  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.
