Phantom oscillations in principal component analysis

Abstract

Principal component analysis (PCA) is a dimensionality reduction technique that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional data. However, this simple interpretation of PCA relies on several unstated assumptions that are difficult to satisfy. When these assumptions are violated, non-oscillatory data may have oscillatory principal components. Here, we show that two common properties of data violate these assumptions and cause oscillatory principal components: smooth-ness, and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations that they produce, which we call "phantom oscillations", impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.