Estimating the intrinsic dimensionality of hyperspectral images

Estimating the intrinsic dimensionality (ID) of an intrinsically low (d-) dimensional data set embedded in a high (n-) dimensional input space by conventional Principal Component Analysis (PCA) is computationally hard because PCA scales cubic (O(n)) with the input dimension [11]. Besides this computational drawback, global PCA will overestimate the ID if the data manifold is curved. In this paper we apply ID OTPM [1], a new algorithm for ID estimation based on Optimally Topology Preserving Maps [7] to image sequences. In particular, we utilize ID OTPM for ID estimation of an AVIRIS data set, a hyperspectral remote sensing image cube, with input dimension of the individual image planes n = 257880. Most interestingly, our experiments suggest that the inter-band dimension db of the AVIRIS data set is between one and two, whereas the spectral dimension ds is about four. These results provide important clues for compression, visualization and classi cation of the the AVIRIS data set.