## 5 Application of Data Analysis Algorithm in Urban Real  
### State Management  
#### Spatial Data Analysis Algorithm  
Spatial statistical analysis algorithms are indispensable tools in the construction of smart cities. They mainly provide scientific and accurate decision support for urban real estate management and optimization through in-depth analysis of geospatial data [40]. This type of algorithm integrates knowledge from multiple fields, such as statistics, geography, and computer science, and uses the geographic information system (GIS) as a platform to effectively mine and analyze spatial data. Spatial statistical analysis algorithms include classic spatial autocorrelation analysis, spatial variogram analysis, and geostatistical analysis methods. These methods play a key role in revealing the spatial distribution characteristics of real estate, quantifying spatial correlation, and predicting spatial trends [41]. First, spatial autocorrelation analysis can detect the correlation between spatial data to determine whether a certain attribute value has a clustering characteristic in space. This helps to understand the spatial distribution laws of urban real estate value, type, and usage, thereby providing a scientific basis for the government to formulate land policies and plan urban layout. Secondly, spatial variogram analysis can describe the degree of variation and structural characteristics of spatial data within a certain range, which is of great significance for understanding the regional differences in the real estate market and formulating targeted regulatory measures. In addition, geostatistical analysis methods can interpolate and predict spatial data such as real estate prices and supply and demand conditions, providing a reference for market evaluation and investment decisions [42]. In addition, spatial statistical analysis algorithms can effectively deal with data quality and consistency issues when processing real estate data in the big data era [43]. By reasonably selecting or improving algorithms, the impact of outliers, missing values, etc., on analysis results can be reduced, and the accuracy of real estate management decisions can be improved. At the same time, spatial statistical analysis algorithms also have certain advantages in protecting data privacy and security and can provide reliable data support for urban managers. As shown in Table 4, in practical applications, spatial statistical analysis algorithms have been successfully applied to many fields, such as urban planning, land consolidation, and real estate market monitoring. Through in-depth mining of urban real estate spatial data, these algorithms help to reveal the inherent laws of urban development and provide strong support for urban optimization. Spatial statistical analysis algorithms are of great value in the construction of smart cities and are expected to promote real estate management and urban optimization to a higher level. At the same time, geospatial data mining algorithms, as a key technology, also play a vital role in the construction of smart cities. They mainly use spatial data in geographic information systems (GIS) to reveal the hidden laws and patterns in the data through mining and analysis, providing a scientific basis for urban real estate management and urban optimization. Geospatial data mining algorithms include many methods, such as spatial clustering, spatial association rule mining, spatial prediction, and spatial classification [50]. These algorithms effectively combine the geographical location, attribute characteristics, and time dimension of spatial data to provide intelligent support for the planning, evaluation, transaction, and supervision of urban real estate. The introduction and comparison of various geospatial data mining algorithms are shown in Table 5.