Abstract
Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets.
Abstract (translated)
从深度卷积网络中提取的聚合二阶特征已被证明对纹理生成，细粒度识别，材料分类和场景理解是有效的。在本文中，我们研究了一类无序聚合函数，旨在最小化干扰或在二阶特征的上下文中均衡贡献，并且我们证明它们可以像它们的一阶对应物一样有效地计算，并且它们具有有利的性质。通过求和进行聚合。另一项工作表明，聚合后的矩阵功率归一化可以显着改善二阶表示的泛化。我们表明矩阵功率归一化隐含地在聚合期间均衡贡献，从而在矩阵归一化技术和先前关于最小化干扰的工作之间建立连接。根据分析，我们提出了{\ gamma} - 民主聚合器，它们在sum（{\ gamma} = 1）和民主汇集（{\ gamma} = 0）之间进行插值，优于两个分类任务。此外，与功率归一化不同，{\ gamma} - 民主聚合可以通过草图在低维空间中计算，允许使用非常高维的二阶特征。这样可以在多个数据集上实现最先进的性能。
URL
https://arxiv.org/abs/1808.07503
