Abstract We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximized. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, where an approximation of the negentropy for Gaussian mixtures is computed. Then, genetic algorithms are used to find the optimal, orthogonal projection basis by maximizing the former approximation. We show that this semiparametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly visualized. The performance of the proposed approach is shown on both artificial and real datasets. Supplementary materials for this article are available online.

中文翻译：

---

基于高斯混合和进化算法的投影追踪

摘要 我们提出了一种基于高斯混合模型 (GMM) 的投影追踪 (PP) 算法。从由 GMM 估计的多元密度获得的负熵被用作要最大化的 PP 指数。对于投影子空间的固定维度，基于 GMM 的密度估计被投影到该子空间，其中计算了高斯混合的负熵的近似值。然后，使用遗传算法通过最大化前一个近似值来找到最优的正交投影基。我们表明，这种半参数化的 PP 方法是灵活的，并且可以通过将多变量数据集投影到子空间上来检测信息量高的结构，在子空间中数据可以被可视化。所提出的方法的性能在人工和真实数据集上都得到了展示。