The separability theory of hyperbolic tangent kernels and support vector machines for pattern classification

Mathini Sellathurai; Simon Haykin

doi:10.1109/ICASSP.1999.759878

The separability theory of hyperbolic tangent kernels and support vector machines for pattern classification

Mathini Sellathurai^*, Simon Haykin

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

A new theory is developed for the feature spaces of hyperbolic tangent used as an activation kernel for non-linear support vector machines. The theory developed herein is based on the distinct features of hyperbolic geometry, which leads to an interesting geometrical interpretation of the higher-dimensional feature spaces of neural networks using hyperbolic tangent as the activation function. The new theory is used to explain the separability of hyperbolic tangent kernels where we show that the separability is possible only for a certain class of hyperbolic kernels. Simulation results are given supporting the separability theory.

Original language	English
Title of host publication	Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing
Pages	1021-1024
Number of pages	4
DOIs	https://doi.org/10.1109/ICASSP.1999.759878
Publication status	Published - 1999
Event	1999 IEEE International Conference on Acoustics, Speech, and Signal Processing - Phoenix, United States Duration: 15 Mar 1999 → 19 Mar 1999

Conference

Conference	1999 IEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated title	ICASSP 99
Country/Territory	United States
City	Phoenix
Period	15/03/99 → 19/03/99

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Acoustics and Ultrasonics

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10.1109/ICASSP.1999.759878

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title = "The separability theory of hyperbolic tangent kernels and support vector machines for pattern classification",

abstract = "A new theory is developed for the feature spaces of hyperbolic tangent used as an activation kernel for non-linear support vector machines. The theory developed herein is based on the distinct features of hyperbolic geometry, which leads to an interesting geometrical interpretation of the higher-dimensional feature spaces of neural networks using hyperbolic tangent as the activation function. The new theory is used to explain the separability of hyperbolic tangent kernels where we show that the separability is possible only for a certain class of hyperbolic kernels. Simulation results are given supporting the separability theory.",

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doi = "10.1109/ICASSP.1999.759878",

language = "English",

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pages = "1021--1024",

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note = "1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 99 ; Conference date: 15-03-1999 Through 19-03-1999",

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Sellathurai, M & Haykin, S 1999, The separability theory of hyperbolic tangent kernels and support vector machines for pattern classification. in Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. pp. 1021-1024, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, Phoenix, Arizona, United States, 15/03/99. https://doi.org/10.1109/ICASSP.1999.759878

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AU - Sellathurai, Mathini

AU - Haykin, Simon

PY - 1999

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N2 - A new theory is developed for the feature spaces of hyperbolic tangent used as an activation kernel for non-linear support vector machines. The theory developed herein is based on the distinct features of hyperbolic geometry, which leads to an interesting geometrical interpretation of the higher-dimensional feature spaces of neural networks using hyperbolic tangent as the activation function. The new theory is used to explain the separability of hyperbolic tangent kernels where we show that the separability is possible only for a certain class of hyperbolic kernels. Simulation results are given supporting the separability theory.

AB - A new theory is developed for the feature spaces of hyperbolic tangent used as an activation kernel for non-linear support vector machines. The theory developed herein is based on the distinct features of hyperbolic geometry, which leads to an interesting geometrical interpretation of the higher-dimensional feature spaces of neural networks using hyperbolic tangent as the activation function. The new theory is used to explain the separability of hyperbolic tangent kernels where we show that the separability is possible only for a certain class of hyperbolic kernels. Simulation results are given supporting the separability theory.

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DO - 10.1109/ICASSP.1999.759878

M3 - Conference contribution

AN - SCOPUS:0032635029

SN - 0-7803-5041-3

SP - 1021

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BT - Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing

T2 - 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing

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ER -

The separability theory of hyperbolic tangent kernels and support vector machines for pattern classification

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