## 1 Introduction  
With the rapid development of urban economy and continuous agglomeration of population, urban rail transit such as subway has been a significant option for alleviating traffic congestion as well as improving public transportation and urban construction. On account of transit network layout and passenger flow benefits, the spatial-temporal concepts have been reshaped, thus leading to the change of people's lifestyle and redistribution of urban spatial structure.  
In this work, we study revealing urban spatial structure through station-oriented clustering using public transit smart card data with a case study on Shenzhen metro system in China. Indeed the application motivation could be facilitating urban regional planning and public infrastructure deployment guided by Transit-Oriented Development (TOD) [1] strategies. For example, typical administrative division is a relatively constant geographical setting developed for regional governance and functional management; nevertheless, distinguished from global administrative division, finer grained functional areas depend on multiple factors and could be reflected by urban mobility. The intuition behind is that public transit behavior reflects geographical agglomeration in terms of passenger riderships among stations, and thus contributes to regional functions and urban spatial structure.  
Along this line, the most common practice is to leverage clustering technique for identifying agglomeration pattern hidden in public transit behavior. Significantly, we observe that given a specific data set, there could be multiple _good_ (i.e., stable clustering in terms of algorithm itself [2]) clustering solutions with different initial settings or clustering algorithms. Besides, on account of various methods for determining optimal number of clusters and evaluating clustering results, there might not exist a single _clusterer_ (a clustering instance of particular algorithm with parameter settings specified and clustering results produced [3]) that is optimal in every respect. Therefore, in order to produce stable, accurate and explanatory clusters, we propose a clustering refinement approach with cluster ensemble using inbound and outbound passenger flow at subway stations.  
The contributions of this study can be highlighted as follows:  
* We propose a clustering refinement approach with cluster ensemble for discovering stable, reliable and rational partitions of subway stations, and meanwhile capable of outlier detection. Specifically, suppose there exists an optimal or suboptimal initialization, and each clusterer produces stable clustering results respectively, clustering refinement procedure is further performed through member based stability across instead of within isomorphic or heterogeneous clusterers.
* We formulate the concept of cluster member based stability. Typically, clustering stability indicates that a \"good\" clusterer is supposed to produce same clustering results on the same data set despite of different parameter settings among repeatedly executions. By contrast, we investigate stability across multiple good clusterers by exploring member shifting pattern between clusterings.
* Through a case study on Shenzhen city, China, we emphasize on interpretability of clustering results upon subway stations considering administrative division together with urban construction and land utilization. In this way, we validate regional functions of subway stations from the perspectives of urban planning as well as daily commuting behavior.  
The remainder of this paper is organized as follows. Related work is summarized in Section 2, and problem statement, data description and preliminary analysis are presented in Section 3. Next, Section 4 introduces cluster member based stability and clustering refinement framework. Clustering results are discussed in Section 5, together with comprehensive interpretation of station clusters. Finally, Section 6 concludes the paper.