Independent Component Analysis: General Formulation and Linear Case
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This chapter formulates the problem of Independent Component Analysis (ICA) as a search for an information-preserving linear mapping which results in statistically independent output components. The mathematical tools used herein originate from information theory and statistical analysis.Keywords:
Component (thermodynamics)
Component analysis
Statistical Analysis
To study the independent component analysis for stock market analysis,the paper first introduced the theory of independent component analysis,then introduced a specific algorithm——Fastica algorithm.In order to analyze the factors influencing the stock turnover,the ICA separation experiments were performed for several stocks′ turnover,and experimental results are analyzed to find some important factors which affect the volume of stock transactions.The reaslt demonstrated that ICA is an effective means to reveal the hidden reasons,and is very suitable for the analysis of the stock market.
FastICA
Component analysis
Stock (firearms)
Inventory turnover
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Recovering the unobserved source signals from their mixtures is a typical problem in array processing and analysis.Independent component analysis(ICA) is a new method to solve this problem.The most common way in independent component analysis is the separation based on information theory.FastICA algorithm and nature step algorithm are the main way in it.Some groups of signals were separated.The analysis and simulations suggest that the FastICA algorithm is the best way.
FastICA
Component analysis
Source Separation
Component (thermodynamics)
Separation (statistics)
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Underdetermined system
Component analysis
Component (thermodynamics)
Source Separation
Representation
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Component (thermodynamics)
Component analysis
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A novel method, integration of independent component analysis (ICA) and envelope analysis (EA), is proposed to diagnose machine sound sources. Microphones measure the acoustic signals. In ICA implementing, the auto-covariance of signals replaces the mixing signal and the three components are separated. Further ICA is applied the data between strikes of the machine, another component is obtained. EA extracts the sounds of machine from these separated components. Applications indicate that ICA can be used to recover the embedded information and improve the diagnosis.
Envelope (radar)
Component (thermodynamics)
Component analysis
SIGNAL (programming language)
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Constrained Independent Component Analysis (cICA) was developed from Independent Component Analysis (ICA), and the concepts and principles of independent component analysis still apply to constrained independent component analysis. This paper introduces the mathematical basis, basic principles and algorithms of constrained independent component analysis. Firstly, the mathematical basis of cICA is introduced. It mainly includes the entropy and negative entropy of irrelevant and whitening, Statistical opposition and multivariate Gaussian density random variables. Then the mathematical model of Constrained FastICA, the identifiability and uncertainty of the model, the FastICA independence criterion, FastICA optimization and preprocessing, FastICA algorithm and simulation examples are introduced. Finally, the shortcomings of fast independent component analysis and the advantages of constrained independent component analysis are analyzed. According to the establishment and evaluation indicators of signals, the basic principles and corresponding algorithms of constrained independent component analysis are introduced. The characteristics of the corresponding simulation show that the algorithm is effective in extracting signal characteristics.
FastICA
Negentropy
Component analysis
Component (thermodynamics)
Identifiability
Independence
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This paper deals with the study of Independent Component Analysis. Independent Component Analysis is basically a method which is used to implement the concept of Blind Source Separation. Blind Source Separation is a technique which is used to extract set of source signal from set of their mixed source signals. The various techniques which are used for implementing Blind Source Separation totally depends upon the properties and the characteristics of original sources. Also there are many fields nowadays in which Independent Component Analysis is widely used. This paper deals with the theoretical concepts of Independent Component Analysis, its principles and its widely used applications.
Component (thermodynamics)
Component analysis
Source Separation
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This chapter contains sections titled: Introduction Spectral Radiance Model Independent Component Analysis and Independent Factor Analysis ICA and IFA Evaluation with Simulated Data Limitations of ICA and IFA in Unmixing Hyperspectral Data Fastica Algorithm Applied to Real Data Dependent Component Analysis Concluding Remarks References
FastICA
Component (thermodynamics)
Component analysis
Spectral Analysis
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Data-driven fMRI analysis techniques include independent component analysis (ICA) and different types of clustering in the temporal domain. Since each of these methods has its particular strengths, it is natural to look for an approach that unifies Kohonen's self-organizing map and ICA. This is given by the topographic independent component analysis. While achieved by a slight modification of the ICA model, it can be at the same time used to define a topographic order (clusters) between the components, and thus has the usual computational advantages associated with topographic maps. In this contribution, we can show that when applied to fMRI analysis it outperforms FastICA.
FastICA
Component analysis
Self-organizing map
Component (thermodynamics)
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This contribution describes the application of topographic independent component analysis to fMRI signal analysis. This new discriminating paradigm represents a combination of signal separation based on traditional independent component analysis with at the same time clustering based on a topographic order. When applied to fMRI analysis, this new method outperforms both traditional independent component analysis as well as other standard clustering techniques.
Component analysis
Component (thermodynamics)
SIGNAL (programming language)
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