## 2 Algorithmic Basis for Urban Residential Vacancy Rate Observation
### Algorithm Overview
The algorithmic basis for observing urban residential vacancy rates involves multiple fields, reflecting the research trend of multidisciplinary cross-integration [58]. Researchers need to analyze specific issues and select appropriate algorithms, and combine multi-source data, interdisciplinary knowledge and practical experience to achieve accurate observation of urban residential vacancy rates. This process not only helps to improve the accuracy and practicality of observations, but also has a far-reaching impact on urban planning, real estate market supervision and housing policy formulation. To better illustrate the relationships and processes among the definition, measurement, algorithm types and their applications in urban residential vacancy rate observation, the following flowchart is provided:  
Faced with the challenges of complex environment, diverse data sources and urban development needs, researchers have made continuous breakthroughs in the exploration and improvement of algorithms [59]. From traditional statistical learning methods to machine learning methods, to deep learning methods and ensemble learning methods, each algorithm has its unique advantages and application scenarios. In the practice of urban residential vacancy rate observation, researchers need to fully understand the principles and limitations of various algorithms, combine the characteristics of actual problems and flexibly use a variety of methods to achieve the best observation effect. The algorithm for observing urban residential vacancy rates is based on a complex system built on traditional statistical learning, machine learning, deep learning and ensemble learning [60]. The continuous improvement and development of this system has provided strong technical support for urban managers, enabling observation work to better adapt to the needs of urban development and cope with the challenges of complex and changing environments and diverse data sources. In the process of urban development, the observation of residential vacancy rate is not only related to the healthy development of the real estate market, but also affectsthe living quality of urban residents [61; 62; 63; 64]. Therefore, it has become an urgent task to conduct in-depth research on the algorithm basis of urban residential vacancy rate observation, give full play to the advantages of various algorithms and provide strong guarantees for the accurate observation of urban residential vacancy rate in China. On this basis, it is expected to provide strong support for China's urban development planning, housing policy formulation and real estate market regulation, and promote the sustainable development of cities. In summary, different types of algorithms have their own advantages and disadvantages in observing urban residential vacancy rates. Traditional statistical learning methods are suitable for processing linear relationships and structured data, but have limited performance on nonlinear problems. Machine learning methods have advantages in capturing nonlinear relationships, but are sensitive to data quality and overfitting issues. Deep learning algorithms perform well in processing high-dimensional and complex data, but have high computational costs. Reinforcement learning and data mining methods are suitable for dynamic environments and exploratory analysis. Time series analysis is good at capturing the temporal dependency of data. The specific algorithm types and their characteristics are summarized in Table 1.