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This study explores machine learning approaches for identifying gifted students by integrating academic and socioemotional characteristics from the data collected with the HOPE teacher rating scale. By using the Gaussian Mixture Model (GMM) and machine learning approaches, including Support Vector Machine (SVM) and Multilayer Perceptron (MLP), the study analyzed data from 1,157 elementary students. Results showed strong correlations between academic and socioemotional score factors (r=0.8), with weighted GMM effectively clustering gifted students while addressing data imbalances. Classification models revealed high accuracy but highlighted challenges in terms of identifying underrepresented students. In addition, Bias analysis indicated significant variations among teachers in rating scores across socioeconomic and ethnic groups, which may have implicit biases in evaluation practices.