非线性框架（Frame）表现及字典学习与神经网络的非梯度反向传播学习算法

训练效率及精度成为神经网络算法，即梯度反向传播与随机梯度下降优化算法这一领域的瓶颈，针对这一问题；也针对我国深度学习研究在算法方面相对于应用方面薄弱的状况，本项目拟通过导入超越梯度信息的反向传播及非基于梯度的优化方法，构建一整套新的神经网络训练算法，以期达到在性能上实现新突破的目的。为此，我们首先导入非线性框架表现及字典学习问题，其本身是机器学习的一个新领域。此问题可以归结为一个非线性、非凸、非光滑目标函数的优化问题，不能用基于梯度的优化算法求解因此具有挑战性。我们通过引入增强拉格朗日乘子及邻近算子等近代优化技术构建有效算法。然后，我们把神经网络训练问题转化为一系列反向传播的非线性框架表现及字典学习问题并用其算法构建神经网络训练的新算法，即所谓非梯度反向传播及算法。最后，将新算法驱动的深度学习神经网络应用到籍由MRI脑梗塞自动诊断与装置免携带目标探测及定位问题并开发出具有实用价值的新技术。

The conventional algorithm for training a neural network is based on the gradient back-propagation and the stochastic gradient descent for optimization. It is well known that the gradient back-propagation suffers the gradient vanishing problem. Though deep learning has become very successful by solving the problem, based on the optimization theory, the gradient-based optimization method is a basic one, and is not so efficient as higher-level methods. How to make the training more efficient becomes a bottleneck of the development of the field. One the other hand, the algorithmic research of deep learning or neural network in China is not so active compared with that on application research. For improving these, in this application, we propose a back-propagation algorithm that propagates quantities beyond gradient, and a non-gradient algorithm for optimizing the network weights. Based on these, we shall construct one novel algorithmic scheme for training the neural network, with expecting a breakthrough on the performance of the neural network, including the deep learning. For this purpose, first, we introduce a so-called problem of nonlinear frame representation and dictionary learning, which self is a worthy of researching new machine leaning field. Since this problem is formulated as an optimization problem of a nonlinear, non-convex, non-smooth objective function, it cannot be efficiently solved by the ordinary method, including the gradient-base method. For solving this challenging problem, we shall be equipped with some modern optimization methods, such as the augmented Lagrangian method and the proximal operator method, so that we can work out efficient algorithms. Then, we transform the neural network training problem into a series of problems of nonlinear frame representation and dictionary learning, so that we can construct a more efficient algorithm, i.e., the non-gradient back-propagation algorithm, for neural network training. Finally, we apply the deep learning convolutional neural network driven by the proposed algorithm for clinical diagnosis by automated stroke lesion segmentation on MR image (MRI), and for the device-free localization (DFL), to reach a better performance than that of using the conventional training algorithm, so that these can become new applicable key technologies.