Information separation via phasor neural networks and its application

本研究旨在建立解释和解析哺乳动物脑功能的人工神经网络模型。提出了协方差场神经网络模型，它是经典模拟神经网络模型的自然推广，并给出了马尔可夫随机场的平均场近似。协方差场神经网络可以将脑电锋电位时序的协方差表示为相位差，这在脑信息处理中具有重要意义，可以进行基于锋电位时序的信息处理。作为一种平均场近似，它给出了更好的近似精度马尔可夫随机场相比，即使是大的重量强度的朴素平均场模型。我们进行了计算机实验来支持这一点。将该模型应用于图像分割，验证了相位差法的分割能力。本文提出了Boltzmann机的均值场学习方法，并通过实验验证了该方法在相位上的快速学习能力;另一方面，本文提出了神经网络的有效学习方法，特别是支持向量机（SVM）的有效学习方法。将SVM学习扩展为高效的多类分类算法，并将二阶锥规划方法应用于SVM学习。此外，我们提出了基于几何方法的最大间隔分类器，它的行为比快速SVM称为SMO更快。最后提出了一种新的基于核主成分分析的学习机，它可以自动确定核参数，从而实现无自由参数学习机。

The research was performed to develop the artificial neural network models for explaining and resolving the mammalian brain function. We proposed the covariance field neural network model which is a natural extension of the classical analogue neural network model, and gives a mean field approximation to Markov random fields. The covariance field neural network can represent the covariance of spike timing as the phase difference, which is important in brain information processing, and can perform information processing based on spike timing. As a mean field approximation it gives much better approximation accuracy for Markov random fields even for the large weight strength compared with the naive mean field model. We performed computer experiments to support this. We also applied this model to image segmentation, and confirmed the segmentation capability with phase-difference. We proposed the mean field learning for Boltzmann machine, and performed some fundamental experiments to confirm the quick training speed for the phase.On the other hand, we proposed the efficient learning methods for neural netoworks, especially for the recently highlighted support vector machine(SVM). We extended SVM learning to the efficient multi-class algorithm, and apply the second order cone programming method to SVM learning. In addition we proposed the maximal margin classifier based on the geometric method, which behaves faster than the quick SVM known as SMO. Finally we proposed a new learning machine based on the kernel PCA, which can automatically determine the kernel parameter so that it can realize the no free parameter learning machine.