A study on optimal generalizing learning schema for neural networks based on theories of image processing filters

基于图像处理滤波器理论的神经网络最优泛化学习模式研究

• 批准号: 02452155
• 负责人: OGAWA Hidemitsu
• 金额: $ 3.65万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-02452155/
• 关键词: Image restoration; Neural network; Learning; Generalization; Filtering; Nonlinear processing; Statics; Over-learning; フイルタ

A theory for neural network learning which is very effective for analyzing the generalization ability and the overlearning problem is developed. This theory is based on the image restoration theories proposed by the head investigator of this project. Although the problems of generalization and image restoration seem to have nothing in common, we have shown that both problems can be dealt with under the same methodology if we formalize them as a kind of inverse problem. This novel approach provides an analytical and quantitative method for the problems of generalization and over-learning which have been so far treated qualitatively. Followings are the major results obtained in this project.・A new framework of generalization which can extract general structures among training samples is developed based on the image restoration theories.・We analyze the generalization ability of the back-propagation using the framework.・We provide a way of choosing, training samples which does not cause the over-learning problem and gives an optimal generalizing ability.・Above theoretical results are examined by some computer simulations.

提出了一种分析神经网络泛化能力和过度学习问题的有效神经网络学习理论。该理论是基于本项目首席研究员提出的图像恢复理论。虽然泛化和图像恢复的问题似乎没有什么共同之处，但我们已经证明，如果我们将它们形式化为一种逆问题，这两个问题可以在相同的方法下处理。这种新方法为迄今为止定性处理的泛化和过度学习问题提供了一种分析和定量的方法。以下是本项目取得的主要成果。·基于图像恢复理论，开发了一种新的泛化框架，可以提取训练样本之间的一般结构。·我们使用该框架分析了反向传播的泛化能力。我们提供了一种选择的方法，训练样本不会导致过度学习问题，并给出了最佳的泛化能力。通过计算机模拟验证了上述理论结果。

项目成果

小川 英光: "パタ-ン集合を最良に近似する部分空間" 電子情報通信学会技術報告. PRU90ー67. 67-72 (1990)

Hidemitsu Okawa：“最接近模式集的子空间”IEICE 技术报告。 67-72 (1990)。

Erkki Oja,Hidemitsu Ogawa and Jaroonsakdi Wangviwattana: "Principal component analysis by homogeneous neural networks,Part I:The weighte subspace criterion" IEICE Trans.on Information and Systems. E75-D No.3. (1992)

Erkki Oja、Hidemitsu Okawa 和 Jaroonsakdi Wangviwattana：“同质神经网络的主成分分析，第一部分：加权子空间准则”IEICE Trans.on Information and Systems。

Y. Yamashita and H. Ogawa: "Optimum image restoration filters and generalized inverse of operators" IEICE Trans. D-II, J75-D-II. 5. (1992)

Y. Yamashita 和 H. Okawa：“最佳图像恢复滤波器和算子的广义逆”IEICE Trans。

Hidemitsu Ogawa and Itsuo Kumazawa: "Mathematical Methods in Tomography" Lecture Notes in Mathematics, Vol. 1497, Radon Transform and Analog Coding. Springer-Verlag. 13 (1991)

小川秀光和熊泽五雄：《断层扫描中的数学方法》数学讲义，卷。

Erkki Oja, Hidemitsu Ogawa and Jaroonsakdi Wangviwattana: "Artificial Neural Networks, Learning in Nonlinear" Constrained Hebbian Networks. Elsevier Science Pub. 16 (1991)

Erkki Oja、Hidemitsu Okawa 和 Jaroonsakdi Wangviwattana：“人工神经网络，非线性学习”约束赫布网络。