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.

翻译：本研究提出一种新型特征编码方法，该方法利用有限正交矩阵群作用下变换的不变性。我们证明，在使用凸损失最小化学习线性分类器时，群不变特征向量包含足够的判别信息。基于此结果，我们为大多数特征编码方法中常用的主成分分析和k-means聚类，以及全局特征函数，提出了一种显式考虑群作用的新型特征模型。尽管全局特征函数通常是复杂的非线性函数，但通过将这些函数构建为基本表示的张量积表示，可以轻松计算该空间上的群作用，从而得到不变特征函数的显式形式。我们在多个图像数据集上验证了该方法的有效性。