Evidence on how energy poverty persistence and vulnerability to key factors are distributed across different population groups remains scarce. This paper seeks to bridge this gap by analyzing the dynamics and determinants of energy poverty within population clusters. The significance of the paper is highlighted in the integration of a two-stage Generalized Method of Moments (GMM) estimation procedure with K-means cluster analysis. K-means clustering is a fundamental tool within AI to understand and find patterns and structure in data without labeled outputs. Two key findings emerge. First, the degree of energy poverty state dependence varies substantially across clusters, with some segments of the population deeply entrenched and facing significant barriers to escape. Second, variables critical for identifying at-risk groups, such as income and energy prices, exhibit different impacts across clusters. These findings highlight the need for targeted policy interventions tailored to the specific vulnerabilities of distinct population segments.