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Linear matrix factorizations (LMFs) such as independent component analysis(ICA), principal component analysis (PCA), and their extensions, have beenwidely used for finding relevant spatial maps in brain imaging data. The laststep of an LMF before interpretation is usually to extract the activated brainregions from the map by thresholding. However, it is difficult to determine anappropriate threshold level. Thresholding can remove the underlying propertiesof spatial maps and their features imposed by the model. In this study, wepropose a threshold-free activated region extraction method which involvessimplifying a brain spatial map to a dendrogram through Morse filtration. Sincea dendrogram is related to the change of clustering structure in Ripsfiltration, we first show the relationship between the Rips filtration of agraph and the Morse filtration of a function. Then, we dendrogramize a spatialmap in order to visualize the activated brain regions and the range of theirimportance in a spatial map. The proposed method can be applied to any spatialmaps that a user wants to threshold and interpret. In experiments, we appliedthe proposed method to independent component maps (ICMs) obtained fromresting-state fMRI data, and the dominant subnetworks obtained by the PCA of acorrelation-based functional connectivity of FDG PET Alzheimer's diseaseneuroimaging initiative (ADNI) data. We found that dendrogramization can helpto understand a brain spatial map without thresholding.

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