## 2 Algorithmic Basis for Urban Residential Vacancy Rate Observation
### Application of the Algorithm in Urban Residential Vacancy Rate Observation
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Algorithm Type** & **Description** & **Applicable Scenarios** & **Advantages** & **Disadvantages** & **Typical Algorithms** \\ \hline Traditional statistical learning & Linear models assuming linear relationships between variables. & Variables: Short-term vacancy rate prediction with structured data (e.g., economic indicators). & High computational efficiency; strong interpretability. & Limited capacity to model nonlinear relationships; & Linear regression, ARIMA \\  & Nonlinear models (e.g., trees, SVM) capturing complex patterns via feature engineering. & Medium-term production; feature importance analysis (e.g., demographic impacts). & Electrirective for medium-dimensional data; & Strugges with high-dimensional data; & Random forests, SVM \\ Deep learning & Hierarchical feature extraction via neural networks for high-dimensional, unstructured data. & Long-term trend forecasting; remote sensing analysis (e.g., nighttime light imagery). & Exceptional performance on complex data; & Requires massive data and computational resources; & CNN, LSTM, transformer \\ Reinforcement learning & Trial-and-error optimization of dynamic strategies in response to vacancy rates. & Policy optimization (e.g., vacancy tax adjustments); & Adaptable to dynamic environments; & Slow convergence; sensitive to reward function design. & Q-Learning, policy gradient \\  & Discovery of hidden & Exploratory analysis (e.g., social media data for & Uncovers latent relationships; supports & Results highly dependent on data quality; domain & Apriori, K-Means \\ Data mining & Patterns via clustering, association rules, etc. & Vocancy clues). & Unsupervised learning. & expertise required. & Sensitive to \\  & Decomposition of temporal & Short-to-medium-term & Effective for capturing & Sensitivity to \\ Time series analysis & patterns (trends, seasonality) & forecasting (e.g., quarterly & temporal dependencies; & non-stationarity; assumes & SARIMA, Prophet \\  & in sequential data. & vacancy fluctuations). & reliable for stationary data. & regularity. & \\ \hline \end{tabular}
\end{table} 
Table 1: Algorithm types for observing urban residential vacancy rates. The introduction of adaptive algorithms has brought new vitality to the observation of urban residential vacancy rates [73]. This type of algorithm can dynamically adjust the observation model according to the different stages of urban development and regional characteristics, thereby improving the real time and accuracy of the prediction. In the process of urban new district development, the residential vacancy rate is affected by various factors such as planning, transportation and supporting facilities. The adaptive algorithm can flexibly respond to these challenges and provide more accurate data support for decision makers. Take Xiong'an New Area as an example. In the early stages of construction, an adaptive algorithm dynamically adjusted the weights of planning, transportation and population factors to predict a vacancy rate of 65% (due to incomplete infrastructure). As the area developed, the algorithm incorporated real-time data on new housing supply and population inflows, revising the mid-term vacancy rate prediction to 30% with an error margin of less than 5% compared to actual monitoring. This prediction enabled the administrative committee to proactively deploy commercial facilities, avoiding risks of urban vacancy [74]. Deep learning algorithms have also shown great potential in the observation of urban residential vacancy rates [70; 73]. In a recent project, a CNN-based model trained on high-resolution remote sensing images automatically learned features like building density and green-area distribution for vacancy rate prediction, achieving high accuracy in different regions. An LSTM-based model analyzed historical vacancy rate time series data along with rental price and new housing supply factors, accurately predicting future trends to assist decision making.