Low-Rank Bilinear Pooling for Fine-Grained Classification

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Abstract
Pooling second-order local feature statistics to form a high-dimensional bilinear feature has been shown to achieve state-of-the-art performance on a variety of fine-grained classification tasks. To address the computational demands of high feature dimensionality, we propose to represent the covariance features as a matrix and apply a low-rank bilinear classifier. The resulting classifier can be evaluated without explicitly computing the bilinear feature map which allows for a large reduction in the compute time as well as decreasing the effective number of parameters to be learned. To further compress the model, we propose a classifier co-decomposition that factorizes the collection of bilinear classifiers into a common factor and compact per-class terms. The co-decomposition idea can be deployed through two convolutional layers and trained in an end-to-end architecture. We suggest a simple yet effective initialization that avoids explicitly first training and factorizing the larger bilinear classifiers. Through extensive experiments, we show that our model achieves state-of-the-art performance on several public datasets for fine-grained classification trained with only category labels. Importantly, our final model is an order of magnitude smaller than the recently proposed compact bilinear model [8], and three orders smaller than the standard bilinear CNN model [19].