Motivation: Most automatic functional annotation methods assign Gene Ontology (GO) terms to proteins based on annotations of highly similar proteins. We advocate that proteins that are less similar are still informative. Also, despite their simplicity and structure, GO terms seem to be hard for computers to learn, in particular the Biological Process ontology, which has the most terms (>29 000). We propose to use Label-Space Dimensionality Reduction (LSDR) techniques to exploit the redundancy of GO terms and transform them into a more compact latent representation that is easier to predict. Results: We compare proteins using a sequence similarity profile (SSP) to a set of annotated training proteins. We introduce two new LSDR methods, one based on the structure of the GO, and one based on semantic similarity of terms. We show that these LSDR methods, as well as three existing ones, improve the Critical Assessment of Functional Annotation performance of several function prediction algorithms. Cross-validation experiments on Arabidopsis thaliana proteins pinpoint the superiority of our GO-aware LSDR over generic LSDR. Our experiments on A.thaliana proteins show that the SSP representation in combination with a kNN classifier outperforms state-of-the-art and baseline methods in terms of cross-validated F-measure. Availability and implementation: Source code for the experiments is available at https://github.com/stamakro/SSP-LSDR.