In this paper, we propose a new method for disjoint principal component analysis based on an intelligent search. The method consists of a principal component analysis with constraints, allowing us to determine components that are linear combinations of disjoint subsets of the original variables. The effectiveness of the proposed method contributes to solve one of the crucial problems of multivariate analysis, that is, the interpretation of the vectorial subspaces in the reduction of the dimensionality. The method selects the variables that contribute the most to each of the principal components in a clear and direct way. Numerical results are provided to confirm the quality of the solutions attained by the proposed method. This method avoids a local optimum and obtains a high success rate when reaching the best solution, which occurs in all the cases of our simulation study. An illustration with environmental real data shows the good performance of the method and its potential applications.

本文提出了一种基于智能搜索的不连续主成分分析的新方法。该方法由具有约束条件的主成分分析组成，使我们能够确定原始变量不相交子集的线性组合的成分。所提出方法的有效性有助于解决多元分析的关键问题之一，即在减少维数方面对向量子空间的解释。该方法以清晰，直接的方式选择对每个主要组成部分贡献最大的变量。提供数值结果以确认所提出方法获得的溶液的质量。这种方法避免了局部最优，并且在达到最佳解决方案时获得了很高的成功率，在我们的模拟研究的所有情况下都会发生这种情况。带有环境实际数据的图示说明了该方法的良好性能及其潜在应用。