One-class learning is the classic problem of fitting a model to data for
which annotations are available only for a single class. In this paper, we
propose a novel objective for one-class learning. Our key idea is to use a pair
of orthonormal frames -- as subspaces -- to "sandwich" the labeled data via
optimizing for two objectives jointly: i) minimize the distance between the
origins of the two subspaces, and ii) to maximize the margin between the
hyperplanes and the data, either subspace demanding the data to be in its
positive and negative orthant respectively. Our proposed objective however
leads to a non-convex optimization problem, to which we resort to Riemannian
optimization schemes and derive an efficient conjugate gradient scheme on the
Stiefel manifold. To study the effectiveness of our scheme, we propose a new
dataset~\emph{Dash-Cam-Pose}, consisting of clips with skeleton poses of humans
seated in a car, the task being to classify the clips as normal or abnormal;
the latter is when any human pose is out-of-position with regard to say an
airbag deployment. Our experiments on the proposed Dash-Cam-Pose dataset, as
well as several other standard anomaly/novelty detection benchmarks demonstrate
the benefits of our scheme, achieving state-of-the-art one-class accuracy.

本文提出了一种新的针对单类学习的目标方法，采用正交归一帧子空间 “夹住” 标记数据，通过同时最小化两个目标来进行优化，即：缩小两个子空间的原点之间的距离，同时最大化正交超平面与数据之间的间隔，达到数据标记的目的，并在提出的 Dash-Cam-Pose 数据集上进行了实验。