Efficient Compact Bilinear Pooling via Kronecker Product

Bilinear pooling has achieved excellent performance in fine-grained recognition tasks. Nevertheless, high-dimensional bilinear features suffer from over-fitting and inefficiency. To alleviate these issues, compact bilinear pooling (CBP) methods were developed to generate low-dimensional features. Although the low-dimensional features from existing CBP methods enable high efficiency in subsequent classification, CBP methods themselves are inefficient. Thus, the inefficiency issue of the bilinear pooling is still unsolved. In this work, we propose an efficient compact bilinear pooling method to solve the inefficiency problem inherited in bilinear pooling thoroughly. It decomposes the huge-scale projection matrix into a two-level Kronecker product of several small-scale matrices. By exploiting the ``vec trick'' and the tensor modal product, we can obtain the compact bilinear feature through the decomposed projection matrices in a speedy manner. Systematic experiments on four public benchmarks using two backbones demonstrate the efficiency and effectiveness of the proposed method in fine-grained recognition.