  This paper describes a neural network layer, named Ursa, that uses a
constellation of points to learn classification information from point cloud
data. Unlike other machine learning classification problems where the task is
to classify an individual high-dimensional observation, in a point-cloud
classification problem the goal is to classify a set of d-dimensional
observations. Because a point cloud is a set, there is no ordering to the
collection of points in a point-cloud classification problem. Thus, the
challenge of classifying point clouds inputs is in building a classifier which
is agnostic to the ordering of the observations, yet preserves the
d-dimensional information of each point in the set. This research presents
Ursa, a new layer type for an artificial neural network which achieves these
two properties. Similar to new methods for this task, this architecture works
directly on d-dimensional points rather than first converting the points to a
d-dimensional volume. The Ursa layer is followed by a series of dense layers to
classify 2D and 3D objects from point clouds. Experiments on ModelNet40 and
MNIST data show classification results comparable with current methods, while
reducing the training parameters by over 50 percent.
