Transcription of Independent Component Analysis: Algorithms and Applications
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Independent Component Analysis: Algorithms and Applications
Independent Component analysis : Algorithms and ApplicationsAapo Hyv rinen and Erkki OjaNeural Networks Research CentreHelsinki University of Box 5400, FIN-02015 HUT, FinlandNeural Networks, 13(4-5):411-430, 2000 AbstractA fundamental problem in neural network research, as well asin many other disciplines, is finding a suitablerepresentation of multivariate data, random reasons of computational and conceptual simplicity,the representation is often sought as a linear transformation of the original data. In other words, each componentof the representation is a linear combination of the original variables. Well-known linear transformation methodsinclude principal Component analysis , factor analysis , and projection pursuit. Independent Component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of nongaussian data sothat the components are statistically Independent , or as Independent as possible.
x, is a row vector. Using this vector-matrix notation, the above mixing model is written as x =As. (4) Sometimes we need the columns of matrix A; denoting them by aj the model can also be written as x = n ∑ i=1 aisi. (5) The statistical model in Eq. 4 is called independent component analysis, or ICA model. The ICA model is a
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