## 2 Study Area
### Step 1: Measuring PSI Indicators at the Census Block Level
All indicators were proved to be correlated with health-related variables. Six clustering methods were applied separately to aggregate the original census blocks into six hierarchies. Each hierarchy contains 47 zoning levels, whereby the cluster numbers ranged from 3 to 50. More specifically, each cluster contains the different number of census blocks based on the homogeneity characteristics of the accessibility-related dataset. Each cluster was used to identify thespatial pattern and geographical boundary of the respective neighborhood units. The six clustering methods used are described below:  
1. K-means clustering (_Kmeans_) is a simple algorithm that uses the unsupervised learning method. We used the K-means algorithm to minimize the average squared distance (absolute distance in K-means) from each data point to the cluster center [65]. The K-means is well explained by [PERSON] and [PERSON] [65]. 2. Hierarchical clustering (_HAC_) builds a hierarchy from the bottom-up until all the data points are in a single cluster, whereby the number of clusters does not have to be defined beforehand. We thus chose the \"average linkage clustering\" method to find the maximum possible distance between points belonging to different clusters. This methodology has been well explained by [PERSON] and [PERSON] [66]. 3. The self-organization maps (_SOM_) method, which is one of the most popular neural network models, can provide a topology preserving mapping from the high dimensional space to map units [67]. We thus used the _SOM_ to convert complex, nonlinear statistical relationships between high-dimensional original objects into simple geometric relationships on a two-dimensional display medium. This method has been fully described by [PERSON] [67]. 4. Spatial \"K\"luster Analysis by Tree Edge Removal (_SKATER_) is an efficient regionalization technique that uses minimum spanning trees (MST) [68]. It transforms the regionalization problem into an optimal graph partitioning problem [35]. In this research, the seven PSI indicators represent unequal attributes to measure the dissimilarity between data points. This procedure has been fully described by [PERSON] et al. [35]. 5. Fuzzy clustering (_Fuzzy_) has the advantage over other methods that the data points possess a membership function, which ranges from 0 to 1, to indicate the strength of membership of all the clusters. We thus used the probabilistic membership to configuration the original census blocks into a multilevel zoning group. Fuzzy clustering is well explained by [PERSON] et al. [69]. 6. Gaussian Mixture Modelling for Model-Based Clustering (_Mcluster_) is useful to establish a statistical model consisting of a finite mixture of Gaussian distributions to fit the data. This algorithm offers a flexible way of inferentially learning the patterns/rules of reality from the original data points, and clusters maximize the similarity between the points. This procedure has been fully described by [PERSON] et al. [70]. Among these six clustering algorithms, _SKATER_ is the connectivity model that groups census blocks over a variety of scales by using a minimum spanning tree. The _SKATER_-based clusters are thus spatially connected. The other five clustering algorithms are based on multivariate normal distributions of seven accessibility-related indicators, and the resulting aggregated clusters were therefore not spatially connected. Different prototypical clustering algorithms were used in this study to demonstrate the potential spatial patterns of the functional neighborhood in a hierarchical way. The resulting multiscale clusters were then used as basic neighborhood unit to further explore the spatial connectivity between neighborhood context and individual perception of place. Step 3: Multilevel Modeling Between Residents' Perceptions of Neighborhood and Context Information of Cluster-Defined Neighborhood  
Individualist or collective interpretations of place are useful to study contextual effects of neighborhoods [71].