## 5 Clustering Results
However, the significant peak characteristics indicate commuters as well despite land use functionality. * Cluster 5 in Figure 9i-l: temporal pattern of Cluster 5 is not that random as Cluster 2, as shown in Figure 9i,j; and meanwhile does not significantly follow the morning and evening peak laws as Clusters 1,3,4, as shown in Figure 9k,l. Therefore, passengers at Cluster 5 stations are neither random nor typical commuters; nevertheless, the traffic pattern basically follows the law of morning-evening traveling in daily life. In order to further understand spatial aggregation of subway stations, we additionally introduce external environmental factors by collecting population size and POI counts from Baidu Map service ([[http://lbsyun.baidu.com](http://lbsyun.baidu.com)]([http://lbsyun.baidu.com](http://lbsyun.baidu.com))) for each individual subway station. POI based variables include the number of hospitals, restaurants, residential units, working units, hotels, shopping centers, schools, banks and bus stops. Note that each variable is obtained by the number of POIs within 500-meter area [64] around each station. Moran's I [65] is a widely used statistic indicator for measuring spatial autocorrelation. In Table 5, Moran's I Index value and associated z-value and p-value are calculated to evaluate the significance of spatial autocorrelation, and all statistics are computed in GeoDa [66]. In general, Moran's I ranges from \(-1\) to \(+1\); positive Moran's I close to \(+1\) indicates clustering and negative Moran's I value near \(-1\) indicates dispersion. Z-value measures standard deviation, and p-value represents significant level. Basically when performing Moran's I test, small p-value and a very high (or a very low, negative) z-value indicate observed pattern is unlikely to exhibit theoretical randomness pattern represented by null hypothesis. In Table 5, Moran's I is calculated as global univariate indicator, and adjusted Moran's I is calculated as [PERSON]'s local Moran's I test with Empirical Bayesian (EB) rate [67] when clustering pattern of subway stations is considered. The significance test is computed by 999 permutations. We observe that Moran's I values of all variables are positive and could be up to 0.7638 (population), which means that environmental factors are spatially autocorrelated with highly significant confidence level (>99%). Moreover, adjusted Moran's I turns to be close to global Moran's I, which suggests the clustering pattern of subway stations is consistent with spatial autocorrelation of environmental factors of urban city. Besides, regression analysis is performed to reconfirm the spatial dependence. As shown in Table 6, after classical Ordinary Least Square (OLS) regression, Moran's I is highly significant (0.00002), indicating strong spatial autocorrelation of the residuals. The significant test results for spatial dependence in linear models are: LM-error (0.00775) \(\succ\) Robust LM-error (0.01966) \(\succ\) LM-lag (0.03238) \(\succ\) Robust LM-lag (0.08694). Thus, regression with spatial error LM-error model is employed to deduce the correlation coefficients of all variables, as listed in the lower section in Table 5. Due to data integrity issues and the inconsistency in timespan (passenger flow data was collected in 2013 while POI data is obtained in 2018), the correlation coefficients between POI counts and clusters are not highly significant (<0.5). However, still, we can see that _hospital_ (0.4646), _hotel_ (0.3972) and _bus stop_ (0.3661) are more positively correlated with the clustering pattern of subway stations, while _school_ (\(-0.4447\)) and _residential_ (\(-0.3882\)) are more negatively correlated. Figure 9: Hourly passenger volume in terms of in-station and out-station by weekdays for example stations in Type I, II, III, IV, V.