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Independent Component Analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are Statistical independence, statistically independent from each other. ICA was invented by Jeanny Hérault and Christian Jutten in 1985. ICA is a special case of blind source separation. A common example application of ICA 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 ... [...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 FastICA#Prewhitening the data, prewhitened data, through a fixed-point iterative method, 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 algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was publis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection Pursuit
Projection pursuit (PP) is a type of statistical technique that involves finding the most "interesting" possible projections in multidimensional data. Often, projections that deviate more from a normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections; this is the "pursuit" aspect that motivated the technique known as matching pursuit. The idea of projection pursuit is to locate the projection or projections from high-dimensional space to low-dimensional space that reveal the most details about the structure of the data set. Once an interesting set of projections has been found, existing structures (clusters, surfaces, etc.) can be extracted and analyzed separately. Projection pursuit has been widely used for blind source separation, so it is very important in independent component analysis. Projection pursuit seeks one projec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Resource Management
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a network of networks that consists of private, public, academic, business, and government networks of local to global scope, linked by a broad array of electronic, wireless, and optical networking technologies. The Internet carries a vast range of information resources and services, such as the interlinked hypertext documents and applications of the World Wide Web (WWW), electronic mail, internet telephony, streaming media and file sharing. The origins of the Internet date back to research that enabled the time-sharing of computer resources, the development of packet switching in the 1960s and the design of computer networks for data communication. The set of rules (communication protocols) to enable internetworking on the Internet arose from research and development commissioned in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Tomography
Network tomography is the study of a network's internal characteristics using information derived from end point data. The word tomography is used to link the field, in concept, to other processes that infer the internal characteristics of an object from external observation, as is done in MRI or PET scanning (even though the term tomography strictly refers to imaging by slicing). The field is a recent development in electrical engineering and computer science, dating from 1996. Network tomography seeks to map the path data takes through the Internet by examining information from “edge nodes,” the computers in which the data are originated and from which they are requested. The field is useful for engineers attempting to develop more efficient computer networks. Data derived from network tomography studies can be used to increase quality of service by limiting link packet loss and increasing routing optimization. Recent developments There have been many published papers and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Diagnosis
Medical diagnosis (abbreviated Dx, Dx, or Ds) is the process of determining which disease or condition explains a person's symptoms and signs. It is most often referred to as a diagnosis with the medical context being implicit. The information required for a diagnosis is typically collected from a history and physical examination of the person seeking medical care. Often, one or more diagnostic procedures, such as medical tests, are also done during the process. Sometimes the posthumous diagnosis is considered a kind of medical diagnosis. Diagnosis is often challenging because many signs and symptoms are nonspecific. For example, redness of the skin ( erythema), by itself, is a sign of many disorders and thus does not tell the healthcare professional what is wrong. Thus differential diagnosis, in which several possible explanations are compared and contrasted, must be performed. This involves the correlation of various pieces of information followed by the recognition and d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank (linear Algebra)
In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. p. 48, § 1.16 This corresponds to the maximal number of linearly independent columns of . This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the " nondegenerateness" of the system of linear equations and linear transformation encoded by . There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics. The rank is commonly denoted by or ; sometimes the parentheses are not written, as in .Alternative notation includes \rho (\Phi) from and . Main definitions In this section, we give some definitions of the rank of a matrix. Many definitions are possible; see Alternative definitions for several of these. The column rank of is the dimension of the column space of , while the row rank of is the dimension of the row space of . A fundamental resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear ICA
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudo Inverse
In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A. A matrix A^\mathrm \in \mathbb^ is a generalized inverse of a matrix A \in \mathbb^ if AA^\mathrmA = A. A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse. Motivation Consider the linear system :Ax = y where A is an m \times n matrix and y \in \mathcal C(A), the column space of A. If m = n and A is nonsingular then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Code
{{Short description, Data representation for machine learning Most real world data sets consist of data vectors whose individual components are not statistically independent. In other words, knowing the value of an element will provide information about the value of elements in the data vector. When this occurs, it can be desirable to create a factorial code of the data, i.e., a new vector-valued Representation (mathematics), representation of each data vector such that it gets uniquely encoded by the resulting code vector (loss-free coding), but the code components are statistically independent. Later supervised learning usually works much better when the raw input data is first translated into such a factorial code. For example, suppose the final goal is to classify images with highly redundant pixels. A naive Bayes classifier will assume the pixels are statistically independent random variables and therefore fail to produce good results. If the data are first encoded in a factoria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blind Signal Separation
Source separation, blind signal separation (BSS) or blind source separation, is the separation of a set of source signal processing, signals from a set of mixed signals, without the aid of information (or with very little information) about the source signals or the mixing process. It is most commonly applied in digital signal processing and involves the analysis of mixtures of Signal (information theory), signals; the objective is to recover the original component signals from a mixture signal. The classical example of a source separation problem is the cocktail party problem, where a number of people are talking simultaneously in a room (for example, at a cocktail party), and a listener is trying to follow one of the discussions. The human brain can handle this sort of auditory source separation problem, but it is a difficult problem in digital signal processing. This problem is in general highly underdetermined system, underdetermined, but useful solutions can be derived under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
