Learning with Algebraic Invariances, and the Invariant Kernel Trick
This work addresses the challenge of incorporating prior knowledge into machine learning models for researchers and practitioners dealing with invariant data structures.
The paper tackles the problem of integrating algebraic invariances like sign symmetries and phase independence into kernel methods, achieving this by applying the kernel trick twice to incorporate such structures.
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA.