  Classical approaches in cluster analysis are typically based on a feature
space analysis. However, many applications lead to datasets with additional
spatial information and a ground truth with spatially coherent classes, which
will not necessarily be reconstructed well by standard clustering methods.
Motivated by applications in hyperspectral imaging, we introduce in this work
clustering models based on orthogonal nonnegative matrix factorization, which
include an additional total variation (TV) regularization procedure on the
cluster membership matrix to enforce the needed spatial coherence in the
clusters. We propose several approaches with different optimization techniques,
where the TV regularization is either performed as a subsequent postprocessing
step or included into the clustering algorithm. Finally, we provide a numerical
evaluation of all proposed methods on a hyperspectral dataset obtained from a
matrix-assisted laser desorption/ionisation imaging measurement, which leads to
significantly better clustering results compared to classical clustering
models.
