Rotation-Invariant Random Features Provide a Strong Baseline for Machine
  Learning on 3D Point Clouds
Owen Melia Eric Jonas Rebecca Willett
Rotational invariance is a popular inductive bias used by many fields in
machine learning, such as computer vision and machine learning for quantum
chemistry. Rotation-invariant machine learning methods set the state of the art
for many tasks, including molecular property prediction and 3D shape
classification. These methods generally either rely on task-specific
rotation-invariant features, or they use general-purpose deep neural networks
which are complicated to design and train. However, it is unclear whether the
success of these methods is primarily due to the rotation invariance or the
deep neural networks. To address this question, we suggest a simple and
general-purpose method for learning rotation-invariant functions of
three-dimensional point cloud data using a random features approach.
Specifically, we extend the random features method of Rahimi & Recht 2007 by
deriving a version that is invariant to three-dimensional rotations and showing
that it is fast to evaluate on point cloud data. We show through experiments
that our method matches or outperforms the performance of general-purpose
rotation-invariant neural networks on standard molecular property prediction
benchmark datasets QM7 and QM9. We also show that our method is general-purpose
and provides a rotation-invariant baseline on the ModelNet40 shape
classification task. Finally, we show that our method has an order of magnitude
smaller prediction latency than competing kernel methods.