This thesis will address the fusion of multiple data sources arising in remote sensing, such as hyperspectral and LIDAR. Fusing of multiple data sources provides better data representation and classification results than any of the independent data sources would alone. We begin our investigation with the well-studied Laplacian Eigenmap (LE) algorithm. This algorithm offers a rich template to which fusion concepts can be added. For each phase of the LE algorithm (graph, operator, and feature space) we develop and test different data fusion techniques. We also investigate how partially labeled data and approximate LE preimages can used to achieve data fusion. Lastly, we study several numerical acceleration techniques that can be used to augment the developed algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nystrom extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nystrom extension
