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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >A Unified Self-Stabilizing Neural Network Algorithm for Principal and Minor Components Extraction
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A Unified Self-Stabilizing Neural Network Algorithm for Principal and Minor Components Extraction

机译：统一的自稳定神经网络算法提取主成分和次要成分

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摘要

Recently, many unified learning algorithms have been developed for principal component analysis and minor component analysis. These unified algorithms can be used to extract principal components and, if altered simply by the sign, can also serve as a minor component extractor. This is of practical significance in the implementations of algorithms. This paper proposes a unified self-stabilizing neural network learning algorithm for principal and minor components extraction, and studies the stability of the proposed unified algorithm via the fixed-point analysis method. The proposed unified self-stabilizing algorithm for principal and minor components extraction is extended for tracking the principal subspace (PS) and minor subspace (MS). The averaging differential equation and the energy function associated with the unified algorithm for tracking PS and MS are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set, and the corresponding energy function exhibit a unique global minimum attained if and only if its state matrices span the PS or MS of the autocorrelation matrix of a vector data stream. It is concluded that the proposed unified algorithm for tracking PS and MS can efficiently track an orthonormal basis of the PS or MS. Simulations are carried out to further illustrate the theoretical results achieved.
机译：最近，已经开发了许多用于主成分分析和次要成分分析的统一学习算法。这些统一的算法可用于提取主要成分，并且如果仅通过符号进行更改，还可以用作次要成分提取器。这在算法的实现中具有实际意义。针对主成分和次要成分，提出了一种统一的自稳定神经网络学习算法，并通过定点分析的方法研究了该算法的稳定性。提出的用于主次分量提取的统一自稳定算法被扩展用于跟踪主子空间（PS）和次子空间（MS）。给出了与跟踪PS和MS的统一算法相关的平均微分方程和能量函数。结果表明，平均微分方程将全局渐近收敛至不变集，并且当且仅当其状态矩阵跨越矢量数据流自相关矩阵的PS或MS时，相应的能量函数才会显示出唯一的全局最小值。结论是，所提出的用于跟踪PS和MS的统一算法可以有效地跟踪PS或MS的正交基础。进行仿真以进一步说明所获得的理论结果。

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