  In this study, a novel feature coding method that exploits invariance for
transformations represented by a finite group of orthogonal matrices is
proposed. We prove that the group-invariant feature vector contains sufficient
discriminative information when learning a linear classifier using convex loss
minimization. Based on this result, a novel feature model that explicitly
consider group action is proposed for principal component analysis and k-means
clustering, which are commonly used in most feature coding methods, and global
feature functions. Although the global feature functions are in general complex
nonlinear functions, the group action on this space can be easily calculated by
constructing these functions as tensor-product representations of basic
representations, resulting in an explicit form of invariant feature functions.
The effectiveness of our method is demonstrated on several image datasets.
