Scene Classification Using Hierarchical Wasserstein CNN

TLDR: This paper finds that for two distributions in hierarchically organized data space, WD has a closed-form solution, which is called “hierarchical WD (HWD),” and uses this theory to construct novel loss functions that overcome the shortcomings of CE loss.

Abstract: In multiclass classification, convolutional neural network (CNN) is generally coupled with the cross-entropy (CE) loss, which only penalizes the predicted probability corresponding to a ground truth class and ignores the interclass relationship. We argue that CNN can be improved by using a better loss function. On the other hand, the Wasserstein distance (WD) is a well-known metric used to measure the distance between two distributions. Directly solving the WD problem requires a prohibitively large amount of computation time, whereas the cheaper iterative algorithms have a variety of shortcomings such as computational instability and difficulty in selecting parameters. In this paper, we address these issues by giving an analytical solution to the WD problem—for the first time, we find that for two distributions in hierarchically organized data space, WD has a closed-form solution, which we call “hierarchical WD (HWD).” We use this theory to construct novel loss functions that overcome the shortcomings of CE loss. To this end, multi-CNN information fusion that provides the basis for building category hierarchies is carried out first. Then, the semantic relationship among classes is modeled as a binary tree. Then, CNN coupled with an HWD-based loss, i.e., hierarchical Wasserstein CNN (HW-CNN), is trained to learn deep features. In this way, prior knowledge about the interclass relationship is embedded into HW-CNN, and information from several CNNs provides guidance in the process of training individual HW-CNNs. We conducted extensive experiments over two publicly available remote sensing data sets and achieved a state-of-the-art performance in scene classification tasks.