This thesis provides a performance comparison of linear and nonlinear subspace-based anomaly detection algorithms. Using a dual-window technique to separate the local background into inner- and outer-window regions, pixel spectra from each region are projected onto subspaces defined by projection vectors that are generated using three common pattern classification techniques; the detection performances of these algorithms are then compared with the Reed-Xiaoli anomaly detector. Nonlinear methods are derived from each of the linear methods using a kernelization process that involves nonlinearly mapping the data into a high-dimensional feature space and replacing all dot products with a kernel function using the kernel-trick. A projection separation statistic determines how anomalous each pixel is. These algorithms are implemented on five hyperspectral images and performance comparisons are made using receiver operating characteristic (ROC) curves. Results indicate that detection performance is data dependent but that the nonlinear methods generally outperform their corresponding linear algorithms.