We propose the Graph Space Embedding (GSE), a technique that maps the input into a space where interactions are implicitly encoded, with little computations required. We provide theoretical results on an optimal regime for the GSE, namely a feasibility region for its parameters, and demonstrate the experimental relevance of our findings. Next, we introduce a strategy to gain insight on which interactions are responsible for the certain predictions, paving the way for a far more transparent model. In an empirical evaluation on a real-world clinical cohort containing patients with suspected coronary artery disease, the GSE achieves far better performance than traditional algorithms.