ICA and GaussianGaussianity: a misleading exampleA Misleading Example in the Book Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition

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A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here at pages 283,284.

The book is Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition.

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here at pages 283,284.

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here at pages 283,284.

The book is Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition.

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edited Oct 18, 2022 at 11:28

Peter K. ♦

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A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here https://www.google.it/books/edition/Pattern_Recognition/gAGRCmp8Sp8C?hl=it&gbpv=1&dq=pattern+recognition&printsec=frontcover at pages 283,284The complete example is available here at pages 283,284.

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here https://www.google.it/books/edition/Pattern_Recognition/gAGRCmp8Sp8C?hl=it&gbpv=1&dq=pattern+recognition&printsec=frontcover at pages 283,284

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is reported:

A number of 1024 samples of a two-dimensional normal distribution was generated with mean μ and covariance matrix Σ. Similarly, 1024 samples from a second normal pdf were generated with the same covariance matrix and mean −μ. For the ICA, the method based on the second- and fourth-order cumulants, presented in this section, was used. The resulting transformation matrix W [...]

The example continues using the ICA showing the independent component found. However, my question is: how was it possible to use ICA if the data comes from two normal/Gaussian distributions (and not just one)?

The complete example is available here at pages 283,284.