基于Hebbian神经网络的主元分析算法研究

主元分析技术具有降维数据、消除冗余特征等特点，已被广泛地应用到模式识别和信号处理等领域。在主元分析的实现方式中，基于Hebbian神经网络的主元分析算法因其具有在线运算、计算复杂度低、适用于非平稳过程等优势是该领域的研究热点和主流算法。当前，现有该类算法中多数存在数值稳定性不高、算子作用机理模糊、收敛性条件苛刻等问题。基于此，本项目以提升算法的综合性能和创新算法的性能分析方法为目标，主要研究基于Hebbian神经网络的多维主元分析算法、子空间跟踪算法、广义主元分析算法以及算法收敛性分析等内容，重点解决该类算法中不同算子的功能特性分析、拓宽算法收敛性条件等关键问题。项目成果有望丰富和发展基于Hebbian神经网络的主元分析算法理论体系，具有非常重要的理论价值和应用价值。

Principal component analysis (PCA), which can reduce data dimension and eliminate redundant features, has been widely used in pattern recognition and signal processing. As an important implementation, the Hebbian neural network-based PCA algorithms have attracted much attentions and become a hot research topic in this field, since they are on-line computation, low computational complexity and suitable for tracking non-stationary process. Up to now, most of the existing algorithms have some shortcomings, such as poor numerical stability, fuzzy operator mechanism and harsh convergence conditions. Based on this, this project aims to improve the algorithm’s comprehensive performance and innovate the characteristic analysis method. The main research points include multiple PCA algorithm, subspace tracking algorithm, generalized PCA algorithm, and the convergence analysis of these algorithm. This project focuses on how to analyze the function of different operators and broaden the convergence conditions. The results of the project, which are expected to enrich and develop the theoretical system of PCA algorithm based on Hebbian neural network, have important theoretical value and application value.