Partial generalized correlation for hyperspectral data

A variational approach is proposed for the unsupervised assessment of attribute variability of high-dimensional data given a differentiable similarity measure. The key question addressed is how much each data attribute contributes to an optimum transformation of vectors for reaching maximum similarity. This question is formalized and solved in a mathematically rigorous optimization framework for each data pair of interest. Trivially, for the Euclidean metric minimization to zero distance induces highest vector similarity, but in case of the linear Pearson correlation measure the highest similarity of one is desired. During optimization the not necessarily symmetric trajectories between two vectors are recorded and analyzed in terms of attribute changes and line integral. The proposed formalism allows to assess partial covariance and correlation characteristics of data attributes for vectors being compared by any differentiable similarity measure. Its potential for generating alternative and localized views such as for contrast enhancement is demonstrated for hyperspectral images from the remote sensing domain.