The Smoothing Artifact of Spatially Constrained Canonical Correlation Analysis in Functional MRI

Figure 3

Estimation of 𝑃₂(𝜔₀,CNR,𝑠,𝑀)=∫^∞_𝜔0𝑝(𝜔,CNR∣𝑠,𝑀)𝑑𝜔/∫^∞₀𝑝(𝜔,CNR∣𝑠,𝑀)𝑑𝜔 from motor activation data using numerical integration for all configurations of size 𝑠∈{1,…,9} for cCCA with the maximum constraint. The joint probability density 𝑝(𝜔,CNR∣𝑠,𝑀) in the integrands are determined with 2D kernel density estimation using a 2D Gaussian kernel (for an example see Figure 2). Note that for CNR>0.6, 𝑃₂ approaches the value 1 rapidly for all 𝑠≠1. This relationship is also true for data obtained from the memory experiment. Note that configurations with 𝑠=1 have no significance in contributing to the smoothing artifact because the smoothing artifact is by definition equal to zero for 𝑠=1.