Kernel PCA for anomaly detection in hyperspectral images using spectral-spatial fusion

Kernel-based methods for anomaly detection have recently shown promising results - surpassing those of model-based statistical methods. This success is due in part to the distribution of the non-anomalous data failing to conform to the distribution model assumed by model-based statistical methods. Alternatively, the skeleton kernel principle component analysis anomaly detector (sKPCA-AD) assumes that a better background model can be learned by constructing a graph from a small, randomly sampled subset of the data (a skeleton). By definition, anomalies are rare and thus the sampling is assumed to be comprised chiefly of non-anomalous samples and correspondingly the learned graph models the background. Error magnitudes in the models' representation of data from the full data set are used as an anomaly measure. Additionally, the smaller skeleton sample makes kernel methods computationally feasible for hyperspectral images. The sKPCA-AD has proven successful using unordered spectral pixel data, however, anomalies are often larger objects composed of many neighboring pixels. In this paper we show that fusing spatial information derived from a panchromatic image with spectral information from a hyper/multispectral image can increase the accuracy of the sKPCA-AD. We accomplish this by creating several joint spectral-spatial kernels that are then used by the sKPCA-AD to learn the underlying background model. We take into account the variability introduced by the random subsampling by showing averaged results and variance over several skeletons. We test our methods on two representative datasets and our results show improved performance with one of the proposed joint kernel methods.