Title: Affinity-VAE for clustering and classification of objects in multidimensional image data. Abstract: In this work we present affinity-VAE: a framework for automatic clustering and classification of objects in multidimensional image data based on their similarity. The method expands on the concept of $\beta$-VAEs with an informed similarity-based loss component driven by an affinity matrix. The affinity-VAE is able to create rotationally-invariant, morphologically homogeneous clusters in the latent representation, with improved cluster separation compared with a standard $\beta$-VAE. We explore the extent of latent disentanglement and continuity of the latent spaces on both 2D and 3D image data, including simulated biological electron cryo-tomography (cryo-ET) volumes as an example of a scientific application. 