## 3 Algorithmic Challenges in Complex Environments
### Data Characteristics in Complex Environments
At the same time, they comprehensively considered multiple influencing factors such as GDP growth rate, population growth rate, housing price index and the intensity of policy regulation (such as purchase restriction policies and the number of adjustments to loan interest rates). By establishing a traditional linear regression model, it was found that the goodness of fit of the model was only 0.45. This indicates that the linear model cannot well explain the changes in the vacancy rate, suggesting the existence of nonlinear relationships in the data. Furthermore, a nonlinear machine learning algorithm, such as Support Vector Regression (SVR), was used to model the data. The results showed that the goodness of fit of the SVR model reached 0.78. And when predicting the vacancy rate in the next year, the mean squared error was 35% lower than that of the linear regression model. This comparison fully demonstrates that in the residential vacancy rate data of this city, there are a large number of complex laws that cannot be described by linear relationships, that is, there are significant nonlinear components. \begin{table}
\begin{tabular}{c c c c} \hline
**Feature Type** & **Description** & **Data Source** & **Dealing with Challenges** \\ \hline Geographical distribution & Geographical location & Geographic information & Irregularity and multi-scale \\  & information of urban residences & system (GIS) & nature of spatial data \\  & Residents’ age, income, & & \\ Demographics & occupation and other statistical & Census, statistics & The diversity and dynamic \\  & information & & \\ Economic activities & Real estate market transactions, & Real estate database, & Fusion analysis of price \\  & rental prices, etc. & market prices & fluctuations and economic \\  & Building & The building structure, age, & Building records, & Cycles \\  & area, etc. of the house & property management & Unstructured and \\  & Transportation, public services & & \\ Infrastructure & and other infrastructure & Government open data, & Data incompleteness and \\  & information & on-site investigation & real-time update requirements \\  & The impact of government & Government & Policy diversity and time \\  & policies on the housing market & announcements, laws & sensitivity \\  & & and regulations & \\ \hline \end{tabular}
\end{table} 
Table 2: Data characteristics in complex environments. The data characteristics in complex environments also include the unpredictability of residents' behavior [89]. The data characteristics in complex environments are manifested in the following aspects: First, the data characteristics of urban residential vacancy rates show significant temporal and spatial heterogeneity. [PERSON] et al. analyzed panel data from 35 Chinese cities and found that vacancy rates vary significantly across regions due to economic disparities and housing policies [90]. [PERSON] et al. used geographically weighted regression to model spatial variations in vacancy rates, revealing that transportation infrastructure and population density are key drivers at the neighborhood level [91]. Residents' choice of housing is not only affected by economic factors, but also closely related to personal preferences, family needs and other factors. These subjective factors make the characteristics of residential vacancy rate data more complex. The algorithm needs to be able to capture this unstructured information to enhance the interpretability and prediction accuracy of the model.To address these challenges, different algorithm types offer varying degrees of adaptability and robustness, as summarized in Table 1.