  Set classification aims to classify a set of observations as a whole, as
opposed to classifying individual observations separately. To formally
understand the unfamiliar concept of binary set classification, we first
investigate the optimal decision rule under the normal distribution, which
utilizes the empirical covariance of the set to be classified. We show that the
number of observations in the set plays a critical role in bounding the Bayes
risk. Under this framework, we further propose new methods of set
classification. For the case where only a few parameters of the model drive the
difference between two classes, we propose a computationally-efficient approach
to parameter estimation using linear programming, leading to the
Covariance-engaged LInear Programming Set (CLIPS) classifier. Its theoretical
properties are investigated for both independent case and various (short-range
and long-range dependent) time series structures among observations within each
set. The convergence rates of estimation errors and risk of the CLIPS
classifier are established to show that having multiple observations in a set
leads to faster convergence rates, compared to the standard classification
situation in which there is only one observation in the set. The applicable
domains in which the CLIPS performs better than competitors are highlighted in
a comprehensive simulation study. Finally, we illustrate the usefulness of the
proposed methods in classification of real image data in histopathology.
