## 2 Algorithmic Basis for Urban Residential Vacancy Rate Observation
### Application of the Algorithm in Urban Residential Vacancy Rate Observation  
In the rapid process of urban development, the residential vacancy rate is an important indicator reflecting the health of the real estate market [65; 66]. For policy makers, urban planners and investors, its accurate observation is of great importance [67]. With the advent of the big data era, the application of algorithms in the observation of urban residential vacancy rates has gradually shown its unique advantages. It can not only effectively cope with complex environments and process diverse data sources, but also meet the diverse needs of urban development. With the support of modern algorithm technology, traditional statistical methods have been significantly improved and enhanced when faced with problems such as large data volume, high noise and high complexity. Machine learning algorithms, such as those based on decision trees, support vector machines and random forests, have become mainstream in observing residential vacancy rates due to their strong nonlinear modeling capabilities. While machine learning and deep learning algorithms excel in capturing complex patterns, traditional statistical methods remain relevant for their interpretability and efficiency. For instance, in cases where data are limited or the focus is on policy-relevant insights (e.g., isolating the impact of a new housing policy), linear regression or time series analysis may be preferable. This trade-off between model complexity and interpretability is widely discussed in the literature, emphasizing the need for context-aware algorithm selection [68]. For example, in a medium-sized city study, the decision tree algorithm analyzed real estate and census data. Based on population structure, it found low vacancy rates for small apartments in young worker-dense areas. It also considered features like average income and distance to the city center, recursively splitting data for accurate vacancy classification. Support vector machines classified vacant and occupied houses using building and location features, achieving high accuracy. They can extract key factors affecting the vacancy rate through feature engineering, revealing relationships with socioeconomic factors. For example, analysis of real estate and census data shows that areas with more young migrant workers have lower small-apartment vacancy rates, while areas with an aging population may have higher large-house vacancy rates. Additionally, neural network algorithms like CNNs (convolutional neural networks) can analyze nighttime light remote sensing images to infer vacancy rates, and LSTMs (long short-term memory network) can predict future trends from time series rental or sales data [69]. For example, by analyzing real estate transaction records and census data together, it can be found that in areas with a high proportion of young migrant workers, the vacancy rate of small-sized apartments is relatively low, while in areas with a high aging population, the vacancy rate of large-sized houses may be relatively high. This indicates that population structure, as a socioeconomic factor, has a significant impact on the residential vacancy rate. [PERSON] et al. applied artificial intelligence-based anomaly detection of energy consumption in buildings to observe the residential vacancy rate, mainly using energy-related data [69]. [PERSON] et al. used evolutionary deep learning for car park occupancy prediction, which has some relevance to residential vacancy rate observation as both involve space-occupancy prediction [70]. However, the former focused on energy-consumption-based analysis while the latter emphasized a specific deep learning algorithm for a related but different occupancy scenario. Their research differed from the others in that it was more centered on the data-fusion methodology itself rather than a specific algorithm application for vacancy rate observation.