Estimation of the Intrinsic Dimensionality in Hyperspectral Imagery via the Hubness Phenomenon

As hyperspectral images are high-dimensional data sets containing a lot of redundancy, a first important step in many applications such as spectral unmixing or dimensionality reduction is estimation of the intrinsic dimensionality of the data set. We present a new method for estimation of the intrinsic dimensionality in hyperspectral images based upon the hubness phenomenon, which is the observation that indegree distributions in a K-nearest neighbor graph will become skewed as the intrinsic dimensionality of the data set rises. The proposed technique is based upon comparing the indegree distributions of artificially generated data sets with the one from the target data set, and identifying the best match with some histogram metric. We show that this method obtains superior results compared to many alternatives, and does not suffer from the effects of interband and spectral correlations.