SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 977-1002, January 2020.
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. The approach can further leverage randomized methods from linear algebra to extend SPCA to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance.

中文翻译：

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通过可变投影进行稀疏主成分分析

SIAM应用数学杂志，第80卷，第2期，第977-1002页，2020年1月。
稀疏主成分分析（SPCA）已成为现代数据分析的强大技术，它通过识别数据中的局部空间结构并消除不同时间尺度之间的歧义，从而改善了对低秩结构的解释。通过将其公式化为价值函数优化问题，我们展示了一种健壮且可扩展的SPCA算法。这种观点导致了一种灵活且计算效率高的算法。该方法可以进一步利用线性代数的随机方法将SPCA扩展到大规模（大数据）设置。我们提出的创新技术还提供了健壮的SPCA公式，即使输入数据严重损坏，该公式仍可获取有意义的稀疏主成分。拟议的算法使用合成数据和真实数据进行了演示，