Clustering methods are popular tools for pattern recognition in spatial databases. Existing clustering methods have mainly focused on the matching and clustering of complex trajectories. Few studies have paid attention to clustering origin-destination (OD) trips and discovering strong spatial linkages via OD lines, which is useful in many areas such as transportation, urban planning, and migration studies. In this paper, we present a new Simple Line Clustering Method (SLCM) that was designed to discover the strongest spatial linkage by searching for neighboring lines for every OD trip within a certain radius. This method adopts entropy theory and the probability distribution function for parameter selection to ensure significant clustering results. We demonstrate this method using bike-sharing location data in a metropolitan city. Results show that (1) the SLCM was significantly effective in discovering clusters at different scales, (2) results with the SLCM analysis confirmed known structures and discovered unknown structures, and (3) this approach can also be applied to other OD data to facilitate pattern extraction and structure understanding.

Station-free bike sharing systems (BSSs) are a new type of public bike system that has been widely deployed in China since 2017. However, rapid growth has vastly outpaced the immediate demand and overwhelmed many cities around the world. This paper proposes a heuristic bike optimization algorithm (HBOA) to determine the optimal supply and distribution of bikes considering the effect of bicycle cycling. In this approach, the different bike trips with separate bikes can be connected in space and time and converted into a continuous trip chain for a single bike. To improve this cycling efficiency, it is important to properly design the bicycle distribution. Taking Shenzhen as an example, we implement the algorithm with OD matrix data from Mobike and Ofo, the two large bike sharing companies which account for 80% of the shared bike market in Shenzhen, over two days. The HBOA results are as follows. 1) Only one-fifth of the bike supply is needed to meet the current usage demand if the bikes are used efficiently, which means a large number of shared bikes in Shenzhen remain in an idle state for long periods. 2) Although the cycling demand is high in many areas, it does not mean that large numbers of bikes are needed because the continuous inflow caused by the cycling effect of bikes will meet most of the demand by itself. 3) The areas with the highest demands for optimal bikes are residential, followed by industrial, public transportation, official and commercial areas, on both working and non-working days. This algorithm can be an objective basis for city related departments to manage station-free BSSs and be applied to design the layout of bikes in small-scale spatial units to help station-free BSSs operate efficiently and minimize the need to relocate the bikes without reducing the level of user satisfaction.

Polycentric urban structures are increasingly advocated to enhance economic efficiency, promote spatial equity, and support environmental sustainability. However, their roles in shaping urban performance remain insufficiently understood, particularly regarding the contributions of clustered and networked patterns to performance across different dimensions and scales. This study adopts a longitudinal framework that distinguishes the evolutionary stages of polycentric urban structures and evaluates multi-dimensional, multi-scale performance, taking Shenzhen, China as a case study. The results show that Shenzhen’s polycentric structure evolved nonlinearly in its clustered pattern and linearly in its networked characteristics, with steady improvements in spatial and economic performance contrasting with the inverted U-shaped trajectory in social performance. Clustered and networked polycentric structures contribute differently: improvements in spatial performance are driven by multiple indicators, major economic indicators (at constant prices) increase with strengthened networked characteristics, and social performance benefits from clustered patterns only when public service provision is coordinated. This research provides new evidence for the co-evolution of polycentric structures and urban performance, suggesting that the effectiveness of polycentric development lies not in choosing between clustered and networked forms, but in strategically integrating them—optimizing scale–distance coordination among centers to enhance the clustered pattern, while differentiating center functions to strengthen networked characteristics.

In recent years, the digital creative industry has manifested a vigorous growth trend along with the continuous upgrading of the Internet and the leap of the national economy. This research identifies the spatial distribution characteristics of digital creative enterprises in Shenzhen, employs big data of spatial information of various facilities such as transportation and commerce as the driving factor to construct a model, takes 1 km grid as the fundamental research unit, and explores the influence mechanism of enterprise location selection through methods like OLS and MGWR. The results are as follows: (1) The overall spatial distribution characteristics of digital creative industry are characterized by “widely distributed throughout the city, with a high concentration within the customs and a weak dispersion outside the customs”. (2) The factors of park foundation, production service, public service and life service exert a significant influence on the spatial distribution of digital creative industries in Shenzhen. Among them, the density of shopping facilities, staff, hotel and bus station exhibits a highly obvious spatial heterogeneity in terms of the influence on enterprise location. (3) The correlation of local scale factors is high and the influence range is precise, which frequently presents complex correlation outcomes in small scales such as streets or communities.