## 2 Algorithmic Basis for Urban Residential Vacancy Rate Observation  
### Definition and Measurement of Urban Residential Vacancy Rate  
As an important indicator for measuring the balance between demand and supply in the real estate market, the urban residential vacancy rate has important guiding significance for government decision making, urban planning and market investment [23; 24; 25]. The so-called urban residential vacancy rate refers to the proportion of unoccupied or unused residential buildings in a city to the total number of residential buildings in a certain period of time. This indicator comprehensively reflects the supply and demand situation of the residential market, the spatial utilization efficiency in the urbanization process, and the allocation effect of social resources. However, accurately measuring the urban residential vacancy rate faces many challenges, including how to reasonably define vacant residential buildings, how to obtain reliable data sources and how to deal with complex environmental factors. In terms of defining vacant housing, in theory, vacant housing should include housing that has been unoccupied for a long time and cannot be used immediately, as well as housing that is occupied but the residence time is extremely unstable and does not meet the normal living characteristics [26; 27; 28]. However, in actual operation, this concept often varies due to differences in urban characteristics, regional culture and statistical methods. For example, some cities may only regard housing that has been unoccupied for several consecutive months as vacant, while ignoring some special cases where there are people living but the residence time is extremely unstable. Therefore, in order to accurately measure the vacancy rate of urban housing, it is necessary to unify and standardize the definition of vacant housing. In terms of measurement methods, the measurement of urban residential vacancy rate depends on sufficient and accurate data support [29; 30]. At present, common data sources mainly include population census, real estate registration, electricity usage, property fee payment and other channels. Among them, population census data have high authority and coverage, but the census cycle is long and the data update speed is slow; real estate registration and electricity usage data can more intuitively reflect the residential vacancy situation, but there may be problems such as incomplete data and inconsistent statistical caliber. In order to overcome the limitations of a single data source, researchers have tried to integrate multiple data sources and use technical means such as statistics and geographic information systems (GIS) to improve the accuracy and reliability of urban residential vacancy rate measurement. The complexity in defining and measuring the urban residential vacancy rate has a profound impact on the application of algorithms. A non-standardized definition of vacant housing can lead to misclassification by algorithms. For example, if some cities define vacant housing as those unoccupied for several consecutive months, while others consider houses with unstable residence times as vacant, algorithms trained on different definitions may produce inconsistent results. This lack of standardization makes it difficult for algorithms to accurately identify vacant houses. In terms of measurement, the limitations of single-source data are a significant obstacle. Population census data, despite its high authority and wide coverage, has a long census cycle and slow data update speed. Real estate registration and electricity usage data, although more intuitive in reflecting the residential vacancy situation, may suffer from incomplete data and inconsistent statistical calibers. These issues mean that algorithms need to be designed to handle multi-source data. They must be able to integrate data from different sources, such as combining real estate transaction data with census data, to improve the accuracy of vacancy rate measurement.