Heterogeneous data sets are typically represented in different feature spaces, making it difficult to analyze relationships spanning different data sets even when they are semantically related. Data fusion via space alignment can remedy this task by integrating multiple data sets lying in different spaces into one common space. Given a set of reference correspondence data that share the same semantic meaning across different spaces, space alignment attempts to place the corresponding reference data as close together as possible, and accordingly, the entire data are aligned in a common space. Space alignment involves optimizing two potentially conflicting criteria: minimum deformation of the original relationships and maximum alignment between the different spaces. To solve this problem, we provide a novel graph embedding framework for space alignment, which converts each data set into a graph and assigns zero distance between reference correspondence pairs resulting in a single graph. We propose a graph embedding method for fusion based on nonmetric multidimensional scaling (MDS). Its criteria using the rank order rather than the distance allows nonmetric MDS to effectively handle both deformation and alignment. Experiments using parallel data sets demonstrate that our approach works well in comparison to existing methods such as constrained Laplacian eigenmaps, Procrustes analysis, and tensor decomposition. We also present standard cross-domain information retrieval tests as well as interesting visualization examples using space alignment.