This thesis is concerned with development and applications of data fusion methods in thecontext of Laplacian eigenmaps. Multimodal data can be challenging to work with using classical statistical and signal processing techniques. Graphs provide a reference frame for the study of otherwise structure-less data. We combine spectral methods on graphs and geometric data analysis in order to create a novel data fusion model. We also provide examples of applications of this model to bioinformatics, color transformation and superresolution, and magnetic resonance imaging.