Three common numerical optimization algorithms are first studied, including conjugate gradient algorithm, quasi-newton algorithm and LM algorithm. The three kinds of algorithms are used to improve BP neural network respectively and the corresponding classification models based on BP neural network are established. Then the models are used in pattern classification of two-dimensional vectors, and their generalization abilities are also tested. The classification results of different classification models based on BP network are compared with each other. Simulation results show that for small or medium scale networks, BP neural network improved by LM algorithm has the most precise classification result, the fastest convergence speed and the best classification ability. The one improved by conjugate gradient algorithm has the biggest error, slowest convergence speed and worst classification ability. While the classification precision, convergence speed and classification ability of quasi-newton algorithm lie between the above two algorithms.%研究了共轭梯度算法、拟牛顿算法、LM 算法三类常用的数值优化改进算法，基于这三类数值优化算法分别对BP神经网络进行改进，并构建了相应的BP神经网络分类模型，将构建的分类模型应用于二维向量模式的分类，并进行了泛化能力测试，将不同BP网络分类模型的分类结果进行对比。仿真结果表明，对于中小规模的网络而言， LM数值优化算法改进的BP网络的分类结果最为精确，收敛速度最快，分类性能最优；共轭梯度数值优化算法改进的BP网络的分类结果误差最大，收敛速度最慢，分类性能最差；拟牛顿数值优化算法改进的BP网络的分类结果误差值、收敛速度及分类性能介于上述两种算法之间。
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