  Low-energy electron microscopy (LEEM) taken as intensity-voltage (I-V) curves
provides hyperspectral images of surfaces, which can be used to identify the
surface type, but are difficult to analyze. Here, we demonstrate the use of an
algorithm for factorizing the data into spectra and concentrations of
characteristic components (FSC3) for identifying distinct physical surface
phases. Importantly, FSC3 is an unsupervised and fast algorithm. As example
data we use experiments on the growth of praseodymium oxide or ruthenium oxide
on ruthenium single crystal substrates, both featuring a complex distribution
of coexisting surface components, varying in both chemical composition and
crystallographic structure. With the factorization result a sparse sampling
method is demonstrated, reducing the measurement time by 1-2 orders of
magnitude, relevant for dynamic surface studies. The FSC3 concentrations are
providing the features for a support vector machine (SVM) based supervised
classification of the types. Here, specific surface regions which have been
identified structurally, via their diffraction pattern, as well as chemically
by complementary spectro-microscopic techniques, are used as training sets. A
reliable classification is demonstrated on both exemplary LEEM I-V datasets.
