  Set classification problems arise when classification tasks are based on sets
of observations as opposed to individual observations. In set classification, a
classification rule is trained with $N$ sets of observations, where each set is
labeled with class information, and the prediction of a class label is
performed also with a set of observations. Data sets for set classification
appear, for example, in diagnostics of disease based on multiple cell nucleus
images from a single tissue. Relevant statistical models for set classification
are introduced, which motivate a set classification framework based on
context-free feature extraction. By understanding a set of observations as an
empirical distribution, we employ a data-driven method to choose those features
which contain information on location and major variation. In particular, the
method of principal component analysis is used to extract the features of major
variation. Multidimensional scaling is used to represent features as
vector-valued points on which conventional classifiers can be applied. The
proposed set classification approaches achieve better classification results
than competing methods in a number of simulated data examples. The benefits of
our method are demonstrated in an analysis of histopathology images of cell
nuclei related to liver cancer.
