More extensive attention has been paid to the heterogeneity of maritime transport network in topological rather than in spatial aspects. However, the importance of links and the roles of neighbors of a node has been ignored if not all. To fill this gap, this article introduced the approach of weighted ego network analysis (WENA) to visualize the spatial heterogeneity of the maritime network at global and local levels. The topological connectivity graph of the global marine network was derived, and its structural properties were analyzed. It is found out that the values of the degree of ports follow power-law distribution, which indicates that the global marine network is scale-free, that is, there are few well-connected ports and a majority of less connected ports. The spatial disparities of the network can be described by a core–periphery pattern. In global, most of the hubs or ports with extremely high values of degree locate in the big-three maritime regions including Far East, North America, and West Europe. Along the peripheral belts of the three regions, there are lots of less connected small ports. A different hierarchical structure of six continents was captured by WENA. It is found that Europe, Asia, North America, and Africa showcase a pyramid-shaped hierarchical structure with a scale-free feature similar to the entire network, while South America and Oceania exhibit the fusiform hierarchy like small-world networks. It is proposed that such spatial inequality and heterogeneity were caused by the geographical environments such as the hub-and-spoke organization, the embedded trade pattern, and the proximity of location. These findings help us to understand the characteristics of the international trade pattern and shed light on the strategies of development for the industry stakeholders.

Fractal geometry has been an important tool in multiple disciplines, but it is usually limited to the geometrical fractal: a shape made of parts similar to the whole in certain ways. Recently there has been increasing interest in structural fractality of complex networks (e.g., biological and Internet hyperlinks) for studying organizational principles and evolutionary rules. In this study, the structural fractality of road networks (a kind of complex geographical network) is examined for better understanding of the complexity and dynamics of the road system. Fifty road networks of the most populous counties in the United States have been used as cases. The Maximum Excluded Mass Burning (MEMB) algorithm rooted in physics has been employed to compute the fractal dimensions by covering the network structure with a series of box sizes (ℓ _s ). It is found that road networks have structural fractality. The values of structural fractal dimension range from 2.94 to 4.90 spanning ℓ _s = 5 to ℓ _s = 15. To examine the self-similar property of the structure of a road network at several scales, small-world and scale-free analyses have been carried out. It was found that road networks are structural self-similarities. The fractal and self-similar structures in a road network help improve the efficiency of flow transmission in the system and keep a balance between chaos and order. These findings help us understand the complexity, organizational rules, and dynamic principles of an urban system and blur the borders across several disciplines. They also provide an empirical guide for urban design and transportation planning.

Band selection for hyperspectral images helps improve the efficiency of data processing and even the accuracy of classification. It is to reduce the dimensionality of a hyperspectral image by selecting representative bands. In such a process, the quantification of band similarity is the fundamental issue, and it is usually achieved by using an information-theoretic measure, such as mutual information or relative entropy. However, these measures are incapable of quantifying similarity in terms of both composition and configuration. To solve this problem, the Boltzmann entropy (BE), which captures both configurational and compositional information, is employed in this letter. More precisely, the difference in BE between two bands is used for such quantification. The corresponding search strategy is designed for band selection. Experimental evaluation was carried out using remote sensing images for classification. The results clearly demonstrate the superiority of the proposed band selection method over traditional information-theoretic methods: an increase of up to 27% in classification accuracy was observed when using the difference in relative BE with 20 selected bands. In addition, another comparison with some state-of-the-art methods was conducted. The results show that the proposed method is still very competitive; it outperformed all the others when the number of selected bands ranges from 18 to 23. This letter, the first of its kind, reveals that the BE may form a new base for information-theoretic approaches to image processing and even for spatial information science in a broad sense.