Diffusion map for clustering fMRI spatial maps extracted by independent component analysis
This is an incremental improvement for researchers analyzing fMRI data, addressing the challenge of clustering in high-dimensional spaces with small sample sizes.
The paper tackled clustering of high-dimensional fMRI spatial maps extracted by ICA, where the number of voxels is much larger than the number of maps, by using diffusion maps for dimensionality reduction before spectral clustering. The result showed that diffusion map-based clustering performed as well as traditional methods and produced more compact clusters when needed.
Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering. In this research, we used the recently developed diffusion map for dimensionality reduction in conjunction with spectral clustering. This research revealed that the diffusion map based clustering worked as well as the more traditional methods, and produced more compact clusters when needed.