摘要：传统的数据分析方法在处理高维数据时，难以准确提取数据的特征、获取数据的内在规律，尤其是大量高维不确定数据增加了存储与分析的难度。流形学习方法作为一种有效的数据特征提取与维数约简方法，能有效地挖掘数据的内在规律、提取准确稳健的数据特征，有利于数据的可靠分析，与非线性表征能力强的前馈神经网络结合，可以有效预测数据的未来趋势，建立高精度的预测模型。

本文的主要目的是利用流形学习算法结合前馈神经网络建立高精度的预测模型。主要分为以下几方面：

1.特征提取与维数约简。特征提取与维数约简在数据分析方面有着重要应用。流形学习方法作为一种有效的数据维数约简方法，即使在高维数据集合高度弯曲、重叠与间断的情况下，仍能充分挖掘数据的内在几何规律，反映数据的变化情况，有利于高精度的数据分析；

2.预测建模。通过利用合理的信息准则，对数据本质信息量进行估计，在保证数据信息量的情况下，进行合理的特征提取与维数约简。基于流形学习来提取准确可靠的数据特征，防止由于数据特征有限或重复信息造成前馈神经网络的权值退化等问题出现，进而结合前馈神经网络建立高精度的预测模型。

3.实验评估。基于经典的Swiss与BrokenSwiss数据等样本，通过以上策略设计，结合MATLAB计算软件来建立高精度的预测模型。实验评估表明：本文所设计的方法能有效地表征数据结构、提取数据特征、实现维数约简、加速收敛速度、提高预测精度以及增强模型的推广能力。

关键词：流形学习；维数约简；BP神经网络；预测模型

ABSTRACT：Dealing with high-dimensional data, traditional data analysis methods is hard to extract the characteristics of data and the inherent law accurately, especially when the difficulty of storage and analysis are added because of large number of uncertain high-dimensional data. Manifold-learning method, as an effective method for extracting date characteristics and reducing the dimension, can effectively excavate the inherent laws of data and extract accurate and steady data characteristics, which are conducive to reliable data analysis. Combined with non-linear feedforward neural network with strong representational  capacity, manifold-learning method can effectively forecast the future trend of the data and establish a high accuracy forecasting model.

The main purpose of this paper is to establish a high-precision forecastion model combining manifold-learning method and feedforward neural network. Mainly pided into the following aspects:

1. Extracting date characteristics and reducing the dimension. Date extraction and dimension reduction play an important role in data analysis. Even the high dimensional data sets are highly curved, overlapped and interrupted, manifold-learning method, as an effective data dimension reduction method, can fully exploit the inherent geometric laws of data, reflecting the change of the data and benefiting the high accuracy date analysis.

2. Forecasting and establishing the model. Using reasonable information criterion to estimate essential information quantity of the date, to extract date characteristics and reduce the dimension reasonably in the case of guaranteeing the amount of data information. Based on accurate and reliable data characteristics extracted in manifold learning, the problem such as feedforward neural network weight degradation caused by limited or repeated information can be prevented and then high-precision forecastion model can be established by combining with feedforward neural network.

3. Experimental evaluation. Based on the classic Swiss and broken Swiss data and above strategy design, the high-precision forecastion model can be established combining with Matlab calculation software. The experimental evaluation results show that the method designed   in   the   paper   can   effectively   represent   the   data   structure,   extract   the data characteristics, realize the dimension reduction, accelerate the convergence speed, improve the forecastion precision and enhance the generalization ability of the model.