<p>Label distribution learning techniques have demonstrated significant potential in enhancing the performance of side-channel analysis, especially under trace-limited conditions. However, existing methods often rely on single-label associations overlooking the complex interdependencies among labels. A novel side-channel analysis framework named HVLDL-SCA integrating both horizontal and vertical label distribution learning is proposed to address this limitation. In this framework, each trace is assigned a unique local influence vector which captures label distributions from neighboring traces and serves as an auxiliary input to improve the prediction of sample traces. Additionally, we introduce a corrective layout influence vector to further enhance prediction accuracy. A novel regularization term is designed to better model local and global label correlations by constraining label relationships in the output, enabling a more comprehensive utilization of inter-label dependencies and accelerating the convergence of guessing entropy (GE). Moreover, an optimized label correlation measurement method and a novel evaluation metric termed Optimize Key Distribution Correlation Metric(EKD-LC) are proposed to assess the generalization capability of the analysis model. Experimental results show that the proposed HVLDL-SCA method surpasses existing approaches by reducing the number of traces required to reach a GE value of zero by more than 5 times, while the EKD-LC metric demonstrates superior robustness.</p>