Principal component analysis (PCA) is widely used for dimensionality reduction and unsupervised learning. The reconstruction error is sometimes large even when a large number of eigenmode is used. In this paper, we show that this unexpected error source is the pollution effect of a summation operation in the objective function of the PCA algorithm. The summation operator brings together unrelated parts of the data into the same optimization and the result is the reduction of the accuracy of the overall algorithm. We introduce a domain decomposed PCA that improves the accuracy, and surprisingly also increases the parallelism of the algorithm. To demonstrate the accuracy and parallel efficiency of the proposed algorithm, we consider three applications including a face recognition problem, a brain tumor detection problem using two- and three-dimensional MRI images.

中文翻译：

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主成分分析的求和污染及位置敏感数据的改进算法

主成分分析 (PCA) 广泛用于降维和无监督学习。即使使用大量本征模，重建误差有时也很大。在本文中，我们证明了这种意想不到的误差源是 PCA 算法目标函数中求和运算的污染效应。求和算子将数据中不相关的部分合并到同一个优化中，结果是降低了整个算法的准确性。我们引入了一个域分解 PCA 来提高准确性，并且令人惊讶地还增加了算法的并行性。为了证明所提出算法的准确性和并行效率，我们考虑了三个应用程序，包括人脸识别问题，