Infinite-dimensional feature aggregation via a factorized bilinear model

Aggregating infinite-dimensional features has demonstrated superiority compared with their finite-dimensional counterparts. However, most existing methods approximate infinite-dimensional features with finite-dimensional representations, which inevitably results in approximation error and inferior performance. In this paper, we propose a non-approximate aggregation method that directly aggregates infinite-dimensional features rather than relying on approximation strategies. Specifically, since infinite-dimensional features are infeasible to store, represent and compute explicitly, we introduce a factorized bilinear model to capture pairwise second-order statistics of infinite-dimensional features as a global descriptor. It enables the resulting aggregation formulation to only involve the inner product in an infinite-dimensional space. The factorized bilinear model is calculated by a Sigmoid kernel to generate informative features containing infinite order statistics. Experiments on four visual tasks including the fine-grained, indoor scene, texture, and material classification, demonstrate that our method consistently achieves the state-of-the-art performance.