastICA can also be alternatively derived as an approximative Newton iteration. Algorithm ''Prewhitening'' the data Let the \mathbf := (x_) \in \mathbb^ denote the input data matrix, M the number of columns corresponding with the number of samples of mixed signals and N the number of rows corresponding with the number of independent source signals. The input data matrix \mathbf must be ''prewhitened'', or centered and whitened, before applying the FastICA algorithm to it. *Centering the data entails demean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Component Analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room. Introduction Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infomax
Infomax is an optimization principle for artificial neural networks and other information processing systems. It prescribes that a function that maps a set of input values ''I'' to a set of output values ''O'' should be chosen or learned so as to maximize the average Shannon mutual information between ''I'' and ''O'', subject to a set of specified constraints and/or noise processes. Infomax algorithms are learning algorithms that perform this optimization process. The principle was described by Linsker in 1988. Infomax, in its zero-noise limit, is related to the principle of redundancy reduction proposed for biological sensory processing by Horace Barlow in 1961, and applied quantitatively to retinal processing by Atick and Redlich. One of the applications of infomax has been to an independent component analysis algorithm that finds independent signals by maximizing entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence (probability Theory)
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models. Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor. A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, persona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RapidMiner
RapidMiner is a data science platform designed for enterprises that analyses the collective impact of organizations’ employees, expertise and data. Rapid Miner's data science platform is intended to support many analytics users across a broad AI lifecycle. It was acquired by Altair Engineering in September 2022. History RapidMiner, formerly known as YALE (Yet Another Learning Environment), was developed starting in 2001 by Ralf Klingenberg, Ingo Mierswa, and Simon Fischer at the Artificial Intelligence Unit of the Technical University of Dortmund. Starting in 2006, its development was driven by Rapid-I, a company founded by Ingo Mierswa and Ralf Klinkenberg in the same year. In 2007, the name of the software was changed from YALE to RapidMiner. In 2013, the company rebranded from Rapid-I to RapidMiner. Description RapidMiner uses a client/server model with the server offered either on-premises or in public or private cloud infrastructures. According to Bloor Research, Rapid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SourceForge
SourceForge is a web service that offers software consumers a centralized online location to control and manage open-source software projects and research business software. It provides source code repository hosting, bug tracking, mirroring of downloads for load balancing, a wiki for documentation, developer and user mailing lists, user-support forums, user-written reviews and ratings, a news bulletin, micro-blog for publishing project updates, and other features. SourceForge was one of the first to offer this service free of charge to open-source projects. Since 2012, the website has run on Apache Allura software. SourceForge offers free hosting and free access to tools for developers of free and open-source software. , the SourceForge repository claimed to host more than 502,000 projects and had more than 3.7 million registered users. Concept SourceForge is a web-based source code repository. It acts as a centralized location for free and open-source software pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R Programming Language
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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IT++
IT++ is a C++ library of classes and functions for linear algebra, numerical optimization, signal processing, communications, and statistics. It is being developed by researchers in these areas and is widely used by researchers, both in the communications industry and universities.de Lima, C.H.M.; Stancanelli, E.M.G.; Rodrigues, E.B.; da S. Maciel, J.M.; Cavalcanti, F.R.P., A software development framework based on C++ OOP language for link-level simulation tools, Telecommunications Symposium, 2006 International, Fortaleza, Brazil, The IT++ library originates from the former Department of Information Theory at the Chalmers University of Technology, Gothenburg, Sweden. The kernel of the IT++ library is templated vector and matrix classes, and a set of accompanying functions. Such a kernel makes IT++ library similar to Matlab/ Octave. For increased functionality, speed and accuracy, IT++ can make extensive use of existing free and open source libraries, especially BLAS, LAPACK and ... [...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] |
Unsupervised Learning
Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and then generate imaginative content from it. In contrast to supervised learning where data is tagged by an expert, e.g. tagged as a "ball" or "fish", unsupervised methods exhibit self-organization that captures patterns as probability densities or a combination of neural feature preferences encoded in the machine's weights and activations. The other levels in the supervision spectrum are reinforcement learning where the machine is given only a numerical performance score as guidance, and semi-supervised learning where a small portion of the data is tagged. Neural networks Tasks vs. methods Neural network tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
