Aplicación del algoritmo expectation–maximization en modelos de clustering para analizar el comportamiento del valor del suelo rural: estudio de caso en el municipio de Sopetrán, Antioquia

Abstract

Land valuation in Colombia has historically relied on traditional methodologies such as the comparative market method, income capitalization, and the cost method. These methods have played a fundamental role in the development of cadastral and appraisal processes in the country, providing a technical framework that has allowed for value estimation for several decades. However, their application in rural contexts presents significant limitations due to the inherent complexity of these territories, where factors such as topographic variability, heterogeneity in soil productivity and potential, regulatory specificities, and the dynamics of the rural market converge (Ballesteros, 2004; IGAC, 2016). This spatial and functional diversity makes it difficult to obtain homogeneous estimates using conventional tools, highlighting the need to review and strengthen the methodological approaches employed. In this context, the implementation of multipurpose cadastre has highlighted the importance of modernizing the methodologies used in the mass valuation of properties, promoting approaches that offer greater levels of automation, accuracy, and adaptability to the country's territorial diversity (IGAC, 2016). While traditional methods remain valid, this situation has created an opportunity to incorporate technological tools that optimize efficiency and improve the quality of valuation processes. In particular, artificial intelligence-based techniques, and specifically clustering algorithms, have gained relevance by allowing the classification of spatial units without the need for predefined categories, facilitating the identification of patterns in scenarios characterized by high heterogeneity, such as rural land (Jain, Murty & Flynn, 1999; Xu & Wunsch, 2005). Within the use of machine learning techniques applied to territorial analysis, the Weka software has become a widely used tool, thanks to its open source nature and the availability of multiple unsupervised learning algorithms (Witten, Frank & Hall, 2011).Among the most commonly used clustering methods are the k-means algorithm, which groups observations by minimizing internal variance (MacQueen, 1967; Lloyd, 1982); hierarchical clustering, which generates hierarchical clustering structures from agglomerative and divisive processes (Murtagh & Contreras, 2012); and density-based algorithms, such as DBSCAN, which identify clusters with irregular shapes and detect outliers in the data (Ester et al., 1996). In addition to these approaches, there is the Expectation-Maximization (EM) algorithm, based on probabilistic models, which iteratively estimates the membership of each observation in different groups by maximizing the likelihood function, making it particularly suitable for analyzing heterogeneous data