Phantom oscillations in principal component analysis

Abstract

Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this simple interpretation fails for timeseries, spatial maps, and other continuous data. In these cases, nonoscillatory data may have oscillatory principal components. Here, we show that two common properties of data cause oscillatory principal components: smoothness and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations produced by PCA, 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.

State-transition Modeling of Blood Transcriptome Predicts Disease Evolution and Treatment Response in Chronic Myeloid Leukemia

“…Because the SVD decomposed the gene expression into linear combinations of orthogonal basis vectors, we were able to assess the contribution of individual genes, DEGs, or entire Hallmark gene sets to CML initiation and growth. Although the SVD can produce artifacts when applied to time-series data, we observed no oscillations or artifacts, and moreover, we observed a strong correlation between state-space trajectories and BCR::ABL expression as an immunophenotypic marker of disease, supporting our interpretation of the principal component as a transcriptome state-space 31 . We observed that the Es ( c 1 ) state was largely characterized by anti-CML DEGs that resisted CML development whereas the Ts ( c 3 ) and Ls ( c 5 ) disease states were characterized by pro-CML DEGs associated with the movement of state-transition toward late disease state.…”

“…Although the correlation with BCR::ABL was by far the best for the CML state-space compared to all other PCs, the correlation was low (R 2 = 0.48; Table S1). Although PCA can be misinterpreted when applied to time-series data with temporal correlations, we are confident in our application and interpretation here because of the correlation with BCR::ABL expression, phenotypic disease manifestation, and the absence of oscillations or other artifacts in the PCs 31,40 . This is due to the orthogonality of the control (tet on) and CML (tet off) mice transcriptome endpoints and dynamics, which enable an orthogonal decomposition of the data and identification of the leukemia signal from the background/noise.…”

The flow of reward information through neuronal ensembles in the accumbens

“…Following head entry, both trajectories deviate from zero, suggesting increased neural activity. Interestingly, they exhibit an initial “twist” (potentially a phantom oscillation because of data smoothing 36 ) between the Go signal and the rat’s exit from the central port. In the Choice epoch, the trajectories undergo a second “twist” and move further away from the origin, reflecting increased engagement.…”

Stability from subspace rotations and traveling waves

“…Sometimes a time-shifting pattern in data (i.e. different neurons with different spike latencies) can result in oscillatory jPCs, even if oscillatory dynamics are not actually in the data 29 . In these cases, all the jPCs show rotations.…”