Learning Natural Image Structure with a Horizontal Product Model

Urs Köster; Jussi T. Lindgren; Michael Gutmann; Aapo Hyvärinen

doi:10.1007/978-3-642-00599-2_64

Learning Natural Image Structure with a Horizontal Product Model

Urs Köster, Jussi T. Lindgren, Michael Gutmann, Aapo Hyvärinen

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

Abstract / Description of output

We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.

Original language	English
Title of host publication	Independent Component Analysis and Signal Separation
Subtitle of host publication	8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings
Editors	Tülay Adali, Christian Jutten, João Marcos Travassos Romano, Allan Kardec Barros
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	507-514
Number of pages	8
ISBN (Electronic)	978-3-642-00599-2
ISBN (Print)	978-3-642-00598-5
DOIs	https://doi.org/10.1007/978-3-642-00599-2_64
Publication status	Published - 2009

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	5441
ISSN (Print)	0302-9743

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10.1007/978-3-642-00599-2_64

http://link.springer.com/chapter/10.1007%2F978-3-642-00599-2_64

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Köster, U., Lindgren, J. T., Gutmann, M., & Hyvärinen, A. (2009). Learning Natural Image Structure with a Horizontal Product Model. In T. Adali, C. Jutten, J. M. T. Romano, & A. K. Barros (Eds.), Independent Component Analysis and Signal Separation: 8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings (pp. 507-514). (Lecture Notes in Computer Science; Vol. 5441). Springer. https://doi.org/10.1007/978-3-642-00599-2_64

Köster, Urs ; Lindgren, Jussi T. ; Gutmann, Michael et al. / Learning Natural Image Structure with a Horizontal Product Model. Independent Component Analysis and Signal Separation: 8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings. editor / Tülay Adali ; Christian Jutten ; João Marcos Travassos Romano ; Allan Kardec Barros. Berlin, Heidelberg : Springer, 2009. pp. 507-514 (Lecture Notes in Computer Science).

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title = "Learning Natural Image Structure with a Horizontal Product Model",

abstract = "We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.",

author = "Urs K{\"o}ster and Lindgren, {Jussi T.} and Michael Gutmann and Aapo Hyv{\"a}rinen",

year = "2009",

doi = "10.1007/978-3-642-00599-2_64",

language = "English",

isbn = "978-3-642-00598-5",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "507--514",

editor = "T{\"u}lay Adali and Christian Jutten and Romano, {Jo{\~a}o Marcos Travassos} and Barros, {Allan Kardec}",

booktitle = "Independent Component Analysis and Signal Separation",

address = "United Kingdom",

}

Köster, U, Lindgren, JT, Gutmann, M & Hyvärinen, A 2009, Learning Natural Image Structure with a Horizontal Product Model. in T Adali, C Jutten, JMT Romano & AK Barros (eds), Independent Component Analysis and Signal Separation: 8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings. Lecture Notes in Computer Science, vol. 5441, Springer, Berlin, Heidelberg, pp. 507-514. https://doi.org/10.1007/978-3-642-00599-2_64

Learning Natural Image Structure with a Horizontal Product Model. / Köster, Urs; Lindgren, Jussi T.; Gutmann, Michael et al.
Independent Component Analysis and Signal Separation: 8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings. ed. / Tülay Adali; Christian Jutten; João Marcos Travassos Romano; Allan Kardec Barros. Berlin, Heidelberg: Springer, 2009. p. 507-514 (Lecture Notes in Computer Science; Vol. 5441).

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

TY - GEN

T1 - Learning Natural Image Structure with a Horizontal Product Model

AU - Köster, Urs

AU - Lindgren, Jussi T.

AU - Gutmann, Michael

AU - Hyvärinen, Aapo

PY - 2009

Y1 - 2009

N2 - We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.

AB - We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.

U2 - 10.1007/978-3-642-00599-2_64

DO - 10.1007/978-3-642-00599-2_64

M3 - Conference contribution

SN - 978-3-642-00598-5

T3 - Lecture Notes in Computer Science

SP - 507

EP - 514

BT - Independent Component Analysis and Signal Separation

A2 - Adali, Tülay

A2 - Jutten, Christian

A2 - Romano, João Marcos Travassos

A2 - Barros, Allan Kardec

PB - Springer

CY - Berlin, Heidelberg

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Köster U, Lindgren JT, Gutmann M, Hyvärinen A. Learning Natural Image Structure with a Horizontal Product Model. In Adali T, Jutten C, Romano JMT, Barros AK, editors, Independent Component Analysis and Signal Separation: 8th International Conference, ICA 2009, Paraty, Brazil, March 15-18, 2009. Proceedings. Berlin, Heidelberg: Springer. 2009. p. 507-514. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-00599-2_64

Learning Natural Image Structure with a Horizontal Product Model

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