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Abstract:
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Exploratory factor analysis is one of the popular techniques in the area of psychological and social research. Interpretation of the estimated loading matrix is important in real data analysis. To achieve a more interpretable loading matrix, rotation methods are often applied to the estimated loading matrix. The (co)variance between the estimated value of the loading matrix is often used as a loss function of rotation methods. However, maximizing (or minimizing) (co)variance does not directly consider sparse loadings. A sparse loading matrix is essential to achieve a simple structure. In this presentation, we propose a rotation method whose loss function corresponds to the Gini coefficient. Gini coefficient is one of the dispersity measures and has nice properties of measurement for sparse. The challenging point is that the Gini coefficient is a non-convex function. To mitigate this challenge, we used the iterative algorithm. We derived the update formula by using a majorization function of the Gini coefficient and local quadratic approximation. The result of applying the proposed method to Thurston’s Box data is similar to applying a rotation method with entropy loss.
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