We consider a hypercube view to perceive the label space of multilabel classification problems geometrically. The view allows us not only to unify many existing multilabel classification approaches but also design a novel algorithm, principal label space transformation (PLST), that captures key correlations between labels before learning. The simple and efficient PLST relies on only singular value decomposition as the key step. We derive the theoretical guarantee of PLST and evaluate its empirical performance using real-world data sets. Experimental results demonstrate that PLST is faster than the traditional binary relevance approach and is superior to the modern compressive sensing approach in terms of both accuracy and efficiency.