## 1 Introduction
This kind of accessibility represents the multidimensional phenomena of accessing a variety of urban services and resources. For instance, neighborhood units with a specified distance to public infrastructure (e.g., public health facility, supermarket, and sidewalks) are closely related to a series of social health status issues [21; 22] and physical activities [23; 24; 25]. Therefore, integrating several multidimensional accessibility-related indicators, based on their spatial correlations and spatial heterogeneities, becomes an increasingly important manner of identifying neighborhoods in urban segregation analyses [26; 27]. The discrepancies between neighborhood context and citizens' perceptions of place are emphasized. Although census blocks are homogenous areas in terms of population density, they may not be suitable for demonstrating the urban segregation in terms of socioeconomic conditions. Clustering methods, which are data exploration tools for dividing multidimensional indicators into clusters, are therefore useful and efficient for aggregating census blocks to create neighborhood units. For instance, the hierarchical classification [28; 29; 30], the k-nearest neighbor collaborative technique [31; 32], the automatic zoning procedure [33; 34], the minimum spanning tree [35; 36], the fuzzy c-means clustering [37], Moran's I [38], and the ward's minimum variance method [39] have been used to examine neighborhood effects on measuring social capital, public health, mortality, deprivation, economic capability, and so on. Nevertheless, the empirical knowledge on neighborhood derivation remains quite limited, and different clustering procedures involving various principles could differ significantly depending on the modeling scale [1]. The uncertainty of the modeling scale refers to the well-known modifiable areal unit problem (MAUP) [33; 40; 41], and there is no decisive way to define the most suitable scale of neighborhoods. Ideally, neighborhood units should have a strong sense of social and place identity, and a strong identity that helps to enhance citizens' awareness and perception of place [42]. The concept of perception of place was proposed in behavioural geography analyses to measure the residential understanding and feeling about human place attachment and place meaning [43]. It describes human relationships with places, expressed in different dimensions of human life and personal experiences [44]. In cities, the perception of place reflects the symbolic meaning people ascribe to places [45; 46]. This awareness and perception of place are determined by citizens' social activities [47; 48]. In this sense, neighborhood context can also be interpreted by citizens' social behaviors and self-perception of place [49; 50; 51]. Previous research has also demonstrated significant associations between objective neighborhood and individuals' perceptions of health and quality of life [52; 53; 54; 20; 55]. This point of neighborhood identification thus provides a possibility to validate the meaning of a neighborhood; it also leads to the requirement of multilevel modeling to examine the feasibility of newly designed neighborhoods versus original census blocks for understanding citizens' attitudes and experiences of neighborhood identity [47; 55]. Therefore, in this study, we aim to explore the uncertainty of MAUP in neighborhood interpretations by comparing the discrepancies between objective neighborhood context and subjective citizens' perceptions of place across multiple scales [56; 57]. The objectives of this research are twofold. First, different clustering algorithms were proposed to aggregate census blocks into multiple neighborhood scales based on multidimensional characteristics of public services inequality. Second, the variability of spatial consistency between objective neighborhood context and subjective individual perception of place was explored across multiple neighborhood scales.