Gradient adaptation under unit-norm constraints

S. C. Douglas; S. Amari; S. Y. Kung

Gradient adaptation under unit-norm constraints

S. C. Douglas, S. Amari, S. Y. Kung

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper, we study gradient-based adaptive algorithms within parameter spaces specified by ∥w∥ = 1, where ∥ · ∥ is any vector norm. Several approximate algorithms for this task have already been developed when ∥w∥ is the L₂ norm. We derive general algorithm forms for arbitrary vector norms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for tangent-vector L₂-norm methods. Simulations showing the performance of the techniques for minor component analysis are provided.

Original language	English (US)
Pages	144-147
Number of pages	4
State	Published - 1998
Externally published	Yes
Event	Proceedings of the 1998 9th IEEE SP Workshop on Statistical Signal and Array Processing - Portland, OR, USA Duration: Sep 14 1998 → Sep 16 1998

Other

Other	Proceedings of the 1998 9th IEEE SP Workshop on Statistical Signal and Array Processing
City	Portland, OR, USA
Period	9/14/98 → 9/16/98

All Science Journal Classification (ASJC) codes

General Engineering

Cite this

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title = "Gradient adaptation under unit-norm constraints",

abstract = "In this paper, we study gradient-based adaptive algorithms within parameter spaces specified by ∥w∥ = 1, where ∥ · ∥ is any vector norm. Several approximate algorithms for this task have already been developed when ∥w∥ is the L2 norm. We derive general algorithm forms for arbitrary vector norms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for tangent-vector L2-norm methods. Simulations showing the performance of the techniques for minor component analysis are provided.",

author = "Douglas, {S. C.} and S. Amari and Kung, {S. Y.}",

year = "1998",

language = "English (US)",

pages = "144--147",

note = "Proceedings of the 1998 9th IEEE SP Workshop on Statistical Signal and Array Processing ; Conference date: 14-09-1998 Through 16-09-1998",

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TY - CONF

T1 - Gradient adaptation under unit-norm constraints

AU - Douglas, S. C.

AU - Amari, S.

AU - Kung, S. Y.

PY - 1998

Y1 - 1998

N2 - In this paper, we study gradient-based adaptive algorithms within parameter spaces specified by ∥w∥ = 1, where ∥ · ∥ is any vector norm. Several approximate algorithms for this task have already been developed when ∥w∥ is the L2 norm. We derive general algorithm forms for arbitrary vector norms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for tangent-vector L2-norm methods. Simulations showing the performance of the techniques for minor component analysis are provided.

AB - In this paper, we study gradient-based adaptive algorithms within parameter spaces specified by ∥w∥ = 1, where ∥ · ∥ is any vector norm. Several approximate algorithms for this task have already been developed when ∥w∥ is the L2 norm. We derive general algorithm forms for arbitrary vector norms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for tangent-vector L2-norm methods. Simulations showing the performance of the techniques for minor component analysis are provided.

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M3 - Paper

AN - SCOPUS:0032292156

SP - 144

EP - 147

T2 - Proceedings of the 1998 9th IEEE SP Workshop on Statistical Signal and Array Processing

Y2 - 14 September 1998 through 16 September 1998

ER -

Gradient adaptation under unit-norm constraints

Abstract

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All Science Journal Classification (ASJC) codes

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