This thesis is about dimensionality reduction for hyperspectral data. Special emphasis is given to dimensionality reduction techniques known as kernel eigenmap methods and manifold learning algorithms. Kernel eigenmap methods require a nearest neighbor or a radius parameter be set. A new algorithm that does not require these neighborhood parameters is given. Most kernel eigenmap methods use the eigenvectors of the kernel as coordinates for the data. An algorithm that uses the frame potential along with subspace frames to create nonorthogonal coordinates is given. The algorithms are demonstrated on hyperspectral data. The last two chapters include analysis of representation systems for LIDAR data and motion blur estimation, respectively.