Local intrinsic dimensionality of hyperspectral imagery from non-linear manifold coordinates

Recent advances in non-linear dimensionality approaches to hyperspectral image analysis have renewed interest in and provided a means to determine the intrinsic dimensionality of hyperspectral data. Of the many theoretical / computational approaches to dimensionality reduction, we discuss the local intrinsic dimensionality derived from the ISOMAP manifold approach. The ISOMAP algorithm itself provides one measure of global dimensionality, the eigenvalue spectrum. However, other estimation techniques are more easily adapted to determine the local dimensionality; chief among these are methods that measure minimum spanning path lengths for subsets of the full image. While intrinsic dimensionality is inherently scene dependent, knowledge of the information content, and underlying dimensionality, can guide data analysis methods and suggest appropriate data compression limits.