G\mathcal{G}-softmax: Improving Intra-class Compactness and Inter-class Separability of Features

Intra-class compactness and inter-class separability are crucial indicators to measure the effectiveness of a model to produce discriminative features, where intra-class compactness indicates how close the features with the same label are to each other and inter-class separability indicates how far away the features with different labels are. In this work, we investigate intra-class compactness and inter-class separability of features learned by convolutional networks and propose a Gaussian-based softmax ($\mathcal{G}$-softmax) function that can effectively improve intra-class compactness and inter-class separability. The proposed function is simple to implement and can easily replace the softmax function. We evaluate the proposed $\mathcal{G}$-softmax function on classification datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) and on multi-label classification datasets (i.e., MS COCO and NUS-WIDE). The experimental results show that the proposed $\mathcal{G}$-softmax function improves the state-of-the-art models across all evaluated datasets. In addition, analysis of the intra-class compactness and inter-class 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 intra-class compactness and inter-class separability are linearly correlated to average precision on MS COCO and NUS-WIDE. This implies that improvement of intra-class compactness and inter-class separability would lead to improvement of average precision.Comment: 15 pages, published in TNNL

Deep Fishing: Gradient Features from Deep Nets

Convolutional Networks (ConvNets) have recently improved image recognition performance thanks to end-to-end learning of deep feed-forward models from raw pixels. Deep learning is a marked departure from the previous state of the art, the Fisher Vector (FV), which relied on gradient-based encoding of local hand-crafted features. In this paper, we discuss a novel connection between these two approaches. First, we show that one can derive gradient representations from ConvNets in a similar fashion to the FV. Second, we show that this gradient representation actually corresponds to a structured matrix that allows for efficient similarity computation. We experimentally study the benefits of transferring this representation over the outputs of ConvNet layers, and find consistent improvements on the Pascal VOC 2007 and 2012 datasets.Comment: To appear at BMVC 201