Extending classical Archetypal Analysis into non-linear latent spaces using deep generative models.
Classical Archetypal Analysis (AA) describes every data point as a convex combination of extreme "pure types" — the archetypes — which sit at the boundary of the data convex hull. It is an inherently interpretable dimensionality reduction method, but is limited to linear feature spaces.
This project implements and explores Deep Archetypal Analysis (DeepAA): integrating the archetype model into the latent space of a Variational Autoencoder (VAE), enabling non-linear, generative archetypal decomposition that scales to complex high-dimensional data such as images.
- Archetypes — extreme, interpretable prototypes that span the latent convex hull; every data point is a mixture of these
- Variational Autoencoder — encoder-decoder architecture that learns a structured probabilistic latent space
- Archetype Loss — distance-dependent loss that drives latent representations toward a convex archetypal structure
- Convex Mixing — latent codes are constrained to be convex combinations of learned archetypes via softmax-constrained weight matrices
Key libraries: torch · numpy · matplotlib · scikit-learn · scipy
Developed as a project for 02456 – Deep Learning at DTU – Technical University of Denmark (Autumn 2025).
João Mata and Manuel Charneca.