Neuroimaging studies produce gigabytes of spatio-temporal data for a small number of participants and stimuli. Recent work increasingly suggests that the common practice of averaging across participants and stimuli leaves out systematic and meaningful information. We propose Neural Topographic Factor Analysis (NTFA), a probabilistic factor analysis model that infers embeddings for participants and stimuli. These embeddings allow us to reason about differences between participants and stimuli as signal rather than noise. We evaluate NTFA on data from an in-house pilot experiment, as well as two publicly available datasets. We demonstrate that inferring representations for participants and stimuli improves predictive generalization to unseen data when compared to previous topographic methods. We also demonstrate that the inferred latent factor representations are useful for downstream tasks such as multivoxel pattern analysis and functional connectivity.

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by and are at least as expressive as spectral clustering. Our training objective, based on the Hilbert Schmidt Independence Criterion, can be optimized via gradient adaptations on the Stiefel manifold, leading to significant acceleration over spectral methods relying on eigen-decompositions. Finally, our trained embedding can be directly applied to out-of-sample data. We show experimentally that our approach outperforms several state-of-the-art deep clustering methods, as well as traditional approaches such as k-means and spectral clustering over a broad array of real and synthetic datasets.