极速非线性判别分析网络

由于线性判别分析仅是线性方法，难以有效应对非线性问题，而对其非线性化是解决这一问题的关键途径。非线性化判别方法主要包括神经网络和核化方法。神经网络判别分析方法虽然继承了神经网络所具有的自适应、分布存储、并行处理和非线性映射等优点，但也遗传了其训练速度慢且易陷入局部最小值缺点；而核线性判别分析方法虽能获得全局最优解析解，但因受制于隐节点数目（等于样本个数），当数据规模大时，计算成本变大。本文受随机映射启发，对神经网络判别分析方法进行极速化改造，实现了一种极速非线性判别分析方法，兼具神经网络的自适应性和全局最优解的快速性。最后在UCI真实数据集上的实验表明，极速非线性判别分析方法具有更优的分类性能。

Extreme Nonlinear Discriminant Analysis Network

As the linear discriminant analysis (LDA) is just a linear method and is difficult to effectively deal with nonlinear problems, non-linearizing LDA is a crucial strategy to enable it to solve such nonlinear problems. Nonlinear LDA is mainly based on two strategies, neural networks and kernelization. A representative of the former strategy is the neural network discriminant analysis (NNDA). Athough NNDA inherits the advantages such as self-adaption, parallel processing, distributed storing and nonlinear mapping of neural networks, its training is quite time-consuming and likely to get trapped in local minimum. While the representative of the latter strategy is the kernel linear discriminant analysis (KLDA). Although KLDA can obtain a global optimal analytical solution, its computational cost is rather high, due to the fact that the number of hidden nodes of KLDA is equal to the size of training samples, especially in large scale scenarios. Inspired by the idea of random map, a novel extreme nonlinear discriminant analysis (ENDA) is proposed by reconstructing NNDA via extreme learning strategy in this paper. ENDA shares both the self-adaption of NNDA and the efficient computation of global optimal solution of KLDA. Finally, experimental results on UCI datasets demonstrate the superiority of ENDA over KLDA and NNDA in classification accuracy.