Data scientists use various machine learning algorithms to discover patterns in large data that can lead to actionable insights. In general, high-dimensional data are reduced by obtaining a set of principal components so as to highlight similarities and differences. In this work, we deal with the reduced data using a bivariate mixture model and learning with a bivariate Gaussian mixture model. We discuss a heuristic for detecting important components by choosing the initial values of location parameters using two different techniques: cluster means, k-means and hierarchical clustering, and default values in the “mixtools” R package. The parameters of the model are obtained via an expectation maximization algorithm. The criteria from Bayesian point are evaluated for both techniques, demonstrating that both techniques are efficient with respect to computation capacity. The effectiveness of the discussed techniques is demonstrated through a simulation study and using real data sets from different fields.

中文翻译：

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基于主成分的高斯混合模型及其应用

数据科学家使用各种机器学习算法来发现大数据中的模式，这些模式可导致可行的见解。通常，通过获得一组主成分来减少高维数据，以便突出相似性和差异性。在这项工作中，我们使用双变量混合模型处理约简数据，并使用双变量高斯混合模型学习。我们讨论了通过使用两种不同的技术选择位置参数的初始值来检测重要组件的启发式方法：聚类均值，k-均值和层次结构群集，以及“ mixtools” R包中的默认值。该模型的参数是通过期望最大化算法获得的。从贝叶斯角度对两种技术都进行了评估，表明这两种技术在计算能力方面都是有效的。通过模拟研究并使用来自不同领域的真实数据集来证明所讨论技术的有效性。