## 4 Discussion
The fine spatial granularity at the CBG level to discover the HMPs is very important since considerable variations in HMPs were observed in CBGs within Los Angeles (Figures 2 and S5-S8), which may have been obscured in a county-level analysis. For example, within LA county, many groups showed different proportions among SPAs. Many existing COVID-19 epidemiology models used global contact rates to model the transmission rates [27; 28; 29]. This study provided a base for delineating the spatial variability in HMPs and offered the opportunity to model COVID-19 at a finer spatial granularity with spatially varying transmission rates controlled by spatially varying HMPs. This study also explored the roles of social determinants of SED factors for HMPs under COVID-19. Even though there were many existing studies on SED disparities of HMPs which confirmed that places with higher social deprivation scores experienced reduced mobility at lower rates and, therefore, a greater growth in COVID-19 cases and deaths [30], our study is the first to identify HMPs solely based on their temporal shapes compared to other methods that use the average HMPs of stratified SED groups. There are two inherent defects to using average HMPs of stratified SED groups: (1) The analysis is bounded to a certain SED variable (e.g., median income or social deprivation scores) and neglects the impacts that form other SED variables. (2) There are still spatial variations in terms of temporal shapes within each SED group which would be under-represented using the average values. We examined the importance and directions of 17 SED factors on the changes in four selected human mobility indicators, and the results implied the different compliance to governmental non-pharma interventions (e.g., shelter-in-place order by the CA government) by different communities. For example, we speculate that the socially disadvantaged communities with a higher percentage of the population in poverty and lower incomes would most likely have less compliance with the shelter-in-place order. Meanwhile, both identified HMPs would be observed less in the older communities. Moreover, the percentage of the under-5 population would largely increase the chance of having an HMP peak in the median home dwelling time indicator but not the complete stay-at-home indicator. This contradictory fact emphasizes the necessity of investigating multiple indicators to obtain a better understanding of the whole picture of human mobility changes during the crisis. We chose CA as our study area to remove the impacts of the time inconsistency of non-pharmaceutical interventions by different government agencies. However, the proposed framework could be expanded from only CA block groups to all national block groups in the future, and it laid out the foundation for studying the impacts of the social determinant variables on health outcomes (i.e., COVID-19 confirmed cases or COVID-19-related deaths) through impacts on social behaviors in the future. The DTW-SOM algorithm is currently publicly available through the Python library \"dtwosm\". Since this study is based on real-time GPS pings, it has the potential limitation of data reliability from the location services. For example, some outlier low median home-dwelling time values were observed on 25 February 2020 (Tuesday), which is neither a national holiday nor a day with any known big public events, elucidating the potential risks from either issue in location services or changes in GPS data processing protocols. This was also confirmed as a data artifact by SafeGraph on 2 March 2020. We ended up with the solution of imputing abnormal data using a median filter. Additionally, cell phone locations do not always correspond to the location of the user, as there may be instances where the device is not in possession of the owner. Future work needs to be focused on methodologies of preprocessing and aggregating the device-level tracking data and the generation of more informative human mobility indicators.