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 ?-democratic aggregators that interpolate between sum (?=1) and democratic pooling (?=0) outperforming both on
several classification tasks. Moreover, unlike power normalization, the ?-
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