In this paper, a novel local ways to implement hyperspectral anomaly detector is presented. Usually, the local detectors
are implemented in the spatial window of image scene, but the proposed approach is implemented on the windows of
spectral space. As a multivariate data, the hyperspectral image datasets can be considered as a low-dimensional manifold
embedded in the high-dimensional spectral space. In real environments, nonlinear spectral mixture occurs more
frequently. At these situations, whole dataset would be distributed in one or more nonlinear manifolds in high
dimensional space, such as a hyper-curve surface or nonlinear hyper-simplex. However, the majority of global and local
detectors in hyperspectral image are based on the linear projections. They are established on the assumption that the
geometric distribution of datasets is a linear manifold. It is incapable for them to deal with these nonlinear manifold data,
even for spatial local data. In this paper, a novel anomaly detection algorithm based on local linear manifold is put
forward to handle the nonlinear manifold problems. In the algorithm, the local neighborhood relationships are
established in spectral space, and then an anomaly detector based on linear projection is carried out in these local areas.
This situation is similar to using sliding windows in the spectral space. The results are compared with classic spatial
local algorithm by using real hyperspectral image and demonstrate the effectiveness in improving the weak anomalies
detection and decreasing the false alarms.