Improved Bilinear Pooling With Pseudo Square-Rooted Matrix

Bilinear pooling is a feature aggregation step applied after the convolutional layers of a deep network and encodes a matrix of local features into a fixed-size bilinear representation. It improves performance in many image classification tasks. Since its emergence, this pooling has seen two major improvements: Compact Bilinear Pooling (CBP) and square-root normalization. Recently, the combination of these two elements has been widely studied. However, due to the lack of good normalization solutions, existing combination approaches showed less efficiency when they are plugged into different networks and less compatibility when they work with existing CBP techniques. To solve this problem, in this paper, we propose to apply Newton iterations, a fast square-root normalization method, to produce a new normalized matrix called pseudo square-rooted matrix. Subsequently, the new matrix allows a CBP technique to encode itself into a compact and normalized bilinear representation. In order to further accelerate the normalization process, our approach has two variants which can handle feature matrix extracted by different networks. Tested on three fine-grained image classification datasets, it provides competitive classification performance while consuming less computational time than other prior works.