Transformers have achieved great success in natural language processing and computer vision. The core and basic technique of transformers is the self-attention mechanism. The vanilla self-attention mechanism has quadratic complexity, which limits its applications to vision tasks. Most of the existing linear self-attention mechanisms will sacrifice performance to some extent for reducing complexity. In this paper, we propose a novel linear approximation of the vanilla self-attention mechanism named CURSA to achieve both high performance and low complexity at the same time. CURSA is based on the CUR decomposition to decompose the multiplication of large matrices into the multiplication of several small matrices to achieve linear complexity. Experiment results of CURSA in image classification tasks show that it outperforms state-of-the-art self-attention mechanisms with better data efficiency, faster speed, and higher performance.

Superpixels can preserve the structure and reduce the redundancy of the original image. Because of these advantages, superpixel generation or superpixel segmentation is widely used as a pre-processing step in many image processing tasks. Although superpixels can be employed to reduce computational complexity, some challenges, such as the non-Euclidean feature learning problem introduced by superpixels, still exist. This survey provides a comprehensive overview of the state-of-the-art superpixel methods, major challenges, commonly used evaluation metrics, applications of superpixels, and potential future directions for the study of superpixels. We first give a review of the state-of-the-art superpixel methods. Next, we use different evaluation metrics to evaluate the performance of 25 up-to-date superpixel methods on different datasets in different noisy environments. After that, we introduce several up-to-date applications of superpixels. Finally, we give several possible future directions for addressing the challenges of superpixels.

We present a novel graph convolutional method called star topology convolution (STC). This method makes graph convolution more similar to conventional convolutional neural networks (CNNs) in Euclidean feature spaces. STC learns subgraphs which have a star topology rather than learning a fixed graph like most spectral methods. Due to the properties of a star topology, STC is graph-scale free (without a fixed graph size constraint). It has fewer parameters in its convolutional filter and is inductive, so it is more flexible and can be applied to large and evolving graphs. The convolutional filter is learnable and localized, similar to CNNs in Euclidean feature spaces, and can share weights across graphs. To test the method, STC was compared with state-of-the-art graph convolutional methods in a supervised learning setting on nine node properties prediction benchmark datasets: Cora, Citeseer, Pubmed, PPI, Arxiv, MAG, ACM, DBLP, and IMDB. The experimental results showed that STC achieved state-of-the-art performance on all these datasets and maintained good robustness. In an essential protein identification task, STC outperformed state-of-the-art essential protein identification methods. An application of using pretrained STC as the embedding for feature extraction of some downstream classification tasks was introduced. The experimental results showed that STC can share weights across different graphs and be used as the embedding to improve the performance of downstream tasks.

Using graph theory to identify essential proteins is a hot topic at present. These methods are called network-based methods. However, the generalization ability of most network-based methods is not satisfactory. Hence, in this paper, we consider the identification of essential proteins as a multi-objective optimization problem and use a novel multi-objective optimization method to solve it. The optimization result is a set of Pareto solutions. Every solution in this set is a vector which has a certain number of essential protein candidates and is considered as an independent predictor or voter. We use a voting strategy to assemble the results of these predictors. To validate our method, we apply it on the protein-protein interactions (PPI) datasets of two species (Yeast and Escherichia coli). The experiment results show that our method outperforms state-of-the-art methods in terms of sensitive, specificity, F-measure, accuracy, and generalization ability.