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Space Complexity Analysis in Hybrid Principal Component Analysis

机译：混合主成分分析中的空间复杂度分析

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Conventional linear PCA approaches do not adequately handle the issues such as intrinsic spatial structural information of pattern, the complexity of calculating covariance matrix, variations restricted to some parts of a pattern, and small sample size problem, etc. To handle the above challenges, several PCAs in feature partitioning framework have been developed to improve the recognition accuracy. Recently developed approaches such as extended cross-correlation sub-pattern principal component analysis (ESubXPCA) operate on the sub-pattern and whole pattern at a time and captures the local and global variation of patterns by maintaining cross-correlations across sub-pattern and whole pattern sets. Along with recognition accuracy and time, space complexity is also an important parameter to study the relative effectiveness of a PCA approach. In this paper, we have formulated the space complexities of various PCAs in feature partitioning framework and compare them with some similar methods both theoretically and experimentally. The experiment conducted on ORL and YALE face datasets with multiple image resolutions. The experimental results show the technique ESubXPCA exhibits minimum feature dimensionality; SpPCA exhibits minimum space requirements for the covariance matrix and to design the complete recognition system.
机译：传统的线性PCA方法无法充分解决诸如模式的固有空间结构信息，计算协方差矩阵的复杂性，限于模式某些部分的变化以及样本量较小等问题。已经开发了特征划分框架中的PCA，以提高识别准确性。最近开发的方法，例如扩展互相关子模式主成分分析（ESubXPCA），一次在子模式和整个模式上运行，并通过在子模式和整个整体之间保持互相关来捕获模式的局部和全局变化。模式集。除了识别准确性和时间以外，空间复杂度也是研究PCA方法相对有效性的重要参数。在本文中，我们在特征划分框架中制定了各种PCA的空间复杂度，并在理论上和实验上将它们与一些相似的方法进行了比较。该实验是在具有多种图像分辨率的ORL和YALE面部数据集上进行的。实验结果表明，该技术ESubXPCA表现出最小的特征维数。 SpPCA展示了协方差矩阵和设计完整识别系统所需的最小空间。

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