Abstract Sparse principal component analysis (SPCA) has been shown to be a fruitful method for the analysis of high-dimensional data. So far, however, no method has been proposed that allows to assign elementwise weights to the matrix of residuals, although this may have several useful applications. We propose a novel SPCA method that includes the flexibility to weight at the level of the elements of the data matrix. The superior performance of the weighted SPCA approach compared to unweighted SPCA is shown for data simulated according to the prevailing multiplicative-additive error model. In addition, applying weighted SPCA to genomewide transcription rates obtained soon after vaccination, resulted in a biologically meaningful selection of variables with components that are associated to the measured vaccine efficacy. The MATLAB implementation of the weighted sparse PCA method is freely available from https://github.com/katrijnvandeun/WSPCA .

中文翻译：

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加权稀疏主成分分析

摘要 稀疏主成分分析（SPCA）已被证明是分析高维数据的有效方法。然而，到目前为止，还没有提出允许为残差矩阵分配元素权重的方法，尽管这可能有几个有用的应用。我们提出了一种新颖的 SPCA 方法，该方法包括在数据矩阵的元素级别上灵活加权。与未加权的 SPCA 相比，加权 SPCA 方法的优越性能显示为根据流行的乘法-加法误差模型模拟的数据。此外，将加权 SPCA 应用于疫苗接种后不久获得的全基因组转录率，可以选择具有生物学意义的变量，这些变量具有与测量的疫苗功效相关的成分。