Risk Related Brain Regions Detected with 3D Image FPCA

Abstract

Risk attitude and perception is reflected in brain reactions during RPID experiments. Given the fMRI data, an important research question is how to detect risk related regions and to investigate the relation between risk preferences and brain activity. Conventional methods are often insensitive to or misrepresent the original spatial patterns and interdependence of the fMRI data. In order to cope with this fact we propose a 3D Image Functional Principal Component Analysis (3D Image FPCA) method that directly converts the brain signals to fundamental spatial common factors and subject-specific temporal factor loadings via proper orthogonal decomposition. Simulation study and real data analysis show that the 3D Image FPCA method improves the quality of spatial representations and guarantees the contiguity of risk related regions. The selected regions provide signature scores and carry explanatory power for subjects' risk attitudes. For in-sample analysis, the 3D Image method perfectly classifies both strongly and weakly risk averse subjects. In out-of-sample, it achieves 73-88% overall accuracy, with 90-100% rate for strongly risk averse subjects, and 49-71% for weakly risk averse subjects.

Spatial functional principal component analysis with applications to brain image data

“…The objectives of our empirical analysis are to recover the risk related regions and also to predict subjects' risk attitude. Chen et al (2015), where the same data set is analyzed. To evaluate the estimation performance of the factors, we also compare the spatial functional factors identified by our approach to those 5 target regions.…”

“…The results show that the 5 risk related regions can be identified by φ j (s) for j = 1, 4, 5, 8 with our approach (75.81% of the variance can be explained by the first 8 factors, where the proportion of j = 1, 4, 5, 8 is 42.60%). In contrast, Chen et al (2015) consider the first 19 factors and find that j = 4, 18, 3(or 12), 5, 19 correspond to these 5 regions respectively. Our method seems to be more efficient in extracting the crucial features when dealing with high-dimensional data.…”

“…Our method seems to be more efficient in extracting the crucial features when dealing with high-dimensional data. In addition, the computational time consuming of our approach is much less compared to Chen et al (2015),…”

“…A straightforward approach would vectorize the 3D image into 1D vector of dimension 10 6 , but this might implicitly break the spatial connections (Heller et al, 2006). Chen et al (2015) proposes to conduct a 3D FPCA, but their approach needs to estimate a 6D smooth covariance function, and the computation cost is quite expensive.…”