Selecting the number of components in PCA via random signflips

Understand

Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep.

• However, classical selection methods (e.g., scree plots, parallel analysis, etc.) lack statistical guarantees in the increasingly common setting of large-dimensional data with heterogeneous noise, i.e., where each entry may have a different noise variance.
• Moreover, it turns out that these methods, which are highly effective for homogeneous noise, can fail dramatically for data with heterogeneous noise.
• This paper proposes a new method called signflip parallel analysis (FlipPA) for the setting of approximately symmetric noise: it compares the data singular values to those of "empirical null" matrices generated by flipping the sign of each entry randomly with probability one-half.