# Grouping Bilinear Pooling for Fine-Grained Image Classification
## 1 Introduction  
Computer vision is an important field of artificial intelligence, and its goal is to realize the extension of human vision function based on intelligent computing. Image classification is the most basic task in computer vision. In general, Image classification can be divided into two categories: coarse-grained image classification and fine-grained image classification. Recognizing images of different classes (cats, dogs, flowers, planes, etc.) is the goal of coarse-grained image classification, and fine-grained visual classification aims at classifying sub-classes of category [1, 2]. Fine-grained visual classification is a challenging visual task due to the small interclass variations and large intra-class variations. Obtaining more discriminative feature representation is the focus of fine-grained image classification. Convolutional Neural Network (CNN) has been widely used in computer vision tasks [3, 4, 5]. By stacking different functional layers, CNN can obtain powerful feature extraction and generalization capabilities. Extracting expressive feature representation is an effective way to improve the accuracy of fine-grained image classification; many enlightening and meaningful works are proposed to make better use of the extracted CNN semantic features. Most studies obtain the feature representation of an input image by pooling high-order features [6, 7], extracting high-value information through attention methods [8, 9] or aggregating the features of different levels [10], then use these expressive representation to subsequent tasks. In addition, some other studies use the high-order statistical information of features to obtain better feature representation, such as Fisher Vector [11, 12],VLAD [13], spatial pyramids [14] and full bilinear pooling [15; 16]. Among them, the full bilinear pooling (FBP) [15] captures the complex correlation between paired features and uses the bilinear representation for classification which makes remarkable achievements in fine-grained image classification. However, the bilinear representation is as high as hundreds of thousands or even millions of dimensions. It is far higher than the aggregating representation obtained by common pooling methods, resulting in huge computational load and memory consumption, and limiting the expansion of the model structure. In order to reduce the dimension of the bilinear representation and obtain compact representation, refs. [16; 17; 18; 19; 20] simplify the bilinear pooling in different ways. In [17], the image classification network based on bilinear pooling is regarded as a linear kernel machine, and it is proved that bilinear pooling enables the linear classifier to have the recognition ability of second-order kernel machine. Then, Random Maclaurin (RM) [21] and Tenor Sketch (TS) [22] are used for low-dimensional approximation, and a compact bilinear pooling (CBP) is established. Ref. [18] uses the Hadamard product instead of bilinear pooling, the Hadamard product also achieves a low-dimensional approximation to bilinear pooling. Refs. [16; 19] reduces the dimensions of representation by carrying out feature mapping on high-order feature layers or simplifying bilinear pooling by matrix factorization to get compact representation. The learnable semantic grouping module is introduced to reduce the computation of bilinear pooling in [20]. Besides, some papers focus on what else compact bilinear pooling can do [23; 24; 25; 26]. Ref. [23] uses multimodal compact bilinear pooling in visual question answering which performs well. In [24], bilinear pooling is used to combine global features and local features for person re-identification. Ref. [25] aggregates local CNN features by carrying out bilinear pooling to obtain 3D object representation and achieves remarkable results in 3D object recognition tasks. In [26], bilinear blocks are proposed to obtain rich modality-temporal representation for RGB-D Action Recognition. Bilinear pooling has potential in different visual tasks.