Longitudinal Self-Supervised Learning

Abstract

Longitudinal neuroimaging or biomedical studies often acquire multiple observations from each individual over time, which entails repeated measures with highly interdependent variables. In this paper, we discuss the implication of repeated measures design on unsupervised learning by showing its tight conceptual connection to self-supervised learning and factor disentanglement. Leveraging the ability for 'self-comparison' through repeated measures, we explicitly separate the definition of the factor space and the representation space enabling an exact disentanglement of time-related factors from the representations of the images. By formulating deterministic multivariate mapping functions between the two spaces, our model, named Longitudinal Self-Supervised Learning (LSSL), uses a standard autoencoding structure with a cosine loss to estimate the direction linked to the disentangled factor. We apply LSSL to two longitudinal neuroimaging studies to show its unique advantage in extracting the 'brain-age' information from the data and in revealing informative characteristics associated with neurodegenerative and neuropsychological disorders. For a downstream task of supervised diagnosis classification, the representations learned by LSSL permit faster convergence and higher (or similar) prediction accuracy compared to several other representation learning techniques.

Self-Supervised Longitudinal Neighbourhood Embedding

“…The objective function encourages the low-dimensional representation of the images to be informative while maintaining a smooth progression trajectory field in the latent space. As the cosine loss is only locally imposed, the global trajectory field can be non-linear, which relaxes the strong assumption in prior studies (e.g., LSSL [31]) that aging must define a globally linear direction in the latent space. Note, our method can be regarded as a contrastive self-supervised method.…”

“…Objective Function. As shown in [31], the speed of brain aging is already highly heterogeneous within a healthy population, and subjects with neurodegenerative diseases may exhibit accelerated aging. Therefore, instead of replacing ∆z with ∆h, we define θ ∆z,∆h as the angle between ∆z and ∆h, and only encourage cos(θ ∆z,∆h ) = 1, i.e., a zero-angle between the subject-specific trajectory vector and the pooled trajectory vector that represents the local progression direction.…”

“…In a separate experiment, we fine-tuned the LNE representation by incorporating the encoder into the classification models. We compared the BACC (accounting for different number of training samples in each cohort) to models using the same architecture with encoders pre-trained by other representation learning methods, including unsupervised methods (AE, VAE [15]), self-supervised method (SimCLR [6]), and longitudinal self-supervised method (LSSL [31]).…”