$\mathcal{G}$ -Softmax: Improving Intraclass Compactness and Interclass Separability of Features

Intraclass compactness and interclass separability are crucial indicators to measure the effectiveness of a model to produce discriminative features, where intraclass compactness indicates how close the features with the same label are to each other and interclass separability indicates how far away the features with different labels are. In this paper, we investigate intraclass compactness and interclass separability of features learned by convolutional networks and propose a Gaussian-based softmax (G-softmax) function that can effectively improve intraclass compactness and interclass separability. The proposed function is simple to implement and can easily replace the softmax function. We evaluate the proposed G-softmax function on classification data sets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) and on multilabel classification data sets (i.e., MS COCO and NUS-WIDE). The experimental results show that the proposed G-softmax function improves the state-of-the-art models across all evaluated data sets. In addition, the analysis of the intraclass compactness and interclass separability demonstrates the advantages of the proposed function over the softmax function, which is consistent with the performance improvement. More importantly, we observe that high intraclass compactness and interclass separability are linearly correlated with average precision on MS COCO and NUS-WIDE. This implies that the improvement of intraclass compactness and interclass separability would lead to the improvement of average precision.