LSOR: Longitudinally-Consistent Self-Organized Representation Learning.

Interpretability is a key issue when applying deep learning models to longitudinal brain MRIs. One way to address this issue is by visualizing the high-dimensional latent spaces generated by deep learning via self-organizing maps (SOM). SOM separates the latent space into clusters and then maps the cluster centers to a discrete (typically 2D) grid preserving the high-dimensional relationship between clusters. However, learning SOM in a high-dimensional latent space tends to be unstable, especially in a self-supervision setting. Furthermore, the learned SOM grid does not necessarily capture clinically interesting information, such as brain age. To resolve these issues, we propose the first self-supervised SOM approach that derives a high-dimensional, interpretable representation stratified by brain age solely based on longitudinal brain MRIs (i.e., without demographic or cognitive information). Called Longitudinally-consistent Self-Organized Representation learning (LSOR), the method is stable during training as it relies on soft clustering (vs. the hard cluster assignments used by existing SOM). Furthermore, our approach generates a latent space stratified according to brain age by aligning trajectories inferred from longitudinal MRIs to the reference vector associated with the corresponding SOM cluster. When applied to longitudinal MRIs of the Alzheimer's Disease Neuroimaging Initiative (ADNI, $N=632$), LSOR generates an interpretable latent space and achieves comparable or higher accuracy than the state-of-the-art representations with respect to the downstream tasks of classification (static vs. progressive mild cognitive impairment) and regression (determining ADAS-Cog score of all subjects). The code is available at https://github.com/ouyangjiahong/longitudinal-som-single-modality.