Let X, Y be sets of items, where X ⊂ M, Y ⊂ M, X ≠ ⌀, Y ≠ ⌀, and X∩Y = ⌀. P(X ∪ Y), the probability that a converted activity chain contained the union of sets
X and Y, represent the association between areas in X and Y as well as the spatial PR-171 Captabin interaction of the areas in the two sets. The acquisition of input database and the measurement of spatial interaction were performed as Algorithm 4. It should be noted that the following pseudocodes lay emphasis on the introduction to the conversion from activity chains into sequences of activity identities. The frequent pattern mining was carried out through the commonly used algorithm of Frequent Pattern Growth (FP-growth), which was unnecessary to go into details.
Algorithm 4 Measurement of spatial interaction. 3.4. Overall Structure of the Three Stages With the introduction of the three stages mentioned above, the framework for spatial interaction analysis based on mobile phone data can be organized as in Figure 4. Figure 4 Framework for spatial interaction analysis. 4. Case Study 4.1. Study Areas To demonstrate the practical application of the analysis framework proposed in this paper, three communities were selected as study areas, as shown in Figure 5. The three study areas were selected from the communities along Metro line 7 in Shanghai with the overall consideration of data quality, construction history, built environment, location, and resident population. The three selected communities are Jing’an, Dahua, and Gucun. Generally speaking,
Jing’an, Gucun, and Dahua are, respectively, the typical representatives of the mature communities in the city center, the newly constructed communities in the suburbs, and the communities in between. The three study areas are illustrated in Figure 4; and the key information of the three study areas is listed and compared in Table 1. Figure 5 Study areas. Table 1 Key information of study areas. 4.2. Study Objects Residents in the study areas were considered as the study objects. Method of mobile-phone-based resident identification proposed in our previous research  was introduced to determine the study objects. A certain mobile subscriber could be labeled as the resident in the study area if the criteria were Entinostat satisfied that the mobile subscriber once stayed in a certain study area for no less than 6 hours during the time period from 9 p.m. to 6 a.m, frequency of which exceeded 20 in a month. As a result, there were 1,363 residents identified in Gucun, 2,955 in Dahua, and 14,901 in Jing’an. U1*, U2*, and U3* denoted the sets of residents in the three study areas, respectively, and acted as the input parameters in the spatial interaction analysis. 4.3. Results and Discussion 4.3.1. Activity Points Activity points are the intermediate results of the spatial interaction analysis.