This is a simulation-based contribution exploring a novel approach to the open-ended formation of multimodal representations in autonomous agents. In particular, we address the issue of transferring ("bootstrapping") feature selectivities between two modalities, from a previously learned or innate reference representation to a new induced representation. We demonstrate the potential of this algorithm by several experiments with synthetic inputs modeled after a robotics scenario where multimodal object representations are "bootstrapped" from a (reference) representation of object affordances. We focus on typical challenges in autonomous agents: absence of human supervision, changing environment statistics and limited computing power. We propose an autonomous and local neural learning algorithm termed PROPRE (projection-prediction) that updates induced representations based on predictability: competitive advantages are given to those feature-sensitive elements that are inferable from activities in the reference representation. PROPRE implements a bi-directional interaction of clustering ("projection") and inference ("prediction"), the key ingredient being an efficient online measure of predictability controlling learning in the projection step. We show that the proposed method is computationally efficient and stable, and that the multimodal transfer of feature selectivity is successful and robust under resource constraints. Furthermore, we successfully demonstrate robustness to noisy reference representations, non-stationary input statistics and uninformative inputs.