## 4 Algorithm Application for Diverse Data Sources  
### Multi-Source Data Fusion  
Multi-source data fusion is a crucial part of the algorithm in the observation of urban residential vacancy rate. Its core purpose is to make full use of diverse data sources to improve the accuracy, comprehensiveness and real-time performance of observation [96]. Similarly, [PERSON] et al. applied a stacked ensemble model to fuse social media data and electricity usage records, achieving 92% accuracy in identifying vacant properties [97]. Multi-source data fusion is crucial for observing urban residential vacancy rates as it integrates diverse data to enhance accuracy, comprehensiveness and real-time performance. In practical applications, the data sources involved in the observation of urban residential vacancy rate are extremely rich, including but not limited to geographic information system (GIS) data, remote sensing images, statistical data, social media data and urban grid management data. Each of these data sources have unique advantages, such as the spatial analysis capability of GIS data, the macro observation perspective of remote sensing images, the accuracy and authority of statistical data, the timeliness and dynamism of social media data and the refined management characteristics of urban grid management data. In the face of these diverse data sources, algorithm application must first solve the data compatibility problem. Through data preprocessing, standardization and normalization, different data sources can be connected in terms of format, scale, accuracy and spatiotemporal resolution [98]. For example, high-resolution remote sensing images can be combined with low-resolution statistical data, and the images can be refined with the help of algorithms. The estimated results of the vacancy rate can be calibrated with statistical data, thereby ensuring observation efficiency while improving observation quality. Furthermore, the multi-source data fusion algorithm needs to have the ability of intelligent feature extraction and correlation analysis [99]. In view of the rich information contained in different data sources, through machine learning, deep learning and other technologies, the characteristic variables that are highly correlated with the vacancy rate are automatically identified, such as the age, structure, use nature and surrounding supporting facilities of the building. At the same time, combined with the spatiotemporal data analysis method, the correlation model between data is established to explore the intrinsic relationship between the residential vacancy rate and multiple factors such as urban economic development, population mobility and urban planning. In the process of data fusion, the algorithm also needs to deal with the uncertainty and redundancy of data [100]. To this end, the probability theory and information theory methods are introduced to screen out the data source that contributes most to the vacancy rate observation by calculating indicators such as mutual information and correlation coefficient between data, and eliminate or reduce data with high uncertainty and high redundancy, thereby improving the efficiency and quality of data fusion. In addition, in order to adapt to the ever-changing needs of urban development, the multi-source data fusion algorithm should have the ability to adapt and dynamically update. This means that the algorithm should not only consider the current data environment, but also predict and adapt to future data change trends. For example, with the expansion and renewal of the city, the vacancy rate characteristics of new residential areas and old residential areas may be significantly different. Therefore, the algorithm design needs to take into account flexibility and robustness to adapt to the dynamic needs of urban development. Multi-source data fusion plays the role of bridging and linking in the application of algorithms to the observation of urban residential vacancy rate.