Graph Convolutional Networks (GCNs) are widely used for skeleton-based action recognition and achieved remarkable performance. Due to the locality of graph convolution, GCNs can only utilize short-range node dependencies but fail to model long-range node relationships. In addition, existing graph convolution based methods normally use a uniform skeleton topology for all frames, which limits the ability of feature learning. To address these issues, we present the Graph Convolution Network with Self-Attention (SelfGCN), which consists of a mixing features across self-attention and graph convolution (MFSG) module and a temporal-specific spatial self-attention (TSSA) module. The MFSG module models local and global relationships between joints by executing graph convolution and self-attention branches in parallel. Its bi-directional interactive learning strategy utilizes complementary clues in the channel dimensions and the spatial dimensions across both of these branches. The TSSA module uses self-attention to learn the spatial relationships between joints of each frame in a skeleton sequence. It also models the unique spatial features of the single frames. We conduct extensive experiments on three popular benchmark datasets, NTU RGB+D, NTU RGB+D120, and Northwestern-UCLA. The results of the experiment demonstrate that our method achieves or exceeds the record accuracies on all three benchmarks. Our project website is available at https://github.com/SunPengP/SelfGCN.

Metaheuristic optimization procedures such as evolutionary algorithms are usually driven by an objective function that rates the quality of a candidate solution. However, it is not clear in practice whether an objective function adequately rewards intermediate solutions on the path to the global optimum and it may exhibit deceptiveness, epistasis, neutrality, ruggedness, and a lack of causality. In this paper, we introduce the frequency fitness H, subject to minimization, which rates how often solutions with the same objective value have been discovered so far. The ideas behind this method are that good solutions are difficult to find and that if an algorithm gets stuck at a local optimum, the frequency of the objective values of the surrounding solutions will increase over time, which will eventually allow it to leave that region again. We substitute a frequency fitness assignment process (FFA) for the objective function into several different optimization algorithms. We conduct a comprehensive set of experiments: the synthesis of algorithms with genetic programming (GP), the solution of MAX-3SAT problems with genetic algorithms, classification with Memetic Genetic Programming, and numerical optimization with a (1+1) Evolution Strategy, to verify the utility of FFA. Given that they have no access to the original objective function at all, it is surprising that for some problems (e.g., the algorithm synthesis task) the FFA-based algorithm variants perform significantly better. However, this cannot be guaranteed for all tested problems. Thus, we also analyze scenarios where algorithms using FFA do not perform better or perform even worse than with the original objective functions.