Due to advances in sensor technology, it is now possible to acquire
hyperspectral data simultaneously in hundreds of bands. Algorithms that
both reduce the dimensionality of the data sets and handle highly
correlated bands are required to exploit the information in these data
sets effectively. We propose a set of best bases feature extraction
algorithms that are simple, fast and highly effective for classification
of hyperspectral data. These techniques intelligently combine subsets of
adjacent bands into a smaller number of features. Both top-down and
bottom-up algorithms are proposed. The top-down algorithm recursively
partitions the bands into two (not necessarily equal) sets of bands, and
then replaces each final set of bands by its mean value. The bottom-up
algorithm builds an agglomerative tree by merging highly correlated
adjacent bands and projecting them onto their Fisher direction, yielding
high discrimination among classes. Both these algorithms are used in a
pairwise classifier framework where the original $C$-class problem is
divided into a set of $C\choose 2$ two-class problems.

The new algorithms $(i)$ find variable length bases localized in
wavelength, $(ii)$ favor grouping highly correlated adjacent bands that,
when merged either by taking their mean or Fisher linear projection, yield
maximum discrimination, and $(iii)$ seek orthogonal bases for each of the
$C\choose 2$ two-class problems into which a $C$-class problem can be
decomposed. Experiments on an AVIRIS data set for a 12-class problem show
significant improvements in classification accuracies while using a much
smaller number of features. Moreover, the proposed methodology facilitates
the extraction of valuable domain knowledge regarding the importance of
certain bands for discriminating specific groups of classes.