  One-class learning is the classic problem of fitting a model to the data for
which annotations are available only for a single class. In this paper, we
explore novel objectives for one-class learning, which we collectively refer to
as Generalized One-class Discriminative Subspaces (GODS). Our key idea is to
learn a pair of complementary classifiers to flexibly bound the one-class data
distribution, where the data belongs to the positive half-space of one of the
classifiers in the complementary pair and to the negative half-space of the
other. To avoid redundancy while allowing non-linearity in the classifier
decision surfaces, we propose to design each classifier as an orthonormal frame
and seek to learn these frames via jointly optimizing for two conflicting
objectives, namely: i) to minimize the distance between the two frames, and ii)
to maximize the margin between the frames and the data. The learned orthonormal
frames will thus characterize a piecewise linear decision surface that allows
for efficient inference, while our objectives seek to bound the data within a
minimal volume that maximizes the decision margin, thereby robustly capturing
the data distribution. We explore several variants of our formulation under
different constraints on the constituent classifiers, including kernelized
feature maps. We demonstrate the empirical benefits of our approach via
experiments on data from several applications in computer vision, such as
anomaly detection in video sequences, human poses, and human activities. We
also explore the generality and effectiveness of GODS for non-vision tasks via
experiments on several UCI datasets, demonstrating state-of-the-art results.
