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The study of representations invariant to common transformations of the datais important to learning. Most techniques have focused on local approximateinvariance implemented within expensive optimization frameworks lackingexplicit theoretical guarantees. In this paper, we study kernels that areinvariant to the unitary group while having theoretical guarantees inaddressing practical issues such as (1) unavailability of transformed versionsof labelled data and (2) not observing all transformations. We present atheoretically motivated alternate approach to the invariant kernel SVM. Unlikeprevious approaches to the invariant SVM, the proposed formulation solves bothissues mentioned. We also present a kernel extension of a recent technique toextract linear unitary-group invariant features addressing both issues andextend some guarantees regarding invariance and stability. We presentexperiments on the UCI ML datasets to illustrate and validate our methods.

Unitary-Group Invariant Kernels and Features from Transformed Unlabeled Data