### Abstract

We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference |

Pages | 1009-1016 |

Number of pages | 8 |

State | Published - 2009 |

Event | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada Duration: Dec 8 2008 → Dec 11 2008 |

### Other

Other | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/8/08 → 12/11/08 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference*(pp. 1009-1016)

**Reducing statistical dependencies in natural signals using radial Gaussianization.** / Lyu, Siwei; Simoncelli, Eero.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference.*pp. 1009-1016, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 12/8/08.

}

TY - GEN

T1 - Reducing statistical dependencies in natural signals using radial Gaussianization

AU - Lyu, Siwei

AU - Simoncelli, Eero

PY - 2009

Y1 - 2009

N2 - We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.

AB - We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.

UR - http://www.scopus.com/inward/record.url?scp=84858781961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858781961&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781605609492

SP - 1009

EP - 1016

BT - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

ER -