Community detection is a vital task in many fields, such as social networks, and financial analysis, to name a few. The Louvain method, the main workhorse of community detection, is a popular heuristic method based on modularity. But it is difficult for the sequential Louvain method to deal with large-scale graphs. In order to overcome the drawback, researchers have proposed several parallel Louvain methods (Parallel Louvain Method, PLM), which suffer two challenges: (1) latency in the information synchronization and (2) communities swap. To tackle these two challenges, we propose a graph partition algorithm for the parallel Louvain method. Different from existing graph partition algorithms, our graph partition algorithm divides the graph into subgraphs called isolate sets, in which vertices are relatively decoupled from others, and the PLM computes and synchronizes information without delay and communities swap. We first describe concepts and properties of isolate sets. In the second place, we propose an algorithm to divide the graph into isolate sets, which enjoys the same computation complexity as the breadth-first search. Finally, we propose the isolate-set-based parallel Louvain method, which calculates and updates vertices information without latency and communities swap. We implement our method with OpenMP on an 8-cores PC. Experiments on 18 graphs show that our parallel method achieves a maximum 4.62 $$\times $$ × speedup compared with the sequential method, and outputs higher modularity on 14 graphs.

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Aircraft recognition has great application value, but aircraft in remote sensing images have some problems such as low resolution, poor contrasts, poor sharpness, and lack of details caused by the vertical view, which make the aircraft recognition very difficult. Especially when there are many kinds of aircraft and the differences between aircraft are subtle, the fine-grained recognition of aircraft is more challenging. In this paper, we propose a non-locally enhanced feature fusion network(NLFFNet) and attempt to make full use of the features from discriminative parts of aircraft. First, according to the long-distance self-correlation in aircraft images, we adopt non-locally enhanced operation and guide the network to pay more attention to the discriminating areas and enhance the features beneficial to classification. Second, we propose a part-level feature fusion mechanism(PFF), which crops 5 parts of the aircraft on the shared feature maps, then extracts the subtle features inside the parts through the part full connection layer(PFC) and fuses the features of these parts together through the combined full connection layer(CFC). In addition, by adopting the improved loss function, we can enhance the weight of hard examples in the loss function meanwhile reducing the weight of excessively hard examples, which improves the overall recognition ability of the network. The dataset includes 47 categories of aircraft, including many aircraft of the same family with slight differences in appearance, and our method can achieve 89.12% accuracy on the test dataset, which proves the effectiveness of our method.

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