Understanding of a brain spatial map based on threshold-free function dendrogramization

Linear matrix factorizations (LMFs) such as independent component analysis (ICA), principal component analysis (PCA), and their extensions, have been widely used for finding relevant spatial maps in brain imaging data. The last step of an LMF before interpretation is usually to extract the activated brain regions from the map by thresholding. However, it is difficult to determine an appropriate threshold level. Thresholding can remove the underlying properties of spatial maps and their features imposed by the model. In this study, we propose a threshold-free activated region extraction method which involves simplifying a brain spatial map to a dendrogram through Morse filtration. Since a dendrogram is related to the change of clustering structure in Rips filtration, we first show the relationship between the Rips filtration of a graph and the Morse filtration of a function. Then, we dendrogramize a spatial map in order to visualize the activated brain regions and the range of their importance in a spatial map. The proposed method can be applied to any spatial maps that a user wants to threshold and interpret. In experiments, we applied the proposed method to independent component maps (ICMs) obtained from resting-state fMRI data, and the dominant subnetworks obtained by the PCA of a correlation-based functional connectivity of FDG PET Alzheimer's disease neuroimaging initiative (ADNI) data. We found that dendrogramization can help to understand a brain spatial map without thresholding.