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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2006 E89-A(10):2812-2817; doi:10.1093/ietfec/e89-a.10.2812
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Copyright © 2006 The Institute of Electronics, Information and Communication Engineers

Special Section on Nonlinear Theory and its Applications -- Papers -- Control, Neural Networks and Learning

Geometric Properties of Quasi-Additive Learning Algorithms*

Kazushi IKEDA1

1 The author is with Kyoto University, Kyoto-shi, 606-8501 Japan. E-Mail: kazushi{at}i.kyoto-u.ac.jp

The family of Quasi-Additive (QA) algorithms is a natural generalization of the perceptron learning, which is a kind of on-line learning having two parameter vectors: One is an accumulation of input vectors and the other is a weight vector for prediction associated with the former by a nonlinear function. We show that the vectors have a dually-flat structure from the information-geometric point of view, and this representation makes it easier to discuss the convergence properties.

Key Words: quasi-additive algorithms, perceptron, information geometry

Manuscript received January 20, 2006. Final manuscript received May 8, 2006.

* This study is supported in part by Grant-in-Aid for Scientific Research (14084210, 15700130, 18300078) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.


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