A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation matrix, that relies on city-block distances, is robust to outliers. Monte Carlo simulations and an application on cars data (with outliers) show the robustness of the Gini PCA and provide different interpretations of the results compared with the variance PCA.

中文翻译：

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主成分分析：广义基尼方法

提出了基于广义基尼相关指数的主成分分析法（Gini PCA）。基尼PCA根据差异对标准PCA进行概括。在高斯情况下，表明标准PCA等同于Gini PCA。还证明了基于广义基尼相关矩阵的降维对离群值具有鲁棒性，而基尼相关矩阵依赖于城市之间的距离。蒙特卡洛模拟和在汽车数据上的应用（带有异常值）显示了基尼PCA的鲁棒性，并且与方差PCA相比，对结果提供了不同的解释。