Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When moving from PCA to sPCA, there are a number of implications that the practitioner needs to be aware of. A relevant one is that scores and loadings in sPCA may not be orthogonal. For this reason, the traditional way of computing scores, residuals and variance explained that is used in the classical PCA cannot directly be applied to sPCA models. This also affects how sPCA components should be visualized. In this paper we illustrate this problem both theoretically and numerically using simulations for several state-of-the-art sPCA algorithms, and provide proper computation of the different elements mentioned. We show that sPCA approaches present disparate and limited performance when modeling noise-free, sparse data. In a follow-up paper, we discuss the theoretical properties that lead to this problem.

本文讨论了稀疏主成分分析(sPCA)方法中的一些问题，尤其是在计算分数、残差和方差解释时，与传统的主成分分析(PCA)方法不同，并展示了该方法在建模无噪声、稀疏数据时表现出不一致和有限的性能。

所有的稀疏PCA模型都是错的，但有些是有用的。第一部分：得分、残差和解释方差的计算